Masaryk University
Faculty of Science
Mapping galactic nuclei:
From the Galactic center to distant quasars
and back
HABILITATION THESIS
presented by
Michal Zajaˇcek
from Malacky, Slovakia
Brno, 2024
Abstract
In this Habilitation Thesis, I first recall how we have mapped the gas and the stellar content in
the central parsec of our Galaxy, which is the closest galactic nucleus to us, about 100 times
closer than galaxies in the Local Group and approximately 1000 times closer than the nearest
galaxy cluster. Around the compact radio source Sgr A* associated with the supermassive
black hole (SMBH), there are fast-moving B-type stars and dust-enshrouded stellar objects
that must have formed recently during the last hundred thousand to a few million years. This
indicates a recent period of star formation preceded by an infall of a large amount of cold
and dense gas. The amount of gas consumed by star formation is linked to the amount of gas
available for accretion. Hence, our Galactic center was likely much more active and luminous
a few million years ago, at the level of an active Seyfert galaxy. There are over a million active
galaxies, but in their case a similar spatial resolution is unavailable. Therefore, mapping of the
distribution of gas in active galactic nuclei (AGN) has traditionally been performed in the time
domain to replace the lack of a sufficient angular resolution to resolve the inner regions. This
so-called reverberation mapping employs reprocessing of the variable X-ray/UV continuum
emission by more distant broad-line region clouds. In my work, I focused on the comparison
of the radius of Hβ-emitting clouds with the distance of MgII-emitting material as well as
the radius corresponding to the FeII pseudocontinuum. In contrast with the radius-luminosity
relations for Hβ and the UV and optical FeII emission, the MgII radius-luminosity relation
is flatter, although it still exhibits a significant correlation. These correlations open a way to
measure supermassive black hole masses in distant quasars using just one-epoch spectroscopy.
One can also employ the MgII radius-luminosity relation to standardize quasars and use them
as alternative probes in cosmology. Finally, it is beneficial to combine the processes taking
place in AGN with the visibly rich and dense stellar content in the Galactic center to see how
an intermittently increased nuclear activity could have been impacting stars and vice versa.
In particular, we studied the interaction of red giants with the activate jet and found that a
large number of repetitive jet-star encounters can effectively ablate the envelopes of red giants.
This can partially address the lack of large red giants in the innermost 0.5 pc of the Galactic
center. In summary, the spatial details accessible for the Galactic center complement the
temporal studies of mostly unresolved AGN. On the other hand, the study of a sample of AGN
with various accretion rates teaches us about the past and the potential future of the Milky Way.
iii
iv ABSTRACT
Keywords: Galactic center – Sgr A* – Central molecular zone – quasars – active galactic nuclei
(AGN) – supermassive black holes – accretion flows – reverberation mapping – broad-line
region – AGN feeding and feedback – cosmology
Contents
Abstract iii
Contents v
1 Introduction 1
1.1 Mapping the Galactic center . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.1 Stellar populations in the central parsec . . . . . . . . . . . . . . . 13
1.1.2 Distribution of gas and accretion-flow structure . . . . . . . . . . . 22
1.2 Mapping distant quasars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.2.1 Reverberation mapping of accretion discs . . . . . . . . . . . . . . 44
1.2.2 Resolving spheres of influence of extragalactic nuclei . . . . . . . . 56
1.2.3 Signs of stellar-mass bodies close to extragalactic SMBHs . . . . . 60
1.3 Synergies between the Galactic center and active galactic nuclei . . . . . . 64
1.4 Galactic nuclei as standardizable candles . . . . . . . . . . . . . . . . . . . 67
1.5 This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2 Paper 1: Radio-Optical Properties of Active Galaxies 75
3 Paper 2: Reverberation-Mapping of HE 0413-4031 95
4 Paper 3: Red-Giant Depletion in the Galactic Center 125
5 Paper 4: Reverberation-Mapping of HE 0435-4312 145
6 Paper 5: Enhanced Doppler Beaming 171
7 Paper 6: Effect of Extinction on Quasar Distances 179
8 Paper 7: UV FeII Emission Model and BLR Time Delays 199
9 Discussion and Conclusions 219
Bibliography 227
v
vi CONTENTS
Curriculum Vitae 243
Significant Research Results 245
First-author refereed publications . . . . . . . . . . . . . . . . . . . . . . . 245
Publications in Nature, Science, and Letter format . . . . . . . . . . . . . . 247
Acknowledgements 249
Photogallery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Chapter
1
Introduction
“Young people, especially young
women, often ask me for advice.
Here it is, valeat quantum. Do not
undertake a scientific career in
quest of fame or money. There are
easier and better ways to reach
them. Undertake it only if nothing
else will satisfy you; for nothing
else is probably what you will
receive. Your reward will be the
widening of the horizon as you
climb. And if you achieve that
reward you will ask no other."
— Cecilia Payne-Gaposchkin
(1900-1979)
Foreword
Understanding the structure of a galactic nucleus is closely linked to the understanding of the
structure of a galaxy, especially our own Milky Way. Since antiquity till the Middle Ages,
the center of the Universe or practically the Galactic Center was associated with the Earth
orbited by planets with a rather complex system of deferents and epicycles. “Non-changing”
stars were attached to the distant celestial sphere. The Milky Way or the apparent brighter
belt on the sky, essentially the largest object in terms of the apparent angular size observed
by a naked eye, was not always associated with distant stars. Aristotle and his followers
mostly interpreted it as an atmospheric phenomenon within the sub-lunar sphere created by
the interactions of celestial spheres with the terrestrial sphere as they revolved around the
Earth. However, there were alternative explanations during the “naked-eye” era as well, in
particular during the Middle Ages, especially proposed by Arabic medieval scholars (Eckart
& Idriz 2023).
1
2 CHAPTER 1. INTRODUCTION
The geocentric system developed by Appolonius of Perga towards the end of the 3rd
century BC, Hipparchus in the 2nd century BC, and mastered by Claudius Ptolemy in Almagest
in the 2nd century AD could address mainly the apparent retrograde motion of planets, yet the
system became progressively more complex and impractical with too many auxiliary circles
(bigger ones called deferents and smaller ones called epicycles) with an additional correction
provided by an offset circle center or equant to account for the changing angular speed of
planets at the perigee and the apogee.
With the (re)introduction of the heliocentric model by Nicolaus Copernicus (1474-1543),
the center of the Universe, and thus also the Galaxy, was associated with the Sun (publication
De revolutionibus orbium coelestium published in 1543, shortly before Copernicus’s death).
This paradigm shift, standing on the shoulders of the ancient astronomer Aristarchus of Samos,
did not, however, provide much practical simplification of the calculations of planetary orbits.
On the contrary, the system became even more complicated than the Ptolemaian geocentric
model, with more and more epicycles needed to account for offsets between the predicted
and the observed positions of planets. A “compromise” geoheliocentric model introduced by
Tycho Brahe in the late 16th century associated the center with the Earth again, which was
supposed to be too heavy to move fast as based on the Aristotelian vision of the heavy and
light elements. The Moon, the Sun, and distant stars orbited around the Earth, while the five
known planets at the time (Mercury, Venus, Mars, Jupiter, and Saturn) orbited around the Sun.
A real paradigm shift from the ideal regular circular motion was introduced by Johannes
Kepler (1571-1630) in Prague, while he had a chance to study the precise positions of the
planet Mars obtained previously by Tycho Brahe. He noticed that the orbital description can
significantly be simplified when the closed trajectory is described by an ellipse, one of the
four conic sections, with the Sun being at one of the foci. This analysis resulted into the
publication of the first two Keplerian laws in 1609 in Prague (Astronomia Nova) and the
third law (the ratio of the cube of the semi-major axis to the square of the orbital period,
a3
/P2
= const, remains constant) was published in 1619 (Harmonice Mundi) in Linz. The
importance of Kepler’s contribution lies in the applied scientific method, that is the application
of a mathematical model (ellipse) to the orbital data. This way the perfect Aristotelian regular
circular motion was abandoned and the Earth was finally shifted from the center of the
Universe and its motion, as for the other planets, was generally not uniform around the center.
An elliptical trajectory as a general orbit for a two-body problem whose special case is the
motion of an object in the central potential dominated by one body was finally derived Sir
Isaac Newton (1642-1726/1727) in his theory of universal gravitation published alongside the
laws of motion in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of
Natural Philosophy) or shortly Principia in 1687.
In the subsequent centuries, the trend of confirming Copernican principle, i.e. that no
location in the Universe is privileged, continued along with the significant developments of
celestial mechanics in the 18th and the 19th century, where the conic sections in the two-body
problem also evolve with time due to the perturbations from other bodies. The ability to
mathematically handle the external gravitational influence led to the prediction of the position
of the outermost planet Neptune by Urbain Le Verrier in 1845-1846 (independently from
John Couch Adams) as based on the observed deviations of the Uranus motion from the
nominal Keplerian orbit. Based on Le Verrier’s calculations, Neptune was then officially
discovered by Johann Gottfried Galle at the Berlin observatory on September 23rd, 1846. The
Neptune position was within one degree from the predicted position, which was a remarkable
accomplishment of the celestial mechanics. Subsequently, the general relativistic description
3
of spacetime introduced by Albert Einstein (1879-1955), in which the spacetime curvature
determines the motion of bodies that, on the other hand, influence the curvature, added
post-Newtonian effects, such as the prograde periapse (Schwarzschild) precession of the orbit
or the nodal precession due to the Lense-Thirring effect. The general relativistic effects were
successfully applied to explain the remnant prograde precession of the Mercury orbit (∼ 43′′
per century after subtracting the effect of other perturbing bodies) and were verified by the
detection of the stellar light deflection by the Sun during the Solar eclipse on May 29, 1919
(Principe-Sobral expedition led by Arthur S. Eddington, Dyson et al. 1920). Let us now return
back to the beginning of the 17th century, when another important milestone of technical
nature was achieved.
The further study of the Milky Way was bolstered by the invention of a telescope by Hans
Lippershey in or around 1608. Galileo Galilei (1564-1642) constructed his own refractive
telescope and he was able to resolve, among other things, individual stars of the Galaxy,
which once and for all discarded the theory of the Milky Way as an atmospheric phenomenon.
The qualitatively correct interpretation of the brighter belt, or the Milky Way, seen on the sky
was given by Thomas Wright in the mid-18th century. He put forward the model of a thin
disc of stars held together by gravitational forces. In this simple model, the Earth is located at
the geometric center of the disc and thus the edge-on view from within the disc creates the
projected belt on the celestial sphere. This model also inspired philosopher Immanuel Kant,
who in Universal Natural History and Theory of the Heavens (1755) also advocated that
observed nebulae are distant galaxies like the Milky Way or separate “island universes”, which
was objected by most of Kant’s peers at the time. Towards the end of 18th century, William
Herschel constructed a more detailed distribution of stars within the Milky Way with the Sun
at the Galactic center (Herschel 1785), which was possible thanks to the detailed observations
with his own telescope. Herchel’s observations were assisted by his sister Caroline. In the
same way as Tycho Brahe is considered one of the best observational astronomers before the
invention of the telescope, Herschel can be considered one of the best astronomers capable of
observations with their own, home-built telescopes (in his case – Newtonian reflectors). It
was the time of enlightenment and technological progress, which resulted in the Industrial
revolution. At this time, astronomy and technological progress had become more intertwined
and it was quite common to discuss new discoveries and ideas within informal scientific
circles, such as the Lunar Society based in Birmingham. Its members were also involved in
the public outreach of the astronomical knowledge of that era. For instance, James Ferguson
invented an orrery, a mechanical apparatus for demonstrating the motion of celestial bodies
according to the Copernican heliocentric view. Typically, it involved the motion of the Moon
around the Earth, the planets around the Sun, even including the motion of the moons of
Jupiter and Saturn known at the time, see Fig. 1.1.
More than hundred years later, based on more sensitive observations by larger telescopes,
Jacobus C. Kapteyn discovered that stars do not move randomly but their proper motions
belong to two opposite streams. This was essentially the first proof of the Galactic rotation.
In 1922, Kapteyn presented a lens-shaped Galactic model with the diameter of only about
∼ 40 000 light years with the Sun still close to the center (within 2 000 light years).
By the 1930s, there were several key measurements that led to the major revision of the
Galactic center location, especially the shift from nearly the Solar position to much larger
distances from the Solar system. This was achieved thanks to the observations by Harlow
Shapley, who performed the measurements of the distances of 69 globular clusters surrounding
the Milky Way. He used the period-luminosity relation of Cepheid variables, which was
4 CHAPTER 1. INTRODUCTION
Figure 1.1: Painting “A philosopher lecturing on the orrery” by Joseph Wright of Derby
completed in 1766. The central figure may represent James Ferguson, one of the members
of the informal circle referred to as the Lunar Society. Ferguson demonstrated the orrery, a
simplified mechanical model of the movement of celestial bodies respecting the Copernican
heliocentric view, in Birmingham in 1761.
discovered earlier by Henrietta Swan Leavitt by observing Cepheid variables in the Magellanic
Clouds (Leavitt 1908; Leavitt & Pickering 1912), to determine their distances. He realized
that globular cluster are not distributed uniformly around the Sun but rather concentrated
towards the constellation of Sagittarius (Shapley 1918). This led to the paradigm shift from the
heliocentrism to galactocentrism and a significant enlargement of the Milky Way to several
10 000 light years. Older measurements did not consider the extinction (absorption and
scattering) of stellar light by the interstellar gas and dust within the Galactic plane. This effect
was discovered by Robert Julius Trumpler while he studied open clusters. More specifically,
he noticed that more distant open clusters appear fainter than they should be (Trumpler 1930).
When the interstellar extinction was taken into account, the position of the Sun with respect
to the Galactic center became even larger. Nowadays, the Galactic extinction at different
wavebands can be determined quite precisely. It is customary to express the extinction using
the colour index EB−V = AB − AV, where AB = Bobs − Bint and AV = Vobs − Vint are the
extinction coefficients in optical B and V bands, respectively. In Fig. 1.2, the colour index
value of EB−V based on the full-sky 100 µm emission of dust (COBE/DIRBE and IRAS/ISSA
data; Schlegel et al. 1998) is clearly correlated with the Galactic structure, being the largest
close to the plane and the smallest around the Galactic poles.
In the first half of the 20th century, the question of whether the Milky Way constitutes the
whole visible Universe or is just one of many galaxies was also finally resolved. Symbolically,
the Great Debate between Harlow Shapley and Heber Curtis took place in Washington,
5
24222018161412108642
RA [hours]
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
+10
+20
+30
+40
+50
+60
+70
+80
DEC[degrees]
Sgr A*
North Galactic Pole
South Galactic Pole
Ecliptic plane (+/- 10 deg)
1.0
0.5
0.0
0.5
Galacticextinctionlog(EBV)
Figure 1.2: Dust extinction map of EB−V (see the colour bar on the right) based on 100 µm
emission map of dust (Schlegel et al. 1998). Along the x-axis we show right ascension (RA)
in hours, while along the y-axis we depict declination (DEC) in degrees. The Galactic center
(Sgr A*) is represented by the star symbol and the North and the South Galactic poles are
shown with the plus signs.
D.C., in 1920. Shapley was advocating for a large Galaxy and observed spiral nebulae were
supposed to be located within it. In contrast, Curtis favoured a smaller Galaxy and spiral
nebulae were considered to be separate galaxies in his view. At the time of the Debate, both
astronomers lacked sufficiently precise observational data to support their different claims.
The problem of spiral nebulae was resolved by Edwin Hubble, who discovered Cepheid
variables in the nearby spiral nebulae (Andromeda, Triangulum) using the freshly completed
2.5-meter Hooker Telescope at Mt. Wilson. Using Leavitt’s period-luminosity relation, the
derived distance clearly indicated that spiral nebulae are indeed other galaxies that are similar
to the Milky Way galaxy. Apart from the Great Debate in 1920, there had been a few earlier
“great debates” concerning the nature of the Milky Way, mainly along the line of its either
atmospheric or stellar nature. Eckart & Idriz (2023) mainly stress the work of Ibn al-Haytham
(Alhazen) (965-1040) who argued that since the Milky Way band does not have a measurable
parallax it must be further than the Moon, whose parallax could be detected. This was in
tension with the prevailing view at the time that the Milky Way is an atmospheric phenomenon
in the sub-lunar sphere, first put forward by Aristotle as mentioned at the beginning.
The direction towards the center of the Milky Way was first broadly indicated by the
measurement of the distribution of globular clusters by Harlow Shapley, which showed that
globular clusters are concentrated towards the Sagittarius constellation. Subsequently, Karl
G. Jansky identified a strong radio source towards the Sagittarius constellation at 20.5 MHz
(14.6 meters) (Jansky 1933) with a rather low resolution of 24◦
× 35◦
. Grote Reber continued
with the radio observations of the persistent emission from the Sagittarius region between
1938 and 1948 at a higher frequency of 160 MHz (1.9 meters) with his nine-meter radio dish.
In 1951, Jack Piddington and Harry Minnett identified a discrete radio source denoted as the
Sagittarius-Scorpius source at 1.21 GHz and 3 GHz using the Potts Hill radio telescope near
Sydney (Piddington & Minnett 1951). The spectrum of the source appeared peculiarly flat.
McGee & Bolton (1954) performed additional radio observations at 0.4 GHz of the Sagittarius-
6 CHAPTER 1. INTRODUCTION
Figure 1.3: Radio and optical images of the brightest quasi-stellar object 3C 273 located
in the constellation of Virgo. Left panel: Radio image at 1.4 GHz obtained by the FIRST
survey (Becker et al. 1995). Right panel: Optical image adopted from the SDSS survey
(Stoughton et al. 2002).
Scorpius source (known also as Sagittarius A) with the 24-meter "hole-in-the-ground" dish at
Dover Heights in Australia and identified it with the position expected for the Galactic center.
The discovery and the identification of Sagittarius A contributed to the redefinition of the
Galactic coordinate system, which was based primarily on the HI observations of the Galactic
rotation (Blaauw et al. 1960). The precisely determined position of Sgr A agreed well with the
center inferred from the rotation motion of HI clouds. Within the extended radio emission of
Sgr A, Balick & Brown (1974) identified a compact radio source unresolved at < 0.1′′
with the
brightness temperature larger than 107
K indicating a non-thermal nature. The identification of
the compact source was possible thanks to a newly commissioned 35-kilometer interferometer
Green Bank - Huntersville consisting of three 26-meter dishes and one 14-meter dish in
Huntersville. The source was located within a few arcseconds from the near-infrared excess
peak along the Galactic plane (Becklin & Neugebauer 1968). The subsequent monitoring
revealed that the point source is multi-wavelength and variable. Because of its compact
variable emission, it was denoted as Sagittarius A* (or Sgr A* for short; Brown 1982) to
distinguish it from the extended Sgr A complex. This nomenclature was adopted later for
other compact radio sources in galactic nuclei, such as M87* (Event Horizon Telescope
Collaboration et al. 2019) or M81* (von Fellenberg et al. 2023).
In the meantime, as the radio emission of the Galactic center associated with Sgr A and
Sgr A* had been pinpointed, broad emission lines with line widths equivalent to several 1000
km/s had been identified in the optical spectra of some galactic nuclei, indicating a high
concentrated mass (type I; Seyfert 1943; Woltjer 1959; Schmidt 1963). Following the development
of radar technologies during WWII, sources of strong radio emission were discovered.
Some of them had prominent bipolar radio lobes with the total magnetic and kinetic (particle)
energy of ∼ 105
− 107
M⊙c2
∼ 1059
− 1061
erg s−1
, assuming a synchrotron mechanism for
the radio emission (Burbidge 1958). Such a large power output was inconsistent with any
known long-lasting chemical, nuclear, or matter-antimatter annihilation process. The radio
astronomy group at the University of Cambridge utilized a 4-element radio interferometer to
make a systematic survey of the radio sky at 159 MHz. The identified sources were denoted as
3C (Third Cambridge catalogue), followed by the entry number (increasing numbers stood for
7
a larger right ascension; see Edge et al. 1959). Using the 5.1-meter Hale telescope on the Mt.
Palomar, Thomas A. Matthews and Allan R. Sandage identified the first optical counterparts
to the radio 3C sources – 3C 48, 3C 196, and 3C 286, which were point-like like stars and
exhibited unusual optical spectra with very broad emission lines (Matthews & Sandage 1963).
Because of the star-like appearance, these objects were called quasi-stellar objects (QSOs)
or quasars. For the brightest QSO 3C 273 (mV ∼ 12.9), Hazard et al. (1963) determined
the precise position of its two components (the core and the jet) using the method of lunar
occultations. By observing the optical counterpart of 3C 273 and obtaining the spectrum
using the Palomar telescope, Maarten Schmidt (Schmidt 1963) identified a series of hydrogen
Balmer lines in the spectrum. For the comparison, in Fig. 1.3 we show radio and optical
images of 3C273 in the left and right panels, respectively, where the radio emission clearly
consists of two components. He noticed that the lines are redshifted to z = 0.158, which
corresponds to the luminosity distance of ∼ 760 Mpc. This definitely proved that QSOs are
not only extragalactic but also that they are located at cosmological distances and have a huge
bolometric energy output of LQSO ∼ 1046
erg s−1
∼ 1013
L⊙ or about two orders of magnitude
more than the total luminosity generated by the stars in the host galaxy. The short variability
within one month implied a compact source size of cδt ≤ 1017
cm ∼ 0.03 pc ∼ 7000 AU for
the generation of such a large luminosity.
Hence, this extraordinary evidence for the large QSO luminosity generated in a small
volume comparable to the Solar System led to proposing extraordinary hypotheses and theories
that were also discussed at the First Texas Symposium in Relativistic Physics in Dallas in
1963 (Schucking 1989). Among several detours, accretion onto compact objects, during
which gravitational potential energy of matter is released in the form of intense radiation
that is observed, turned out to be the most feasible (Salpeter 1964; Zel’dovich & Novikov
1965). In parallel to new optical and radio observations of QSOs, and actually even before
them, there had been several key theoretical developments that had shown that highly compact
mass concentrations surrounded by the space-time boundary or the event horizon, from which
even light cannot escape, can form in nature. The first such an idea was proposed by John
Michell, and independently by Pierre-Simon Laplace, in the 18th century and it was based
on the Newtonian corpuscular theory of light (Schaffer 1979), where the critical radius can
be obtained by setting the escape velocity to the speed of light, i.e.
√
2GM/R = c, which
leads to RS = 2GM/c2
. The solid foundation stone to those models was laid though the
General Theory of Relativity presented by Albert Einstein in 1915, and mainly the spherical
symmetric solutions to the vacuum Einstein’s field equations found by Schwarzschild (1916)
for a non-rotating and an uncharged mass and by Reissner (1916) and Nordström (1918) for a
non-rotating and charged point source and mass, respectively. However, the true singularity at
the center of the coordinate system surrounded by the event horizon was rather difficult to
grasp since no information, for instance even light waves, could travel out of it. Therefore,
many physicists including Albert Einstein himself were sceptical of the formation of these
“frozen stars” in nature (Einstein 1939). In contrast, for an idealized spherical collapse of a star,
J. Robert Oppenheimer and Hartland Snyder showed that if the final mass of the star exceeds
a certain limit (Tolman-Oppenheimer-Volkoff or TOV limit of about ∼ 1.5 − 3 M⊙), there is
nothing, not even the pressure of degenerate matter, that can prevent the collapse of the object
into singularity (Oppenheimer & Snyder 1939), hence the gravitational collapse will continue.
Despite Oppenheimer’s & Snyder’s paper on the continuing gravitational collapse, most of the
community remained sceptical about the formation of singularities in nature and considered
them as pure mathematical curiosities. As Einstein, they rather tried to invoke mechanisms
8 CHAPTER 1. INTRODUCTION
that would decrease the mass below the TOV limit, such as strong stellar winds or rotation.
The discovery of QSOs with large bolometric luminosities of 1045
− 1047
erg s−1
generated
within a small volume opened space for extraordinary hypotheses, including the accretion of
matter onto highly compact objects that have collapsed into singularities surrounded by an
event horizon. Moreover, considering the steady spherical accretion, the upper limit on the
luminosity generated by accretion is given by the Eddington luminosity1
,
LEdd =
4πGM•mpc
σT
= 1.26 × 1038 M•
1 M⊙
erg s−1
, (1.1)
which implies the mass of at least ∼ 107
− 109
M⊙ to generate the luminosity of QSOs. Such
a large mass in a small volume with the radius of ≲ 0.03 pc cannot be due to a cluster of
Solar-mass stars since such a configuration would be unstable. Also, a main-sequence star of
such a large mass would be highly unstable and short-lived. Essentially, any single object of
this mass will inevitably collapse into a singularity. The central singular object in QSOs, if
accreting close to the maximum possible (Eddington) rate, needs to consume
˙MEdd =
4πGM•mp
ηradσTc
= 2.2
M•
108 M⊙
M⊙ yr−1
, (1.2)
for ηrad = 0.1, which represents the radiative efficiency that compares the energy of the gas
element at infinity with the one at the innermost stable circular orbit (ISCO). Hence, the
consumption rate is equivalent to a few stars like the Sun per year. The accretion of matter
onto collapsed highly massive or supermassive objects turned to be the most plausible among
extraordinary models.
Around the time of the First Texas Symposium, the exact axisymmetric solution for a
rotating mass was presented (Kerr 1963), and shortly afterwards, the most general stationary
solution of Einstein field equations was found (Newman et al. 1965), which concerns masses
possessing both the spin and the electric charge. Hence, it took about 45 years to find exact
solutions for a rotating mass with axisymmetric spacetime. For convenience, we summarize
the exact solutions of Einstein field equations with the basic parameters of mass M•, angular
momentum J, and the electric charge Q in Table 1.1, including the authors of these solutions
and the years when they were found.
Table 1.1: Overview of exact stationary solutions of Einstein field equations.
Charge/Angular Momentum J = 0 J 0
Q = 0 Schwarzschild Kerr
References Schwarzschild (1916) Kerr (1963)
Q 0 Reissner-Nordström Kerr-Newman
References Reissner (1916), Nordström (1918) Newman et al. (1965)
1
The Eddington luminosity is, apart from the mass of the compact object M•, a function of just fundamental
constants: gravitational constant G, speed of light c, and the Thomson cross-section σT.
9
Figure 1.4: Origin of the word black hole. A newspaper snippet of the first published article
on black holes published by Ann Ewing on January 18, 1964 in Science News Letter (Ewing
1964).
The formation of spacetime singularities in nature turned out to be feasible after Roger
Penrose showed based on his analysis of the topological properties of spacetime (conformal
structure; Penrose 1963) that the gravitational collapse into singularity is a general property
of imploding stars when they reach a certain point, at which the formation of singularity
becomes inevitable regardless of the initial geometry or the rotation of the collapsing star. In
other words, a so-called trapped surface needs to form (Penrose 1965). It is also at this time
when the term black hole first appeared. In the written form, the term appeared in the popular
Science News Letter “Black Holes” in Space written by Ann Ewing (Ewing 1964), which was
published on January 18th, 1964, see also Fig. 1.4. The article reported on degenerate compact
objects discussed at the annual meeting of the American Association for the Advancement
of Science (AAAS) in Cleveland, Ohio. The term was likely used directly at the meeting,
potentially by the session chair Dr. Hong-yee Chiu, who might have adopted it from Robert
Dicke. Three years later John A. Wheeler used the term black hole again at the annual meeting
of the AAAS and after his keynote lecture was published in 1968 (Wheeler 1968), it started to
be widely used in both popular and academic literature. Given the large masses of the order
of ∼ 108
− 109
M⊙ to explain the large luminosities of quasars, the term supermassive black
holes (hereafter SMBH) was adopted to distinguish them from the remnants of massive stars,
i.e. stellar black holes. Electromagnetic emission of stellar black holes in binary systems
started to be detected in the 1960s and 1970s thanks to the sounding rockets and the Uhuru
satellite carrying the first X-ray detectors (Giacconi et al. 1972). Since 2015 merging stellar
black hole binaries have also been detected via gravitational-wave emission (Abbott et al.
2016). Between stellar and supermassive black holes, there is a category of intermediate-mass
black holes (IMBHs) with the masses in the range of ∼ 102
− 105
M⊙ with the firm detections
only at the lowest and the highest values of this range (Greene et al. 2020).
At the time when SMBHs started to be associated with the large luminosity of QSOs,
so was the compact radio source Sgr A* considered to be located at the very center of
the Milky Way. The question was if there is a link between Sgr A* and those luminous
SMBHs in QSOs. Or perhaps the Milky Way does not host an SMBH? Or could it be that
Sgr A* is currently accreting much less than the SMBHs in the monitored QSOs that are at
cosmological distances, and thus younger than the Milky Way? In 1969, Donald Lynden-Bell
made the connection between the nuclear emission in nearby galaxies and distant quasars, and
denoted the lower-luminosity nuclei as “collapsed old quasars”, suggesting an evolutionary
link (Lynden-Bell 1969). Two years later, in 1971, Donald Lynden-Bell and Martin Rees
10 CHAPTER 1. INTRODUCTION
suggested the existence of an SMBH in the Galactic center (Lynden-Bell & Rees 1971). They
also outlined its basic properties and suggested to use broad emission lines, very long baseline
interferometry, and infrared emission (and its variability) to detect the SMBH. As already
mentioned, in 1974, Sgr A* was detected using the long-baseline radio interferometry (Balick
& Brown 1974), and shortly afterwards, Sgr A* started to be associated with the SMBH.
The rest of the introduction to this Habilitation Thesis deals with the mapping of both the
Galactic center and distant quasars and how these are related. Some answers have been found
in previous studies, including my papers, yet many remain to be tackled in the future. In
Section 1.1, we will look more closely at the SMBH in the Galactic center and its immediate
surroundings within its sphere of gravitational influence of ∼ 2 pc. In Subsection 1.1.2, we
will consider the distribution of gas of different phases, while in Subsection 1.1.1, we will
focus on stars and different stellar populations. The most active galaxies – or quasars – are
then the topic of Section 1.2. There are several differences and contrasts between the Galactic
center and quasars but also some similarities – in both cases, the main dynamical “engine”
is the SMBH. Most importantly, there is an evolutionary connection. The current state of
the Galactic center is common at low redshifts and represents the end product of the quasar
state – the Galactic center could be described as the old or almost dead quasar or the “cinder”
of the once very active SMBH (Lynden-Bell 1969). However, the last increased activity of
the Galactic center did not necessarily take place billions of years ago. Some traces of the
significant increase in the nuclear activity can be dated back to only a few millions years ago.
We will discuss these evolutionary connections as well as more generally the feeding and the
feedback of galactic nuclei in Section 1.3. Finally, in Section 1.4 we will discuss the possibility
of using galactic nuclei as standardizable sources for cosmology. As we discussed, galactic
nuclei are characterized by a large range of accretion rates and therefore also luminosities,
hence they may not seem as ideal probes to constrain cosmological parameters. In addition,
galactic nuclei are variable on the timescales of weeks to months, which also makes their
standardization more difficult. However, there are two (and potentially more) non-linear
power-law relations between quasar quantities that can be used to determine luminosity
distances to them and therefore use them as standardizable candles. First, it is the relation
between the radius of the broad-line region and the driving monochromatic luminosity, or the
R − L relation. Second, there is a correlation between the UV monochromatic luminosity LUV
typically measured at 250 nm and the X-ray monochromatic luminosity LX determined at 2
keV, or the LX − LUV relation. We will discuss the achieved constraints so far and the main
systematic effects that seem to influence these relations.
1.1 Mapping the Galactic center
To understand the evolution of galaxies across the cosmic history, in particular how the activity
of galactic nuclei evolves, it is essential to map their kinematic and geometrical structure. In
this regard, it is practical to start with the extreme cases. On one hand, there are SMBHs
that are very difficult to detect at the centers of galaxies because of their low luminosity due
to a low level of accretion, i.e. significantly below the maximum stable spherical accretion,
so-called the Eddington limit, see Eq. (1.2). Our Galactic center hosts such an “underfed”
SMBH associated with the compact variable source Sgr A*. On the other hand, there are
SMBHs that can accrete the equivalent of several Suns per year or actually they can reach or
even exceed the Eddington limit. Such SMBHs are in the nuclei of quasars, the most active
1.1. MAPPING THE GALACTIC CENTER 11
galaxies, and they outshine the total stellar radiation of their host galaxies by several orders of
magnitude.
The center of the Milky Way with the distance of ∼ 8.1 kpc determined using different
methods (Genzel et al. 2010) is the closest galactic nucleus to us, about ∼ 93times
closer than the closest nucleus hosting a low-accreting SMBH in M31 in the Local
Group (∼ 752 kpc; Riess et al. 2012) and ∼ 531-times closer than the closest active
galactic nucleus (AGN) in NGC 4395 (∼ 4.3 Mpc; Thim et al. 2004). With the
diffraction-limited near-infrared observations, it is possible to resolve structures as small
as ∼ (λ/D)dSgrA∗ = (λ/2.2 µm)(D/8 m)−1
(dSgrA∗/8 kpc) ∼ 454 AU. Since the mean distance
between stars is typically larger, the Galactic center (GC) is the only galactic nucleus where
one can observe individual stars as well as study the properties of the dense Nuclear Star
Cluster (NSC) as a whole. Since the NSC represents one of the densest stellar environments
in the Galaxy, the GC can be utilized as a unique test-bed for stellar dynamics in the dense
cluster environment (Schödel et al. 2014b).
Furthermore, the multi-wavelength observations of the Galactic center reveal a multiphase
gaseous-dusty environment, including denser molecular and neutral material outside the inner
parsec and ionized warmer gas and hot X-ray emitting plasma within the inner parsec. The
kinematic structure of the gaseous medium is quite complex. There are clear signs of the
Keplerian motion of the gas on one hand, but most of the gas is actually outflowing, with a
small fraction going inwards towards the extremely low-luminous SMBH (Morris & Serabyn
1996). The reasons behind low accretion onto Sgr A*, despite a large accumulation of gas
within the Central Molecular Zone (≲ 200 pc from Sgr A*; CMZ), are likely the combination
of star formation (matter is converted into stars, Henshaw et al. 2023) and the loss via
thermally driven outflows, partially collimated by the large-scale magnetic field. The latter
is partially caused by gas heating driven by shocks due to numerous supernovae and by the
X-ray radiation field provided by numerous X-ray binaries (Morris 1993; Hailey et al. 2018).
In fact, the matter needs to lose angular momentum substantially in order to inspiral from
Galactic scales towards the bound orbit around the SMBH. The specific angular momentum
of gas (per unit mass) at the scale of ∼ 500 pc and considering the speed of ∼ 250 km s−1
is lgal ∼ rv ∼ 3.9 × 1028
cm2
s−1
. If the matter orbits close to the innermost stable circular
orbit or te ISCO around the SMBH, for instance at r = 6 gravitational radii (rg) for a
non-rotating (Schwarzschild) black hole, its angular momentum is l• ∼ rv ∼ rgc(r/rg)1/2
∼
4.3 × 1022
cm2
s−1
. Hence, the difference is six orders of magnitude in terms of the specific
angular momentum. The gas needs to bridge the length-scales between ∼ 500 pc or the CMZ
scales to the scales of the event horizon of the SMBH, which can be scaled by the gravitational
radius rg,
rg =
GM•
c2
∼ 5.9 × 1011 M•
4 × 106 M⊙
cm . (1.3)
One gravitational radius corresponds to about 0.039 AU or about one tenth of the mean
distance of Mercury from the Sun. The overall difference in the length-scale between the
CMZ and the event horizon corresponds to the factor of ∼ 2.6 × 109
.
The CMZ contains about ∼ 5 to 10% of molecular gas of the Milky Way, which gives rise
to the densest concentration of massive stars and star clusters in the Galaxy, including the
most massive star-formation complexes – Sgr A and Sgr B2 (Morris & Serabyn 1996; Ferrière
et al. 2007). The total mass of the dense gas (nH2
≳ 104
cm−3
) is ∼ 3 − 7 × 107
M⊙ (Bally
et al. 1987, 1988; Morris & Serabyn 1996; Ferrière et al. 2007). The inflow of gas towards
12 CHAPTER 1. INTRODUCTION
Figure 1.5: Multi-wavelength images of the Central Molecular Zone on the scale of
120 pc. Left panel: The inner 120 pc of the CMZ as observed by MeerKAT (0.9-1.6 GHz,
blue; SARAO) and Herchel PACS HI+H2 column density (red; inferred from dust continuum
emission; see also Molinari et al.,2011), which traces the 100-pc Ring of molecular material
presumably along the stable x2 orbit. Composite image produced by John Bally. Arrows
denote different structures including molecular complexes the Brick, Sgr B2, Sgr B1, 50 km/s,
20 km/s clouds, Sgr A complex, and Sgr C. The dashed yellow oval-shaped region denotes
the Galactic center bubble between the Sgr A complex and the Brick. The red rectangle
represents the 40-pc region shown in the right panel. Right panel: The 40-pc region of the
CMZ. The composite image was created by the combination of the 1-8 keV image (blue,
Chandra; Wang et al., 2002), the optical image (yellow, HST; NASA/ESA/STScI/Q.D.Wang),
and the NIR-MIR image (3.6 − 24 µm, red, Spitzer; Churchwell et al., 2009). Images adopted
from Bryant & Krabbe (2021).
the CMZ is governed by the gravitational potential of the Galactic stellar bar that extends
on the scale of ∼ 3 kpc from the Galactic center (Morris & Serabyn 1996). It is revealed by
the radial-velocity profiles of CO and HI gas as a function of the Galactic longitude. From
this analysis, it has been inferred that the Galactic bar is oriented ∼ 20 − 45◦
with respect to
our line of sight. In comparison with the Galactic disc, which is dominated by the rotational
motion in the Galactic plane, the bar potential allows for a larger-amplitude vertical motion.
This is also apparent in the maps of the surface density of the interstellar gas that exhibit
a peak in the density at ∼ 3 − 4 kpc and a drop inside 3 kpc, where the bar potential starts
to dominate. In principal, the bar is triaxial and its potential allows for different families of
gas-star orbits. The most prominent ones are x1 orbits along the major bar axis and x2 orbits
that are perpendicular to x1 and follow the minor bar axis (Contopoulos & Mertzanides 1977).
The combination of x1 and x2 orbits along with the bar orientation and the sense of cloud
motion can address the observed distribution of major molecular complexes, the clumpiness as
well as the asymmetrical distribution of the CMZ. In Fig. 1.5, we show the multi-wavelength
images of the inner 120 pc (radio+far IR; left image) and the inner 40 pc (X-ray+optical+NIRMIR;
right panel). In these composite images, one can notice the major molecular complexes
that exhibit a star-formation activity, in particular Sgr A complex, Sgr B1, Sgr B2, and
Sgr C. It is quite visible that in the positive Galactic longitudes (east of Sgr A*) there is a
higher column density of molecular material in comparison with negative Galactic longitudes
(west of Sgr A*). The western part is characterized by the occurrence of discrete 24 µm
sources. One interpretation is that the star-formation activity within the central 100-pc Ring,
along which molecular complexes are distributed, is not synchronized. We can rather see
1.1. MAPPING THE GALACTIC CENTER 13
star-formation process at different stages. In this picture, the region to the west could have
already experienced a major starburst that led to the ejection of the cold molecular material
via winds of massive young stars and supernova wind bubbles (see e.g. Bally & Hi-GAL
Team 2014, and references therein).
Most of the star formation within the CMZ takes place in the inner 100 pc, more specifically
in the molecular complexes along the 100-pc Ring (Molinari et al. 2011), where one
can localize the densest stellar clusters – the Arches, the Quintuplet, and the NSC. Because
of the intense star-formation activity, winds of massive stars interact with the denser neutral
and molecular material and push it away, creating the Galactic center bubble, see the yellow
oval-shaped region in Fig. 1.5. The manifestation of this are the Arched filaments to the
north. The molecular clouds along the 100-pc Ring are one to two orders of magnitude denser
than in the Galactic plane and exhibit an order of magnitude larger line widths, indicating
extra velocity shear and turbulence. Despite increased star formation in comparison with
the Solar neighbourhood (∼ 0.02 − 0.1 M⊙ yr−1
; Morris & Serabyn 1996; Yusef-Zadeh et al.
2009b; Longmore et al. 2013), the star-formation rate per unit mass of high-density gas is
actually lower than in the Galactic plane. This decreased efficiency could be due to several
mechanisms typical for the Galactic center region, especially increased turbulence, tidal
stresses and shocks, stronger magnetic field, shocks due to cloud-cloud collisions, and their
combination (Kruijssen et al. 2014).
To understand the overall dynamics of the gas inflow through the Galactic 3-kpc bar, CMZ
with the 100-pc Ring, and all the way to the innermost parsec is one of the major challenges
of the current Galactic dynamics. A partial understanding has been reached by applying the
theory of x1-x2 orbits within the bar on the distribution of molecular clouds and dense stellar
clusters within the CMZ. In Fig. 1.6 (left panel), we illustrate the motion of the molecular
material along the innermost stable x1 orbit, while most of the star-forming clouds move
along the inner x2 orbits that are perpendicular to x1 orbits. This can address the projected
distribution of prominent molecular clouds with dense star-forming clusters along the 100-pc
Ring, see Fig. 1.6 (right panels). The stable x1 − x2 orbits provide a way to transport the
denser material from kiloparsec scales to 100−pc scales, where other mechanisms, such as
cloud-cloud collisions, can yield a lower angular-momentum material that falls in towards
parsec scales from the SMBH.
Overall, the CMZ with the Sgr A complex including Sgr A*, has played a major role in
understanding star formation in the extreme conditions, the impact of the stellar feedback on
the surrounding dense gas, and the overall gas transport from larger Galactic scales towards
the SMBH. In fact, the Galactic center seems to be an example of a galactic nucleus where
the SMBH is currently not the main feedback provider. Numerous massive stars control the
SMBH growth and in fact keep it to a minimum via their stellar wind outflows and supernova
feedback.
1.1.1 Stellar populations in the central parsec
The Galactic center Nuclear Star Cluster (NSC) has the size comparable to globular clusters
but it is many times more massive. In fact, the stellar density is one of the largest among
stellar environments in the Galaxy. For this reason, the NSC is a unique dynamical testbed
for the stellar cluster whose inner part is dominated by the potential of the SMBH (Schödel
et al. 2014b). Based on the monitoring of fast-moving B-type stars, it has been possible to
determine the exact value of the mass of the compact radio source Sgr A*, M• ≃ 4 × 106
M⊙
14 CHAPTER 1. INTRODUCTION
l=1.3 complex
50 km/s cloud
20 km/s cloud
Sgr C
x2
orbits
x1 orbits
To Earth
Bania's Clump 2
Sgr B2
24μmsources
Figure 1.6: Motion of dense molecular material towards the Galactic center. Left panel:
Illustration of the top-view of the Central Molecular Zone (CMZ; the inner 500 pc). The
orange-shaded oval depicts the orientation of the Galactic bar with respect to the line of sight
(the angle of ∼ 20 − 45◦
). Stars and gas move in the bar potential on stable x1 orbits along
the bar major axis. The lower angular-momentum x1 orbits become self-intersecting - this is
where the denser molecular complex Bania’s Clump 2 may be located on the front side of
the CMZ. Most of the CMZ molecular emission is associated with the x2 orbits, which are
perpendicular to x1 orbits and are represented by three ellipses. Densest molecular clouds, in
particular Sgr B2, 50 km/s cloud, 20 km/s cloud, and Sgr C move in the bar potential on these
orbits and form the prominent 100-pc Ring (see the right panel). The illustration was inspired
by Bally & Hi-GAL Team (2014). Right panel: The far-infrared image of the inner 94 pc
obtained by the Herschel SPIRE at 250 µm (top panel). The black solid line shows the x2
orbit that mimics the infinity sign, but in 3D it exhibits a closed-loop-like shape. The densest
molecular clouds seem to follow this inner x2 orbit in the bar potential as is apparent from
the dust temperature map (bottom) obtained from the dust continuum emission between 70
and 500 µm (Molinari et al. 2011). This geometrical configuration of molecular clouds along
with dense star-forming regions represents the 100-pc Ring. Adopted from Bryant & Krabbe
(2021).
(Genzel 2022), which is associated with the SMBH at the center of the Milky Way. This was
possible based on the detection of stellar proper motions within one arcsecond of Sgr A*
(Eckart & Genzel 1996, 1997; Ghez et al. 1998) and later by also detecting accelerations
along the orbit (Ghez et al. 2000). This eventually led to the determination of elliptical orbits
of several tens of stars orbiting the SMBH (Eckart et al. 2002; Schödel et al. 2002; Gillessen
et al. 2009, 2017).
In comparison with other galaxies, the NSC can be studied on sub-parsec and even
milliparsec scales and it can be resolved into millions of stars whose spectral type and proper
motion can be investigated. From these analyses it was found that the NSC is predominantly
composed of late-type stars with the spectral types M, K, and G (>1 Gyr; Pfuhl et al. 2011).
The distribution of stellar velocities is approximately isotropic, with the slow, solid-like
rotation parallel to the rotation of the Galaxy (bar). The NSC is elliptical in shape and
flattened along the Galactic plane with the symmetry ratio of q = 0.71 ± 0.02. It is also
point-symmetric with respect to Sgr A* and has a half-light radius of rhl = 4.2 ± 0.4 pc. Based
on the mid-infrared images corrected for extinction, it was possible to constrain the luminosity
of the NSC, L4.5µm = (4.1 ± 0.4) × 107
L⊙ and the total mass of MNSC = (2.5 ± 0.4) × 107
M⊙
1.1. MAPPING THE GALACTIC CENTER 15
line of sight
Galactic center
Figure 1.7: Localization of the Nuclear Star Cluster, Nuclear Stellar Disc, and the
Central Molecular Zone within the Galaxy. Left panel: Illustration of the location of
the Galactic center, including the Nuclear Stellar Disc and the Central Molecular Zone,
in the Galaxy. Right panel: Composite infrared image (3.6+4.5+8 µm) obtained from the
Spitzer images where the Central Molecular Zone is depicted as a blue dashed oval, i.e. the
region with the largest concentration of molecular gas. In this region, the large molecular
complex/star-forming region Sgr B is shown as well as the HII regions Sgr C and Sgr E. The
Nuclear Stellar Disc is an elongated bright structure, which is located within the CMZ and
partially overlaps with it. At the very center, a nearly spherical Nuclear Star Cluster is located,
which has a half-light radius of ∼ 4.2 pc. Both figures were adopted with some modifications
from Schoedel et al. (2024).
(Schödel et al. 2014a), which gives an average mass-to-light ratio of (M/L)4.5µm ∼ 0.6, though
it is clearly radius-dependent as there are numerous young massive OB/Wolf-Rayet stars
within the inner 0.5 pc (see the discussion below).
The NSC is embedded within the larger, elongated Nuclear Stellar Disc (NSD), which has
the total mass of ∼ 109
M⊙ and the length-scale of ∼ 120 pc (Launhardt et al. 2002). It thus
overlaps substantially with the CMZ, or the 100-pc Ring, see also Fig. 1.7 for the schematic
illustration (left panel) and the composite infrared image showing the main structures within
300 pc (right panel). It is elongated along the Galactic plane, which implies the supply of
material for the NSD build-up along the main axis of the bar. The star formation and the gas
feeding was, however, not continuous as previously expected (Nogueras-Lara et al. 2020). The
bulk of the NSD mass formed 8 Gyr ago or more, while there was another intense starburst
∼ 1 Gyr ago, forming ∼ 5% of the NSD mass. A few percent of stars formed within 500
Myr, with the continuation until 30 Myr ago. This suggests that in the Galactic center region,
star formation is quite episodic with long periods (∼ several Gyr) of quiescence. The NSD
is kinematically cool with the coherent rotation pattern with the velocity of ∼ 120 km s−1
parallel to the Galactic plane. Its vertical extent is only ∼ 50 pc, hence it is significantly flatter
than the NSC with q ∼ 0.2 − 0.4 (Schönrich et al. 2015).
In Fig. 1.8, we illustrate the different stellar structures – Nuclear Stellar Disc on 100-pc
scales, Nuclear Star Cluster on the 10-pc scale, the region of fast-moving “S stars” (Eckart &
Genzel 1996, 1997; Ghez et al. 1998) in the central parsec. In the further discussion, we focus
on this region, which is well inside the sphere of gravitational influence of the SMBH. By the
sphere of influence we mean the region with the radius where the circular velocity around
Sgr A* equals the velocity dispersion σ⋆ of the stars in the NSC, hence we have,
rSI =
GM•
σ2
⋆
∼ 2.1
M•
4 × 106 M⊙
σ⋆
90 km s−1
−2
pc , (1.4)
16 CHAPTER 1. INTRODUCTION
Figure 1.8: Towards the population of fast-moving “S stars” orbiting around Sgr A*.
Panel (a): Spitzer/IRAC 4.5 µm depicting the elongated Nuclear Stellar Disc on the scale
of 275 pc (based on Schödel et al. 2014a). Panel (b): The ISAAC composite image
(1.19+1.71+2.25 µm) of the Nuclear Star Cluster on the scale of 6 pc, which corresponds
to the cyan box in panel (a). Based on the data analyzed in Nishiyama & Schödel (2013).
Panel (c): The NACO/VLT holographic image of the central half-parsec (Schödel et al. 2013),
which corresponds to the white box in panel (b). The S cluster surrounding Sgr A*, which is
at the center of all the images but typically very faint unless it is flaring, is depicted by a black
circle. All of the three images were adopted from Schödel et al. (2014b).
where σ⋆ ∼ 90 km s−1
is estimated from the M• − σ⋆ relation (Gültekin et al. 2009). For the
spherical cluster around the SMBH, this would correspond to the radius where the total stellar
mass M⋆(r < rSI) = 2M• ∼ 8 × 106
M⊙ (Merritt 2013).
Inside rSI stars undergo two-body relaxation by exchanging energy and angular momentum
in the dominant potential of the SMBH. The characteristic non-resonant relaxation timescale
is,
τr =
0.34σ3
⋆
G2ρ⋆ < m⋆ > ln Λ
≃ 4.2
σ⋆
90 km s−1
3 ρ⋆
2.1 × 105 M⊙pc−3
−1
< m⋆ >
1 M⊙
−1
ln Λ
15
−1
Gyr , (1.5)
where ρ⋆ is the stellar mass density estimated as the total stellar mass density within the
sphere of influence, ρ⋆ ≈ 6M•/(4πr3
SI), < m⋆ > is the mean stellar mass, which we set to 1 M⊙,
and ln Λ is the Coulomb logarithm, which can be estimated as ln Λ ∼ ln (M•/m⋆) ∼ 15 in the
potential of the SMBH (Merritt 2013). After τr, hence about half billion years for the Galactic
center, the stellar system is expected to be dynamically relaxed – i.e. the orbital energy and
angular momentum are exchanged to such an extent that the system does not possess any
fingerprint of the initial orbital distribution. The relaxed system dominated gravitationally by
the SMBH is expected to have an increasing density profile towards the SMBH, which can be
utilized to reveal especially quiescent SMBHs in the nearby Universe (Peebles 1972). More
precisely, the stellar density in such a cluster exhibits a power-law distribution as a function
of the distance from the SMBH. This is a so-called Bahcall-Wolf cusp and the theoretical
dependencies are ρ⋆(r) ∝ r−7/4
for stars with the same mass (Bahcall & Wolf 1976) and
ρ⋆(r) ∝ r−3/2
for a two-mass stellar distribution (Bahcall & Wolf 1977).
Concerning the late-type stellar population in the inner parsec, it is old, specifically ∼ 80%
of the stellar mass formed 10 Gyr ago or more (Schödel et al. 2020). The velocity distribution
is isotropic and the spatial distribution is slightly flattened along the Galactic plane as already
1.1. MAPPING THE GALACTIC CENTER 17
mentioned. Given its large age, the late-type population should be approaching a relaxed state,
which should be demonstrated by a cusp-like distribution. Previous studies, however, found a
core-like distribution for late-type stars within 0.5 pc (Sellgren et al. 1990; Buchholz et al.
2009). This hinted at a certain mechanism that led to the depletion of older red giants in the
inner region, such as stellar collisions (Genzel et al. 1996) or their repetitive interaction with
a massive starburst/accretion disc (Amaro-Seoane & Chen 2014) and/or a jet (Zajaˇcek et al.
2020).
In contrast, subsequent more sensitive studies revealed that faint late-type stars do exhibit
a cusp-like distribution (Habibi et al. 2019; Schödel et al. 2020), bringing non-resonant
two-body relaxation into play. The same study by Schödel et al. (2020) showed that just
brighter, bigger red giants (with K-band magnitudes of mK ≲ 14.5) exhibit a flat, core-like
distribution, which hints at a depletion mechanism that is size-selective, affecting mostly
larger giants with loose envelopes. Furthermore, there are indications from the overabundant
population of low-mass X-ray binaries in the central parsec (Muno et al. 2005; Hailey et al.
2018) that stellar-mass black holes also exhibit a cusp-like distribution, which indicates that
these populations (late-type stars and compact objects) are likely in a steady-state, dynamically
relaxed state.
The apparent overabundance of young massive stars in the central ∼ 0.5 pc has remained
puzzling since massive OB/Wolf-Rayet stars as well as B-type stars in the central 0.5” –
so-called S stars – were spectrally identified. This was dubbed as the “paradox of youth”
(Ghez et al. 2003). It has been considered a paradox since the tidal field of Sgr A*, intense
radiation, large gas turbulence, strong magnetic field, and shock waves should significantly
inhibit in situ star formation in the Galactic center (Morris 1993). An alternative to the in situ
star-formation processes are successive inspirals of star clusters from the CMZ. This scenario
has two basic problems: (i) a characteristic inspiral timescale of the cluster from the CMZ is
typically much longer than the inferred age of massive OB stars (∼ 5 million years); (ii) the
cluster would be prone to tidal disruption before reaching the central parsec unless its core is
very dense. An intermediate-mass black hole (IMBH) could stabilize the cluster core so that
the stars are stabilized till they reach the central parsec. However, the IMBH would have to
have the mass of ∼ 10% of the initial cluster mass, which has been considered unrealistic for
typical star-forming cluster masses (Kim et al. 2004).
A fraction of OB stars are a part of the coherent kinematic disc-like structure known as
the Clockwise Disc (CWD; Levin & Beloborodov 2003) within the inner 0.5 pc. This stellar
disc has a mean inclination of ∼ 122◦
± 7◦
, a mean angle of the line of nodes ∼ 99◦
± 3◦
,
and an opening angle of 10◦
(see Genzel et al. 2010, and references therein). The disc-like
structure of stars suggested, in combination with the fact that OB stars cannot be relaxed, that
stars formed in a massive gaseous disc that underwent gravitational instability, which resulted
in the formation of massive stars (Levin & Beloborodov 2003).
Several analytical and numerical models have been proposed to reproduce star formation
close to the SMBH. Two star-forming channels emerged (Mapelli & Gualandris 2016):
• disc mode, where an infalling cloud forms a disc that is preceded by a cloud-cloud
collision (Hobbs & Nayakshin 2009) or the collision of the cloud streamer with itself
(Wardle & Yusef-Zadeh 2008). The formed disc around the SMBH becomes gravitationally
unstable (Levin & Beloborodov 2003) when the Toomre’s criterion for instability
is met: Q = csΩK/(πGΣ) < 1, where cs is the gas sound speed, ΩK is the Keplerian
angular velocity, and Σ is the surface density of the disc;
18 CHAPTER 1. INTRODUCTION
• infalling cloud mode, in which a cloud with a low angular momentum, potentially
preceded by a cloud-cloud collision within the CMZ, falls towards the SMBH where
it is tidally compressed at the periapse in the direction perpendicular to its motion,
which triggers gravitational collapse, fragmentation, a subsequent formation of a stellar
association (Jalali et al. 2014).
Since massive young stars in the Galactic center are too young to be dynamically relaxed,
their orbital distribution should bear signs of the formation mechanism. This can be used
to test the proposed star-formation channels. von Fellenberg et al. (2022) spectroscopically
identified 195 young OB stars within ∼ 1.2 pc that exhibit Brγ absorption line in their spectra.
They found that the angular momentum distribution of these stars deviates significantly from
an isotropic distribution, which is characteristic for the surrounding population of late-type
stars (see e.g. Schödel et al. 2014b). More specifically, ∼ 75% of young stars belong to
coherent dynamical structures resembling discs, i.e. only a minority appears to be randomly
distributed. von Fellenberg et al. (2022) identified five clusters of angular momenta on the
inclination/ascending-node length plane. Two clusters stand for the warped clockwise disc
(CWD), whose inner part has the mean semi-major axis of ∼ 0.084 pc and the outer part
of ∼ 0.28 pc. Another feature represents the counter-clockwise disc (CCWD) on larger
scales, which has the mean semi-major axis of ∼ 0.3 pc. There are two more, previously
non-identified features denoted as F2 and F3 with mean semi-major axes of ∼ 0.2 pc and
0.4 pc. All of these features are consistent with in-situ star formation. In particular, the
simulation runs of cloud-cloud collisions close to the Galactic center (Hobbs & Nayakshin
2009) typically result in the gas settling close to the SMBH in the form of a star-forming disc.
In addition, there are typically a few remnant gaseous streamers, in which star formation also
takes place. These additional streamers could then explain the presence of CCWD, F2, and
F3 features in the analysis of von Fellenberg et al. (2022).
The innermost cluster of fainter, B-type stars or so-called S stars (Eckart & Genzel 1996,
1997) was originally considered to be nearly isotropic (Gillessen et al. 2009; Genzel et al.
2010). This was also confirmed by Gillessen et al. (2017), who determined orbits for 40
stars, 32 of which are distributed isotropically with the thermal distribution of eccentricities,
i.e. the one that follows n(e)de = 2ede (Jeans 1919). Such a distribution is expected for
old, relaxed cluster. In contrast, S stars were found to be at least an order of magnitude
younger than the two-body relaxation timescale, see Eq. (1.5), with the age comparable to
the CWD and CCWD disc stars (< 15 Myr and 6.6+3.4
−4.7 Myr for the S2 star; Habibi et al.
2017). This implies that CWD stars and S stars formed simultaneously or potentially they
have a common origin. One proposed mechanism to link the formation of OB/WR stars
within the CWD and B-type S stars is the disc-formation mechanism (Chen & Amaro-Seoane
2014). It is plausible that the initial gaseous disc extended closer to the SMBH, producing
both more massive O-type stars and less massive B-type stars in the inner arcsecond. Due
to the Kozai-Lidov-like resonance and the oscillations of the eccentricity and the inclination
induced by the outer part of the massive disc, more massive O-type stars were driven onto
high-eccentric orbits, on which they got tidally disrupted. Lighter B-type stars increased
their orbital eccentricities more slowly and they also acquired larger inclinations, which can
address their nearly isotropic, thermalized distribution. The rapidly evolving region or RER
suggested by Chen & Amaro-Seoane (2014) can thus elegantly connect the origin of the
disc-like distribution of OB stars and the inner cluster of B-type S stars. Furthermore, based
on the analysis of 112 S stars, 39 of which had orbital solutions, Ali et al. (2020) found a
1.1. MAPPING THE GALACTIC CENTER 19
significant deviation of their inclination and proper-motion distributions from the isotropic
(uniform) distribution. The S cluster rather seems to consist of two nearly edge-on stellar
discs that are oriented ±45◦
from the Galactic plane. The pole of the structure is inclined
by ∼ 25◦
from the line of sight. Moreover, each disc hosts stars of both angular-momentum
directions. Such a two-disc structure could be a fingerprint of the formation mechanism
of the S cluster a few million years ago – such as the RER mechanism due to the outer
gaseous disc. Alternatively, it could be caused by the gravitational torques induced by a more
distant perturber, such as an IMBH that could hypothetically be hosted by one of the denser
stellar associations in the central parsec (IRS13; Peißker et al. 2024a). The systems of stars
dominated by the SMBH potential typically undergoes a fast vector resonant relaxation, which
causes the orbital inclinations to be randomized. Such a stellar system behaves similarly to
liquid crystals (Roupas et al. 2017) in a way that it can undergo first- and second-order phase
transitions between ordered-nematic and disordered-isotropic states. In the ordered phase, it
can actually consist of two discs inclined by ∼ 90◦
as found by Ali et al. (2020) and such a
state is metastable.
Within the S-cluster region, a mysterious population of G-objects has been identified,
whose members are characterized by a prominent infrared excess due to the spectral energy
distribution dominated by dust emission with the effective temperature of ∼ 500 − 600 K
(Ciurlo et al. 2020; Peißker et al. 2020b). In Fig. 1.9, we show their projected distribution
around Sgr A* within the central parsec. The semi-major axes of G objects mostly coincide
with the inner S cluster of B-type stars, i.e. a⋆ ≲ 0.02 pc. These objects also exhibit rather
broad hydrogen and helium emission lines with FWHMs of ∼ 100 − 200 km s−1
, which is
indicative of an ionized gaseous-dusty envelope. The most representative G-object G2, which
was intensively monitored between 2012-2016, was originally considered to be a tidally
dissolving gaseous-dusty cloud with a head-tail structure (Gillessen et al. 2012, 2013). After
its pericenter passage in the first half of 2014, it did not disintegrate and continued orbiting
Sgr A* on the Keplerian trajectory (Witzel et al. 2014; Valencia-S. et al. 2015). The emission
maps revealed its compact structure along the whole orbit up until at least 2019 (Peißker et al.
2021b), including both K− and L−band continuum emission as well as Brγ-line emission.
This has contributed to favouring the model scenarios that considered G2 and potentially all
G-objects to be dust-enshrouded stars (Eckart et al. 2013; Scoville & Burkert 2013; Zajaˇcek
et al. 2014) rather than core-less gas and dust clumps, see also Fig. 1.10 for the illustration of
this enigmatic population of dust-enshrouded stars. In the meantime, several other models
have been proposed, some of which pertain to planet formation in the Galactic center; see
Zajaˇcek et al. (2024d) for a comprehensive overview. The origin of G objects within the S
cluster remains puzzling. They could plausibly be young stellar objects of class I (Zajaˇcek
et al. 2017) or potentially binary-merger products (Stephan et al. 2016).
Regardless of the G-object origin (in situ or migration scenarios), they appear to be
associated with the young stellar population of S stars and CWD stars as revealed by their
kinematic structure that deviates from an isotropic orbital configuration (Peißker et al. 2024b).
Given their dusty envelopes revealed by infrared excess, they could in principle be even
younger than S stars (∼ 0.1 − 1.0 Myr). Based on the spectral energy distribution fits, the
bolometric luminosity is lower than for typical S stars – for the G2 object, it is LG2 ∼ 10 L⊙.
Therefore, G objects represent a lower-mass population within the S cluster that could have
formed with a certain delay with respect to high-mass star formation (e.g. from the remnant
gas that was compressed by stellar winds) or these objects could be evolving more slowly in
comparison with higher-mass B-type stars.
20 CHAPTER 1. INTRODUCTION
Figure 1.9: Projected distribution of G objects around Sgr A* and with respect to the
Minispiral and prominent stars of the inner parsec. This multiwavelength image spanning
across ∼ 0.8 pc is the combination of K-band (red) and L-band (blue) images taken by
NACO at the European Southern Observatory. The green colour depicts the ALMA 100 GHz
continuum image reduced by Moser et al. (2017). The figure inset stands for a zoom-in of the
yellow region at the very center. It depicts 11 G objects identified in the L-band emission that
are in orbit around Sgr A*. The image was adopted from Peißker et al. (2024b).
To understand kinematical structure of stellar populations in the central parsec, it is
instructive to compare estimated ages of early-type and late-type stars with the typical
timescales of dynamical processes relevant for the NSC. These processes include two-body,
non-resonant relaxation, see Eq. (1.5), as well as resonant relaxation processes (scalar and
vector) that are relevant for stars bound to the SMBH (Hopman & Alexander 2006; Alexander
2017). When we imagine a star on an elliptical orbit around the SMBH, we can imagine it as
a wire with a certain linear mass density when averaged over the orbital orbit. Such elliptical
wires then induce torques on each other. The total torque for N stars within the distance r from
the SMBH is
√
N(< r)Gm⋆/r and this is responsible for the process of resonant relaxation
over many orbits. Another process relevant single stars and binaries is the von Zeipel-LidovKozai
(vZLK) resonance that takes place in the hierarchical three-body problem. This could
be either a binary-SMBH system or the SMBH-star perturbed by an outer massive body (a
stellar/gaseous disc or an IMBH). On the vZLK timescale, the orbital eccentricity and the
1.1. MAPPING THE GALACTIC CENTER 21
Figure 1.10: Illustration of the mysterious population of G objects close to the Galactic
center. Currently, about 10 objects with a prominent near-infrared excess have been identified
within the inner arcsecond (Ciurlo et al. 2020; Peißker et al. 2020b). The figure depicts
prominent gaseous-dusty envelopes that embed stars. Such a model can address the observed
infrared excess as well as broad hydrogen and helium recombination lines. The G objects orbit
the central SMBH associated with Sgr A* (dark object at the center of the image surrounded
by a whitish hot accretion flow) on Keplerian elliptical orbits to a good approximation. Image
credit: Jack Ciurlo
inclination are interchanged for the inner binary (a stellar binary or the SMBH-star system)
due to the conservation of the z-component of the orbital angular momentum. Consequently,
during a high-eccentricity phase, the vZLK mechanism can trigger binary mergers or tidal
disruptions of binary stars or single stars by the SMBH.
In Fig. 1.11, we compare dynamical timescales with the estimated age of known stellar
populations in the Galactic center. In this figure, if the timescale of a given dynamical process
is smaller than the age of a stellar population, it is expected to have affected the angular
momentum distribution of those stars. For this plot, we assumed the isotropic background
(old) cluster with the mass density distribution ρ⋆(r) = 1.35 × 105
(r/2 pc)−1.4
M⊙ pc−3
, which
yields M⋆(< 2 pc) ≈ 2M•. We see that vector resonant relaxation could in principle be
affecting the inner portions of the S cluster + CW/CCW discs (depending on the mean stellar
mass). This can lead to orbital plane randomization. Late-type stars should have already been
affected by vector resonant relaxation and the inner portion also by scalar resonant relaxation.
This should have driven older stars on loss-cone orbits where they got tidally disrupted. G
objects are likely too young to be affected by any resonant relaxation process. However, if a
significant fraction of them originated as binary systems, these systems are expected to be
undergoing a merger process due to the vZLK mechanism. In fact, as suggested by Stephan
et al. (2019), they could be the manifestation of the merger process in the S cluster since a
stellar merger is typically accompanied by the formation of a circumstellar gaseous-dusty
envelope that gives rise to infrared excess.
22 CHAPTER 1. INTRODUCTION
10−5
10−4
10−3
10−2
10−1
100
distance from Sgr A* [parsecs]
10−2
10−1
100
101
102
103
104
105
106
time[106
years]
non − resonant relaxation
scalar RR
vector RR
S stars
G objects(?)
CW/CCW disc
Late − type stars
binary
tidalradius
stellartidalradius
τSMBH
vZLK (merger)
τdisk
vZLK (disruption)
Figure 1.11: Comparison of characteristic dynamical timescales with the age of earlytype
and late-type stellar populations. We depict radial dependencies for the vector and
scalar resonant relaxation, non-resonant relaxation, and the von Zeipel-Lidov-Kozai (vZLK)
resonance induced by the SMBH on the binary system (merger) or the vZLK oscillations
of the SMBH-star system perturbed by a distant massive stellar disc of 104
M⊙ with the
mean radius of 0.23 pc (disruption). For the calculations, we adopted the stellar mass density
ρ⋆(r) = 1.35×105
(r/2 pc)−1.4
M⊙ pc−3
and two mean stellar masses, 1 M⊙ and 10 M⊙, depicted
by black and gray colours, respectively. The vertical dotted magenta line stands for the tidal
disruption radius of a binary system with the component separation of 1.59 AU and the total
mass of 3.86 M⊙. The vertical dash-dotted red line represents the tidal disruption radius of a
Solar-type star.
1.1.2 Distribution of gas and accretion-flow structure
The dense NSC surrounding Sgr A* coexists with multiphase gas and dust in the circumnuclear
medium. A fraction of the gas originates in the CMZ, while the rest is supplied by the winds
of massive young stars. In Fig. 1.12, we show the most characteristic gaseous-dusty structures
along with the stars in the NSC. The ionized gas is shown in blue (continuum observations at
250 GHz and the H39α line emission, ALMA observations, 0.75” beam size), the molecular
gas is depicted in green (CS(5-4) line map, ALMA observations, 0.75” beam size). The dense
molecular/neutral gas is represented as the white region, which is an inverted image and the
region thus represents depression in the X-ray emission due to gas/dust extinction. The stellar
population is shown in red and yellow colours (3.8 µm with the ESO VLT and narrow-band
filters 1.19, 1.71, and 2.25 µm with ISAAC).
Within or close to the sphere of influence of Sgr A*, rSI ∼ 2 pc, a distinct loop-like feature
consisting of neutral and molecular gas is the clumpy Circum-Nuclear Disc (CND) with the
number density range of ∼ 103
− 108
cm−3
, the mean temperature of T ∼ 100 K, the total
gas mass of ∼ 106
M⊙, and the mean rotational velocity of ∼ 110 km s−1
(Genzel et al. 1985;
1.1. MAPPING THE GALACTIC CENTER 23
Figure 1.12: Composite multi-wavelength image depicting the coexistence of a dense
Nuclear Star Cluster with the gaseous-dusty structures close to the Galactic Center
(region 5.6×5.6 pc). The blue colour indicates an ionized gas concentrated mostly along
the three arms of the Minispiral (250 GHz continuum + H39α data; ALMA, 0.75” beam
size; Moser et al. 2017). The green patches correspond to CS(5-4) emission produced by the
molecular material along the inner rim of the Circumnuclear disc (ALMA, 0.75” beam size;
Moser et al. 2017). The white loop-like region is an inverted image of the X-ray emission
towards the Galactic center – it represents the depression in the X-ray surface brightness
caused mainly by the denser neutral/molecular gas in the Circumnuclear disc (Mossoux &
Eckart 2018). The cyan regions pertain to the N2H+
(1 − 0) emission (Moser et al. 2017),
which in several cases corresponds to the regions of severe extinction in the near-infrared
domain (encircled regions). Warm dust and stars in the inner parsec are depicted by a red
colour (L’ band–3.8 µm, NACO at VLT@ESO; Sabha et al. 2012). Stars within the dense
Nuclear Star Cluster are represented by a yellow colour (ISAAC@VLT composite image:
1.19+1.71+2.25 µm narrow near-infrared bands; Nishiyama & Schödel 2013). Image adopted
from Eckart et al. (2019).
24 CHAPTER 1. INTRODUCTION
Guesten et al. 1987; Mezger et al. 1989; Christopher et al. 2005; Requena-Torres et al. 2012;
Mills et al. 2017; Hsieh et al. 2021). The rotational motion of the CND dominates its motion.
The peak of the molecular emission is close to ∼ 1.6 pc with the extension to 4 − 7 pc from
Sgr A* in projection. The density drops quite sharply at ∼ 1.5 pc. This central region is rather
dilute and filled with ionized gas, therefore it is often denoted as the central cavity. It is
refilled with a rarefied ionized gas from the inner rim of the CND due to the interaction with
the outflow of the NSC driven mostly by massive OB stars (Blank et al. 2016). The CND
has high-density clumps with the mean length-scale of ∼ 0.05 − 0.2 pc. Hsieh et al. (2021)
identified of the order of 1000 CND clumps of this size using CS line maps. These can be
categorized into warm ones with the temperature of ∼ 50 − 500 K and number densities of
∼ 103
− 105
cm−3
and colder ones with the temperature of ≲ 50 K and the number density in
the range of 106
− 108
cm−3
. Using the unmagnetized virial theorem with the inclusion of the
tidal force, Hsieh et al. (2021) found that most of the CND clump mass (∼ 84%) is tidally
stable, yet the clumps do not collapse into stars due to a turbulent motion that increases the
critical density. However, it is plausible that occasionally, because of the velocity dispersion
among the clumps, two of them collide, which can help cross the density threshold and induce
star formation. At the same time, cloud-cloud collision removes angular momentum via
dissipation and afterwards the cloud starts inspiraling towards Sgr A*. This way young stellar
associations can be found relatively close to the SMBH (Jalali et al. 2014) where in principle
stars should not form due to high critical densities in excess of ∼ 108
cm−3
.
The central cavity is not isotropic – there are denser ionized regions concentrated along
the three arms of the minispiral. The Northern arm and Western arc seem to originate from
the inner rim of the CND (Christopher et al. 2005). Under the assumption that the gas motion
is dominated by the potential of Sgr A*, all of the three arms can be fitted with the three
bundles of Keplerian orbits – ellipses with Sgr A* at the focus of each ellipse (Zhao et al.
2009, 2010). The Northern and Eastern arms are relatively highly elliptical (e ∼ 0.8) while the
Western arc is only mildly elliptical (e ∼ 0.2). The gas along the three arms does not orbit in
the same plane – the Eastern arm is nearly perpendicular to the Northern arm and the Western
arc, which share the common plane. This hints at the origin of these two components at the
inner rim of the CND. The three arms consist of mostly ionized gas with the number density
in the range of ∼ (3 − 21) × 104
cm−3
and the temperature of 5 000 − 13 000 K. The mass of
the ionized gas within the minispiral is estimated to be ∼ 350 M⊙ (Zhao et al. 2010), hence
3 − 4 orders of magnitude smaller than the mass of the CND. Under the assumption that the
minispiral gas is kept ionized due to external photoionization, the required Lyman continuum
photon flux of 3 × 1050
s−1
implies that there should be ∼ 250 O9-type main-sequence stars
within the central parsec. Within the uncertainties, this is comparable to the number of
identified 195 OB/Wolf-Rayet stars within the CWD/CCWD/F2/F3 structures (von Fellenberg
et al. 2022).
Concerning the stability of the CND and the minispiral against tidal disruption in the
potential of Sgr A* and the NSC, we can compare the characteristic densities of gas clumps
in these regions with the critical number density given by the Roche limit. At the influence
radius of ∼ 2 pc, the total mass of the SMBH + NSC is Mtot ∼ 12 × 106
M⊙, hence we obtain
1.1. MAPPING THE GALACTIC CENTER 25
Central Cavity
Westernarc
Sgr A*Circumnucleardisc
Northernarm
+50 km/s cloud
+20 km/s cloud
Eastern arm
~ 1 pc
interaction region?
Molecular ridge
Galacticplane
SgrA
East
Minicavity
Nuclear Star Cluster
l=1.3 complex
50 km/s cloud
20 km/s cloud
Sgr C
x2
orbits
x1 orbits
To Earth
Bania's Clump 2
Sgr B2
24μmsources
Figure 1.13: Illustration of different structures and gas phases of the circumnuclear
medium close to the Galactic center. On larger scales, ∼ 3 − 15 parsecs, there are two
molecular clouds, +20 km/s and +50 km/s (magenta colour). In the gravitational sphere of
influence of Sgr A*, the density of the Circumnuclear disc (CND; molecular and neutral
gas; blue colour) drops by several orders of magnitude (central cavity – light blue). At the
inner rim of CND, the ionized streamers of the minispiral (red) partially originate. CND and
the minispiral coexist with the dense Nuclear Star Cluster (orange stars). The Minispiral
dominates the thermal emission of the Sgr A West region while the supernova remnant Sgr A
East is responsible for its non-thermal emission. The figure inset in the right upper corner
shows the location of the whole region (red circle) within the central bar potential.
the critical CND density for tidal stability as follows,
nCND
Roche >
3Mtot
2πmHr3
CND
2.9 × 107 Mtot
12 × 106 M⊙
rCND
2 pc
−3
cm−3
, (1.6)
which is only met for the densest clumps with nCND ≈ 108
cm−3
. The rest of the clumps will
likely disperse on the orbital (tidal) timescale of τtidal ∼ 7.6 × 104
(rCND/2 pc)3/2
(Mtot/12 ×
106
M⊙)−1/2
years. As for the minispiral, we adopt its characteristic distance from Sgr A* as
the mean of the periapses of the three Keplerian bundles, rmini ∼ 0.4 pc. This gives the limit
26 CHAPTER 1. INTRODUCTION
for the stability,
nmini
Roche > 1.2 × 109 M•
4 × 106 M⊙
rCND
0.4 pc
−3
cm−3
, (1.7)
where we adopted just the mass of the SMBH as this is the dominant contribution at those
scales within the influence radius. According to Eq. (1.7), none of the minispiral clumps
surpasses the critical density, therefore it is a transient feature with the expected tidal timescale
of ∼ 60 000 years, which is estimated as the mean of the orbital periods of the three arms
according to the orbital elements of Zhao et al. (2009). On the other hand, the material in
the minispiral is likely being partially replenished from the inner rim of the CND (Blank
et al. 2016), in particular the Western Arc and the Northern Arm. Hence, in this regard,
the minispiral lifetime is set by the CND existence, whose tidal timescale is comparable
to that of the minispiral. The CND material originates within the CMZ, more specifically
from the molecular/neutral material orbiting along the inner stable x2 orbit, see Fig. 1.6,
which is perpendicular to the main axis of the Galactic bar. The closest giant molecular
clouds to the CND are +20 km s−1
(M–0.13–0.08) and +50 km s−1
(M– 0.02–0.07) clouds
(Guesten & Henkel 1983), which are located ∼ 3 − 15 pc from Sgr A*. There appears to be
an interaction between +20 km s−1
cloud and the CND, which is revealed by the bridge of
material between them as revealed in the position-velocity plots (Takekawa et al. 2017). This
type of cloud-cloud interaction could be a mechanism for the accretion of new molecular
material onto the CND and subsequently inwards towards the Central Cavity. In Fig. 1.13, we
illustrate different structures and phases of the Sgr A* circumnuclear medium, in particular
with the focus on their mutual relation, potential interaction, and inward material transport.
As stars belonging to the NSC occupy the same volume as the minispiral and the CND,
they interact with the gas of different phases. Typically, the relative velocity between the star
and the ambient medium vrel = v⋆ − va is mildly supersonic, which we can infer from the
estimate of the Mach number,
M =
vrel
cs
≈ 20.4
M•
4 × 106 M⊙
1/2
Ta
104 K
−1/2
r
0.5 pc
−1/2
, (1.8)
where we used vrel = [2GM•/r(1 − cos ι)]1/2
for the relative velocity at the angle ι with respect
to the (minispiral) streamers. The speed of sound is calculated as cs ≃ [kBTa/(µmH)]1/2
. For
the estimate in Eq. (1.8), we adopted ι = 90◦
, hence the star passes through the streamer at a
right angle. Wind-blowing stars with the mass-loss rate of ˙mw and the terminal wind velocity
vw will drive a bow shock into the ambient medium. The shocked stellar wind is separated
from the bow shock by contact discontinuity whose stagnation radius is (Wilkin 1996)
Rbs =
˙mwvw
4πρav2
rel
1/2
≃
˙mwvwr
8πGM•µmHna
1/2
≈ 4.3
˙mw
10−5 M⊙ yr−1
1/2
vw
103 km s−1
1/2 r
0.5 pc
1/2
M•
4 × 106 M⊙
−1/2
na
5 × 104 cm−3
−1/2
mpc ,
(1.9)
where the second expression assumes the perpendicular interaction (ι = 90◦
) and the Keplerian
orbital motion of a star around the SMBH. The numerical estimate for the stagnation radius
1.1. MAPPING THE GALACTIC CENTER 27
of a stellar bow shock, Rbs ∼ 4.3 mpc ∼ 883 AU, was calculated for the typical stellar-wind
parameters of Wolf-Rayet stars that are present in the central parsec (Krabbe et al. 1995;
Najarro et al. 1997; Bryant & Krabbe 2021). When we compare it with the smallest linear
scales that can be studied with eight-meter class telescopes at 2 µm, x ∼ (λ2µm/D8m)dSgrA∗ ≈
418 AU, we see that such bow-shock structures should be resolved if their surface brightness
is sufficiently large. Indeed, several stellar bow shocks have been found along the minispiral
arms and they have been used for constraining the ambient medium properties (gas flow and
density) or stellar kinematics depending on which parameters are initially better constrained
(see e.g. Sanchez-Bermudez et al. 2014; Zajacek et al. 2018; Karas et al. 2021, and references
therein).
Sgr A* is a compact non-thermal radio source within the Sgr A West thermal region (Balick
& Brown 1974). It is to a high precision associated with the SMBH of M• ≃ 4 × 106
M⊙
based on the correspondence of radio and infrared reference frames. The radio and infrared
reference frames could have been combined with the precision of ∼ 0.03′′
thanks to a group of
late-type stars with a maser emission (SiO and H2O masers) that have been identified in both
infrared and radio domains (Menten et al. 1997). With this accuracy, it was possible to infer
an upper limit on the infrared luminosity of Sgr A* at 2.2 µm, νLν ≲ 1.1 × 1035
erg s−1
, which
implies a highly sub-Eddington accretion rate. Based on the Faraday rotation measurements
at 227 and 343 GHz, Marrone et al. (2007) constrained the accretion rate within 200 rg
to ˙M = 2 × 10−9
− 2 × 10−7
M⊙ yr−1
for the disordered and ordered magnetic field cases,
respectively. Adopting the intermediate value, ˙M ∼ 10−8
M⊙ yr−1
, we obtain the following
Eddington ratio,
˙m =
˙M
˙MEdd
=
σTηradc
4πGmp
˙M
M•
∼ 1.1 × 10−7 ηrad
0.1
˙M
10−8 M⊙ yr−1
M•
4 × 106 M⊙
−1
. (1.10)
For comparison, for the Eddington-rate limit, ˙m = 1, the actual accretion rate for Sgr A*
would be ˙M ∼ 0.09 M⊙ yr−1
or nearly 10% of the Solar mass per year. For such a low accretion
rate as indicated by Eq. (1.10), the accretion flow does not cool fully via radiative losses. The
energy released via viscous turbulence leads, to a dominant extent, to the entropy increase,
which is transported inwards by accretion and eventually it is lost beyond the event horizon.
This is so-called advective cooling and such accretion flows as in the Sgr A* system are
referred to as Advection-Dominated Accretion Flows or ADAFs. Because only a small fraction
of the viscously released energy is lost via radiation, ADAFs are radiatively inefficient and
hot in comparison with standard accretion discs (Yuan & Narayan 2014). This is also related
to their larger geometrical thickness and small optical depth due to more diluted plasma.
Observationally, Sgr A* is also consistent with ADAF model predictions since the peak
of the spectral energy distribution (SED) is in the mm-submm domain close to 1 millimeter.
This is quite different from SEDs of standard thin disc solutions (Shakura-Sunyaev, NovikovThorne)
that peak in the UV domain for SMBHs, which is also known as the Big Blue Bump.
The SED peak of Sgr A* close to one millimeter is also associated with the transition from
optically thick synchrotron emission at lower frequencies to optically thin synchrotron and
inverse Compton emission towards higher frequencies (shorter wavelengths). In Fig. 1.14, we
show the ADAF model of Sgr A* for different accretion rates in the range ˙M = 2 × 10−9
−
−2 × 10−7
M⊙ yr−1
as inferred from the Faraday rotation measurements (Eddington ratio of
28 CHAPTER 1. INTRODUCTION
˙m = 2 × 10−8
− 2 × 10−6
; Marrone et al. 2007). In this figure, we also depict radio-mm
detections of Sgr A* in the optically thick domain and close to the SED peak (see Zajaˇcek
et al. 2016, for the data collection). For the ADAF model calculations, we utilized the model
by Mahadevan (1997), which has been updated by Pesce et al. (2021) and implemented in
the python code LLAGNSED2
that takes two basic parameters – SMBH mass and relative
accretion rate (Eddington ratio). In the ADAF model, the electromagnetic emission at a given
frequency depends on the electron temperature Te, which is calculated self-consistently using
the equation of energy-rate balance,
δQ+
+ Qie
= Q−
rad + Qadv,e , (1.11)
where on the left-hand side, δQ+
is the fraction of the viscously dissipated energy rate that is
transferred to electrons, (1 − δ)Q+
is transferred to ions, Qie
is the energy rate transferred from
warmer ions to electrons via Coulomb coupling. On the right-hand side, the energy losses
include the advection term Qadv,e, i.e. the electron energy rate lost via advection, and Q−
rad
is the energy loss rate corresponding to radiation. For the construction of the ADAF SED,
the radiation term Q−
rad is relevant since it consists of frequency-integrated monochromatic
luminosities corresponding to synchrotron, inverse Compton, and bremsstrahlung processes,
Q−
rad = Lsynch + LComp + Lbrems . (1.12)
We show these different emission contributions in Fig. 1.14 with coloured lines (red stands
for the synchrotron emission, green for inverse Compton, and blue for the bremsstrahlung
component) for the case with the intermediate Eddington ratio of ˙m = 2×10−7
. The prominent
mm/submm bump in Fig. 1.14 is attributed to relativistic, thermal electrons in the inner portion
of the ADAF (Dexter et al. 2010). The radio synchrotron emission at lower frequencies is
attributed to a fraction of the electron thermal energy (∼ 1.5%) injected into non-thermal
electrons in the inner ADAF (Yuan et al. 2003). Alternatively, it could also be caused by a
compact, self-absorbed jet that has a low surface-brightness (Falcke & Markoff 2000). The
quiescent, faint X-ray emission at higher energies is due to the bremsstrahlung emission of
colder electrons closer to the Bondi radius (Baganoff et al. 2003; Wang et al. 2013).
Although the accretion rate onto Sgr A* is very low, there is a plenty of gaseous material
in its surroundings. Even without considering several ∼ 100 M⊙ of the minispiral gas and
∼ 106
M⊙ of the neutral/molecular gas within the CND, stars alone can supply enough mass
for accretion via their stellar winds. As reported by von Fellenberg et al. (2022), there
are about 200 OB/Wolf-Rayet stars within ∼ 0.4 pc from Sgr A*. Given that young, HeIemission
line massive stars typically have large mass-loss rates of ∼ 10−5
M⊙yr−1
(Najarro
et al. 1997), as much as ˙Mwind ≲ 10−3
M⊙ yr−1
can be available for accretion. Based on
Chandra X-ray observations centered on the extended emission peaking close to Sgr A*
(FWHM∼ 1.4′′
), Baganoff et al. (2003) inferred the asymptotic values of the number density
and the temperature of the spherical, Bondi-like inflow, nB ∼ 26 cm−3
and kBTB ∼ 1.3 keV
(TB ∼ 1.5 × 107
K). This implies the capture (Bondi) radius where the gravitational pull of
Sgr A* overcomes the thermal pressure of hot, X-ray emitting plasma,
rB ≃
2GM•
c2
s
=
2GM•µmH
kBTB
∼ 0.14
M•
4 × 106 M⊙
TB
1.5 × 107 K
−1
pc , (1.13)
2
https://github.com/dpesce/LLAGNSED
1.1. MAPPING THE GALACTIC CENTER 29
8 10 12 14 16 18 20 22
log( [Hz])
24
26
28
30
32
34
36
38
log(L[ergs1])
m=2×10 8
m=2×10 7
m=2×10 6
synchrotron; m=2×10 7
inverse Compton; m=2×10 7
bremsstrahlung; m=2×10 7
radio-mm data
Figure 1.14: Spectral Energy Distribution (SED) of Sgr A* modelled using advectiondominated
accretion flow. Different black lines correspond to ADAF continuum spectra
for different relative accretion rates – Eddington ratios of ˙m = 2 × 10−8
− 2 × 10−6
. For the
intermediate rate of ˙m = 2 × 10−7
, we also depict contributions of synchrotron (red dotted
line), inverse Compton (green dash-dotted line), and bremsstrahlung radiation mechanisms
(blue dashed line). For comparison, radio-mm detections of Sgr A* are included as orange
points (see Zajaˇcek et al. 2016, for the collection details). For the calculations, we adopted
the ADAF model according to Mahadevan (1997), which is implemented in the python code
LLAGNSED by Pesce et al. (2021).
which corresponds to rB ∼ 7.3 × 105
rg. The accretion rate at the Bondi radius then is,
˙MB ≃ πr2
BcsµmHnB =
4πG2
M2
•
c3
s
µmHnB
∼ 10−5 M•
4 × 106 M⊙
2
TB
1.5 × 107 K
−3/2
nB
26 cm−3
M⊙ yr−1
, (1.14)
hence all of this material can be supplied by stellar winds of stars located within rB or
whose pericenters reach or cross rB ( ˙MB < ˙Mwind). Since the accretion rate within 200 rg is
constrained to be ˙M ∼ 2×10−9
−2×10−7
M⊙ yr−1
based on the Faraday-rotation measurements
of Sgr A* (Marrone et al. 2007), only a small fraction of ˙M/ ˙MB ≲ 0.02 or ≲ 2% of the
Bondi accretion rate gets accreted through the event horizon. Therefore most of the material
accreted at the Bondi radius is eventually lost via outflows. One of the properties of ADAFs
30 CHAPTER 1. INTRODUCTION
is the power-law dependence of the inflow rate on the distance from the SMBH – the inflow
rate gets smaller with the radius due to an outflowing material,
˙Min = ˙MB
rin
rB
p
∼ 1.2 × 10−7
˙MB
10−5 M⊙ yr−1
rin
100 rg
0.5
rB
7.3 × 105 rg
−0.5
M⊙ yr−1
, (1.15)
which for p = 0.5 and rin = 100 rg gives ˙Min ∼ 10−7
M⊙ yr−1
that is consistent with the
Faraday-rotation constraints for the ordered magnetic-field configuration (Marrone et al.
2007). The inner radius rin is scaled to ∼ 100 rg, which corresponds to the distance of the
transition zone between the outer convection-dominated flow and the inner region dominated
by the advection of viscously generated energy density (Abramowicz et al. 2002). The
power-law index p is constrained to adopt the values between ∼ 0.3 and unity according to
the radial density profiles based on general relativistic magnetohydrodynamic simulations
(Yuan et al. 2003; Pen et al. 2003; Yuan et al. 2012; Yuan & Narayan 2014; Ressler et al.
2020). The presence of the outflow leads to the flattening of the radial density profile of
the accretion flow with respect to the steady spherical Bondi inflow, which has nB ∝ r−3/2
.
Wang et al. (2013) analyzed the obtained X-ray continuum and line spectrum and conclude
that the best description is provided by an ADAF with nADAF ∝ r−3/2+s
, where s ≈ 1. This is
consistent with the detected weak hydrogen-like Fe Kα line. Thus the no-outflow solution
can be discarded for Sgr A*.
Further support for the nuclear outflow is provided by several aligned stellar bow shocks.
The closest bow-shock sources to Sgr A* are X7 (Muži´c et al. 2010; Peißker et al. 2021a)
and X8 (Peißker et al. 2019) located at the mean projected distances of 0.4” (∼ 0.016 pc)
and 0.425” (∼ 0.017 pc), respectively. Another prominent stellar bow-shock source is X3
(Muži´c et al. 2010; Peißker et al. 2023), which is located further from Sgr A* in projection at
∼ 0.1 pc. Its symmetry axis is also approximately aligned with those of X7 and X8. On the
other hand, these three bow-shock sources have different proper-motion directions that, at the
same time, are misaligned with respect to bow-shock symmetry axes. Hence, the common
symmetry axis of the bow shocks indicates the presence of a large-scale, collimated outflow
directed away from Sgr A*. Muži´c et al. (2010) estimated the velocity of a few 1000 km s−1
for such an outflow. First, the nuclear outflow could be produced by the collective wind
within the NSC. Second, it could be associated with the ADAF as discussed above. In the
first case, if we approximate the NSC by a spherical distribution of wind-blowing stars, there
have been several analytical and numerical solutions of the inflow-outflow structure of the
gaseous medium around the SMBH (Quataert 2004; Cuadra et al. 2008; Generozov et al. 2015;
Yalinewich et al. 2018; Ressler et al. 2019). In the steady-state 1D model, a stagnation zone
develops where the radial flow velocity goes through zero and thus divides the outflow region
for radii larger than the stagnation radius from the inflow region for radii that are smaller. In
both regions, the radial flow velocity can reach supersonic values, especially when the mass
injection rate per unit volume is sufficiently steep as a function of radial distance (q ∝ r−η
for
η > 9/4; Yalinewich et al. 2018). Given the surface-brightness density power-law slope Γ of
the NSC and the radial density profile of the circumnuclear gas ρ ∝ r−ν
, the stagnation radius
can be expressed in analogy to the Bondi radius, just replacing the sound speed with the mean
stellar-wind velocity vw, which is valid to a good approximation for vw > σ⋆. The estimates
1.1. MAPPING THE GALACTIC CENTER 31
circularization radius
outflow region
Sgr A*
inflow region
stagnationradius
 
gravitational influence radius
Figure 1.15: Schematic representation of the stagnation zone in the nearly spherical
Nuclear Star Cluster. In addition, we also show the sphere of gravitational influence of
Sgr A* (rSI ∼ 2 pc), inflow, and outflow regions that are below or above the stagnation radius
rst. In case the stellar-wind material inside the inflow zone has a remnant angular momentum,
it circularizes at the circularization radius, rcirc. The illustration is not drawn to the scale, it
just shows a qualitative relation among different length-scales.
for the stagnation radius rst in the Galactic center then are (Generozov et al. 2015),
rst ≈
13 + 8Γ
4 + 2Γ
−
3νst
2 + Γ
GM•
νstv2
w
≈



0.30 M•
4×106 M⊙
vw
500 km s−1
−2
pc , core (Γ = 0.1) ,
0.16 M•
4×106 M⊙
vw
500 km s−1
−2
pc , cusp (Γ = 0.8) ,
(1.16)
where we approximated the gas density slope close to the stagnation radius νst = −(d ln ρ/d ln r)|rst
according to Generozov et al. (2015), νst ≈ 1/6[(4Γ + 3)], which for the core-like stellar
distribution gives νst ≈ 0.57 and for the cusp-like distribution, we obtain νst ≈ 1.03. We
illustrate the stagnation radius, inflow, outflow zones around the SMBH embedded within a
nearly isotropic NSC in Fig. 1.15. Since the stagnation radius for the Galactic center appears
to be located at a larger distance from Sgr A* by an order of magnitude in comparison with
the location of the aligned bow-shock sources X7 and X8, see Eq. (1.16), it is more plausible
that the stars interact with a nuclear outflow launched within the ADAF inflow zone. Such
an outflow is likely collimated by a large-scale magnetic field, which is ordered on both
larger and smaller scales and has a dominant poloidal component outside the denser clouds
32 CHAPTER 1. INTRODUCTION
as it has been inferred by several independent studies from close to the innermost stable
circular orbit to the CMZ (Morris 2015; GRAVITY Collaboration et al. 2018). Hence, the
nuclear outflow is expected to have a bipolar geometry. In the inner parsec, high resolution
spectral studies indicate such a bipolar outflow with a small inclination with respect to the
Galactic plane. Based on the ALMA mm/sub-mm spectral and continuum studies including
the hydrogen recombination lines H30α, H39α, H52α, and H56α, Yusef-Zadeh et al. (2020)
detected a red-/blue-shifted ionized gas outflow with the radial velocity of ±500 km s−1
, with
an indication of higher velocities reaching −2500 km s−1
and 4000 km s−1
on milliparsec
scales (see also Murchikova et al. 2019, for the detection of a broad, double-peaked H30α line
interpreted as a rotating disc structure). On the scale from tens of milliparsecs to parsec scales,
the outflow with an opening angle of ∼ 30 − 60◦
and the position angle close to the Galactic
plane coincides in projection with several linear and bow-shock sources detected in radio
(linear features j1 − j5 and comet-shaped sources F1, F2, and F3; Yusef-Zadeh et al. 2016;
Royster et al. 2019; Yusef-Zadeh et al. 2020) and infrared domains (bow-shock sources X7,
X8, and X3; Muži´c et al. 2010; Peißker et al. 2019, 2021a). In addition, it may also be related
to the enhanced emission along the minicavity as well as the enhanced X-ray emission of
the IRS13 region. We illustrate the mutual positions of the plausible bipolar ionized outflow,
comet-shaped/linear features, the Galactic plane, the Minispiral streamers, the minicavity, and
the stagnation radius in Fig. 1.16. Yusef-Zadeh et al. (2020) estimate the mass-outflow rate of
the putative nuclear outflow/jet to be ˙Mout ∼ 1.4 × 10−5
M⊙ yr−1
, which is consistent with the
inflow rate through the event horizon being a small fraction ≲ 2% of the inflow rate at the
Bondi radius since most of it is lost in the outflow.
There are several observational signatures that the plasma that accretes towards Sgr A* or
moves away from it, is magnetized. On larger scales, close to the Bondi radius, a magnetar
designated as PSR J1745–2900 was detected. Based on the Faraday-rotation measurements
of the magnetar radio emission, Eatough et al. (2013) put a lower limit on the line-of-sight
magnetic field component, B ≳ 8 mG, at the deprojected distance of r ≳ 0.12 pc. On
the smallest scales close to the innermost stable circular orbit, the constraints come from
the multi-wavelength emission of Sgr A*. In the optically thin part of the Sgr A* SED,
see the inverse Compton–bremsstrahlung components in Fig. 1.14, Sgr A* exhibits several
(3-5) ∼ hour-long flares in the infrared domain. About one flare per day is detected in
the X-ray domain, with the one-to-one correspondence between X-ray and infrared flares
(every X-ray flare has an infrared counterpart). Based on the emission properties of these
synchrotron (infrared/submm/mm flares) and synchrotron-self-Compton flares (X-ray flares),
it was possible to constrain the magnetic field close to the ISCO to ∼ 10 − 100 G (Eckart
et al. 2012; Witzel et al. 2021). A simple accretion model of the magnetized ADAF fed
by stellar winds can explain the ∼ 10 − 100 G field close to the ISCO due to the inflow of
magnetized hot plasma that drags magnetic field lines inwards from the scales of ∼ 0.1 pc
(Bondi radius). To obtain some estimates of the power-law scaling of the circumnuclear
magnetic field, we introduce the magnetization parameter of the plasma, βp = Pgas/Pmag,
which expresses the ratio of the plasma gas pressure to the magnetic pressure. Assuming
that the magnetization parameter of the ADAF does not change significantly with the radius,
we obtain the basic scaling relation [np(r)Tp(r)]/Bp(r)2
= const, where np(r), Tp(r), and
Bp(r) correspond to plasma number density, temperature, and magnetic field radial profiles.
Adopting the power-law scaling Tp ∝ r−θ
and np ∝ r−3/2+s
according to Wang et al. (2013),
1.1. MAPPING THE GALACTIC CENTER 33
stagnation radius
Northern Minispiral Arm
Eastern Arm
Sgr A*
Galactic plane
Minicavity
bipolar outflow - radio jet
ionized gas with a
double-peak spectral profile
Nuclear Star Cluster
X7
X3
comet-shaped bow shocks
3''~0.12 pc
j1
j2
j5
j3
j4
F1
F2F3
X8
WesternArc
Figure 1.16: A schematic of the fast bipolar ionized outflow close to the Galactic plane
coinciding with the position of several bow-shock/linear features. In particular, we show
the Minispiral arms, the minicavity, the bow-shock sources X3, X7, X8, F1, F2, and F3 as
well as radio linear filaments j1-j5. The position and the orientation of the bipolar ionized
outflow is indicated by blue/red-shaded regions representing the Doppler shift. The stagnation
radius of rst ∼ 4′′
(cusp-like profile) is depicted by a dash-dotted circle.
we obtain the radial magnetic field profile as follows,
Bp(rin) = Bp(r)
rin
rm
−3/4+1/2(s−θ)
∼ 28
rin
10 rg
−3/4
rm
0.1 pc
3/4
G , (1.17)
where the last relation is expressed for the best fit to the X-ray spectra, which leads to s ≈ 1
and θ ≈ 1, i.e. the temperature radial profile is close to the virialized profile. For the Bondi
flow, i.e. s = 0 and θ ≈ 1, we get Bp(r) ∝ r−5/4
, which yields Bp(rin) ∼ 6330 G for rin = 10 rg
(close to the ISCO). Therefore, the outflow rate that nearly balances the inflow rate is in
agreement with the magnetic field scaling across the hot flow around Sgr A*, while no-outflow
Bondi flow gives too large values inconsistent with the observations.
Although Sgr A* accretes at a very low level in comparison with AGN, especially quasars,
it is quite variable across all wavelengths, including radio, mm, submm, infrared, and X-ray
domains. Especially in the optically thin part of its SED, in the near-infrared and X-ray
domains, it exhibits several flares per day (see e.g. Witzel et al. 2021, and references therein).
By flares we mean an hour-long, order-of-magnitude flux excursions with the peak flux
34 CHAPTER 1. INTRODUCTION
being comparable in the near-infrared domain to relatively bright S stars. They have a multiwavelength
nature, with the simultaneous X-ray/NIR flares and time-lagged submm-mm-radio
flares, which can be addressed in the framework of an adiabatically expanding self-absorbed
plasmoid model (Eckart et al. 2006; Yusef-Zadeh et al. 2006; Eckart et al. 2008; Yusef-Zadeh
et al. 2008, 2009a; Eckart et al. 2012). Specifically, as the blob of relativistic electrons
expands and cools off on a certain timescale, the energy peak shifts towards lower frequencies
(van der Laan 1966). It is not clear what the physical cause of these flares. Previously, a toy
model was used to explain near-infrared/X-ray flares where a radiating, bright inhomogeneity
in the inner ADAF orbits close to the ISCO. As we view this orbiting “hot spot” at a specific
inclination (Broderick & Loeb 2006; Meyer et al. 2006; Zamaninasab et al. 2011), the rate at
which the flux is modulated during one orbit changes due to a different amount of contribution
of the Doppler boosting and strong gravitational lensing (see also Karas & Bao 1992; Stuchlík
& Bao 1992, for early studies). The observed timescale of the near-infrared flares is close to
one hour. If we associate this timescale with the “hot-spot” orbit, then the expected orbital
radius in gravitational radii is,
r
rg
=
c3
Pflare
2πGM•
− a•
2/3
≃ 9.47
Pflare
1 hour
2/3
M•
4 × 106 M⊙
−2/3
, (1.18)
where we assumed the zero spin (a• = 0) in the numerical estimate. Hence, since r ≈ 9 rg,
the “hot spot” is expected to orbit close to the ISCO. In terms of the angular diameter, it
corresponds to ∼ 94 µas. Such tiny scales were resolved thanks to near-infrared interferometry,
specifically the instrument GRAVITY utilizing the Very Large Telescope Interferometry at the
European Southern Observatory, that detected the clockwise orbital motion of the emission
centroid in the K-band (2.2 µm; GRAVITY Collaboration et al. 2018) during a near-infrared
flare. The orbital period of the loop-like “hot spot” motion coincided with the period of the
polarization rotation of the hot-spot infrared synchrotron emission (45 ± 15 minutes). This is
consistent with the poloidal magnetic-field geometry since the toroidal field would lead to two
polarization rotations per one orbit. Using photon ray-tracing of a hot-spot emission moving on
a geodesic trajectory, GRAVITY Collaboration et al. (2020b) constrained the source diameter
to ≲ 5 rg, its orbital radius to 9 rg, and the orbital inclination to ∼ 140◦
. Such a source size is
consistent with the constraints given by the Very Long Baseline Interferometry observations
at 1.3 mm (Doeleman et al. 2008), where the mm emission is not affected by interstellar
scattering. The detected intrinsic source diameter of 37+16
−10 µas, which corresponds to 7.5+3.2
−2.0 rg,
is smaller than the apparent size of the event horizon of the SMBH of M• ≃ 4 × 106
M⊙
(θEH ≃ 6
√
3GM•/(c2
dSgrA∗) →∼ 51.2 µas). This implies that the emitting source is not
centered on Sgr A* and could correspond to the hot spot or a ring-like structure with a
non-uniform surface brightness. With the involvement of more submm/mm telescopes, it
was possible to reconstruct the image of Sgr A*, including the spiral-like polarized emission
tracing the magnetic field structure (Event Horizon Telescope Collaboration et al. 2024).
The thick emission ring has the diameter of ∼ 51.8 ± 2.3 µas consistent with the shadow of
the SMBH, however, a substructure on smaller scales cannot be excluded. In fact, using
the polarized millimeter light curves of Sgr A* in 2017 obtained by ALMA, Wielgus et al.
(2022) can reconstruct the polarization-angle rotation during an X-ray flare using the model
of an orbiting hot spot embedded in a poloidal magnetic field and viewed at a small angle of
1.1. MAPPING THE GALACTIC CENTER 35
Milky Way
Minispiral
Sgr A*
Figure 1.17: Polarized emission of gas and dust flows on different scales. In the left panel,
we show the polarized millimeter emission of hot plasma along the Sgr A* ring (Event Horizon
Telescope Collaboration; Event Horizon Telescope Collaboration et al. 2024). The middle
panel depicts the far-infrared polarized emission of warm dust along the Minispiral arms on pcscales
(NASA/SOFIA/HST-NICMOS observations). The right top panel shows the polarized
millimeter emission of dust along the whole Galactic plane (ESA/Planck Collaboration).
Credit: S. Issaoun/EHT Collaboration.
∼ 20◦
. The orbital radius that can reproduce the observations is ∼ 10 rg and the Gaussian-like
hot-spot diameter is ∼ 6 rg, which is overall consistent with the NIR GRAVITY results. In
Fig. 1.17, we show the polarized millimeter emission of hot plasma along the Sgr A* ring
(inner ADAF), the far-infrared polarized emission of warm dust along the Minispiral arms
on pc-scales, and the polarized mm-emission of dust along the Galactic plane. This helps to
illustrate the coherency of the magnetic field structure and its overall dynamical relevance
from the largest Galactic scales to the smallest ones.
The physical mechanism behind Galactic center flares is still uncertain. Because of the
dynamically relevant magnetic field that is highly ordered on both larger and smaller scales
(Morris 2015; GRAVITY Collaboration et al. 2018) they may be associated with heating
and expansion associated with magnetic reconnection events in analogy to coronal mass
ejections on the Sun (Yuan et al. 2009). This is also hinted by the power-law distribution
of the flare flux-density distribution in both near-infrared and X-ray domains typical of selfcriticality
phenomena (Li et al. 2015). It also appears likely that the flow transitions from the
so-called Standard and Normal Evolution (SANE; Balbus & Hawley 1992) where the angular
momentum is transported outwards by the turbulence generated by the magneto-rotational
instability to the Magnetically Arrested state (Bisnovatyi-Kogan & Ruzmaikin 1974, 1976;
Narayan et al. 2003), in which the magnetic pressure due to the accumulated poloidal magnetic
flux dominates the flow dynamics. As magnetized plasma is accreted, poloidal magnetic flux
is dragged inwards and accumulates close to the SMBH. At a certain radius rMAD magnetic
36 CHAPTER 1. INTRODUCTION
energy becomes larger than the local gravitational potential energy of the flow,
GM•ρADAF
r
=
B2
8π
rMAD
rg
≃
(8πµmHnB)2/3
c2
B4/3
rB
GM•
1/3
∼ 56
nB
26 cm−3
2/3 B
0.5 G
−4/3
rB
0.14 pc
1/3
M•
4 × 106 M⊙
−1/3
, (1.19)
where we used the expression ρADAF ≃ µmHnB(r/rB)−0.5
for the mass density of the ADAF
(Wang et al. 2013) scaled to the Bondi values (Baganoff et al. 2003). Inside the magnetospheric
radius rMAD the flow fragments and the accretion proceeds via diffusion through the dominant
poloidal magnetic field accompanied by magnetic interchanges and reconnection events.
These result in localized heating and plasma expansion whose observational demonstration
could be detected flares and hot spots. The radial velocity in the MAD part is much smaller
than the free-fall velocity. We illustrate the structure of the hot flow on the scale of a
few hundred gravitational radii in Fig. 1.18, where we depict the MAD regime with the
reconnection events as well as orbiting hot spots close to the ISCO.
Since stellar winds supplied by OB/Wolf-Rayet stars are sufficient to feed the ADAF in
the Galactic center, the question where the material circularizes and forms a rotating structure
arises. We consider that the gas is captured initially close to the Bondi radius, i.e. from stellar
orbits close to r⋆ ∼ rB ∼ 0.1 pc. At these scales, the total gas velocity (orbital+intrinsic wind
velocity) cannot exceed the escape velocity from Sgr A*, that is vg ≲
√
2GM•/r⋆. When
the gas circularizes at the radius rcirc, it retains a fraction λ of the original orbital angular
momentum of gas at the distance r⋆. Finally, we have
rcircvcirc ≈ λr⋆vg ≲ λ 2GM•r⋆
rcirc ≲ 2λ2
r⋆ ≃ 0.002
λ
0.1
2
r⋆
0.1 pc
pc . (1.20)
Thus, assuming that the circularized gas can retain about 10% of the original angular momentum
(the rest is lost via outflows and shocks), the circularized flow is expected to form at the
length-scale of two orders of magnitude below the Bondi radius. This is comparable to the
radial extent of the putative disc of colder material detected by Murchikova et al. (2019) as
well as to the orbits of fast-moving S stars (the semi-major axis of the S2 star is ∼ 0.005 pc),
which can in principle interact with such a rotating structure.
1.2 Mapping distant quasars
Since the discovery and identification of active galactic nuclei and especially their highluminosity
members – quasars (AGN and QSOs, respectively; Schmidt 1963), it has been
obvious that the power generated is tremendous, being at least equal to the luminosity of
the whole galaxy or in case of quasars exceeding it by several orders of magnitude. The
model that was shortly adopted involved the conversion of gravitational potential energy of
gas accreting onto the supermassive black hole (SMBH) into heat and radiation that we detect.
As much as ∼ 10% of the gas rest-mass energy can be converted into radiation, which follows
1.2. MAPPING DISTANT QUASARS 37
Figure 1.18: Illustration of the hot flow close to the Galactic center. In particular, we show
how the flow is fed by stellar winds of young massive OB/Wolf-Rayet stars. Subsequently,
the flow circularizes at a smaller radius rcirc. Due to the accumulation of the poloidal magnetic
field, the ADAF transitions into the MAD state at rMAD where magnetic reconnection events
take place. In the innermost part of the ADAF, reconnection events in the differentially
rotating hot flow can also be responsible for the observed near-infrared/X-ray flares associated
with orbiting hot spots (see the figure inset in the lower right corner).
from the virial relation 2 < EK > + < EP >= 0. This relation together with the energy
conversation, < E >=< EK+ < EP >, implies that half of the change in potential energy can
be converted into radiative power,
Lacc =
1
2
GM•
˙M
rISCO
≈
1
12
˙Mc2
≡ ηrad
˙Mc2
(1.21)
where for the inner radius at which the energy is dissipated we used the innermost stable circular
orbit (ISCO) rISCO = 6GM•/c2
of a non-rotating (Schwarzschild) black hole. Depending
on the ISCO value, which in turn is related to the SMBH spin a•, the value of the radiative
efficiency ηrad in Eq. (1.21) can be greater (for a prograde spin) or smaller (for a retrograde
spin). Considering ηrad = 1/12 and the quasar bolometric luminosity of Lacc = 1047
erg s−1
,
which corresponds to about thousand times the luminosity generated by 100 billion Sun-like
38 CHAPTER 1. INTRODUCTION
stars (Milky Way-like galaxy), the mass-accretion rate onto the SMBH is,
˙M ≃ 21.1
ηrad
1/12
−1
Lacc
1047 erg s−1
M⊙ yr−1
. (1.22)
Assuming that the SMBH accretes at most at its Eddington limit, see Eqs. (1.1) and (1.2), that
is Lacc ≲ LEdd, this gives us a lower limit on the SMBH mass,
M• ≳
LaccσT
4πGmpc
≃ 8 × 108 Lacc
1047 erg s−1
M⊙ . (1.23)
The constraint given by Eq. (1.23) shows that Sgr A* with M• = 4×106
M⊙ cannot really reach
the parameters of a quasar, i.e. exceeding the luminosity of all the stars in the Galaxy by several
orders of magnitude. It could at most reach the luminosity level comparable to the total Galaxy
output when it accretes at the Eddington limit, LEdd(Sgr A*) ≃ 5 × 1044
erg s−1
∼ 1011
L⊙.
Such lower-luminosity AGN hosted by spiral galaxies are also referred to as Seyfert galaxies
(Seyfert 1943).
In the current Universe, nearly all massive galaxies host at least one SMBH. Most (∼ 90%)
of these galaxies are currently quiescent or their accretion rate is several orders of magnitude
below the Eddington limit, hence the flow is rather advection dominated. Yet, their number
density per comoving volume, when the expansion of the Universe is accounted for by
dividing (1 + z)3
, is comparable or nearly the same as the number density of quasars at higher
redshifts. These statistical arguments lead to the conclusion that most of the current massive
galaxies are “dead” quasars, which is also known as Soltan’s argument (Soltan 1982). This
revolutionary idea, which implies the co-evolution of galaxies and SMBHs, was originally put
forward by Lynden-Bell (1969) and when extended to lower luminosities of Seyfert galaxies,
it also concerns the Milky Way and its past evolution (Lynden-Bell & Rees 1971).
More specifically, the studies between redshifts z = 0 and z = 2 show that the comoving
number density of quasars brighter than MB = −25.9 at z = 2 was ∼ 1000-times larger than
today (z = 0). However, when the total number density of quasars is considered between z = 2
and z = 0, the value does not change significantly. In other words, the luminosity function
ϕ(M) per comoving volume and magnitude bin is just shifted horizontally (Richards et al.
2005) - quasars are becoming fainter, which can be addressed by their evolution. Between
z = 2 and z = 6, the comoving number density pattern becomes more complex – the number
density has a peak at z ≈ 2.5 and starts decreasing towards z = 3. The comoving number
density of quasars drops by a factor of ∼ 10 between the peak at z ≈ 2.5 (the Universe age
of t = 2.645 Gyr) and z = 4 (the Universe age of t = 1.558 Gyr). This early deficiency of
quasars hints at the growth phase of SMBHs between ∼ 1.5 and 2.5 Gyrs after the Big Bang,
although the current James Webb Space Telescope (JWST) data in combination with deep
Chandra X-ray observations seem to suggest that the SMBH formation and rapid growth
took place already very early, within the first 1000 Gyrs after the Big Bang, as is revealed by
the presence of “little red dots” (Matthee et al. 2024). These are small, photometrically red
galaxies (in the infrared domain) that exhibit very broad Balmer emission lines, which hints
at their association with AGN already in the period ∼ 0.5 − 1.5 Gyr after the Big Bang.
One example is the galaxy UHZ1 at z = 10.1 or just 470 million years after the Big
Bang, which has the mass of ∼ 4 × 107
M⊙ assuming the Eddington rate (Natarajan et al.
1.2. MAPPING DISTANT QUASARS 39
JWST detects
infrared light of
distant quasars
Figure 1.19: Comparison of two basic scenarios for the black-hole seed formation in the
early Universe. On the left side, a seed black hole forms after a population III star explodes
as a supernova type II. The black hole continues growing by accretion from the surrounding
material. On the right side, the black-hole seed forms as a result of a direct collapse of a
starless gaseous disc. Subsequently, this more massive seed can merge with the galaxy in
the vicinity and quickly grow by accretion from the gaseous and stellar material to reach the
SMBH mass. Such an early luminous quasar can be detected in the infrared domain by e.g.
the James Webb Space Telescope (see Natarajan et al. 2024, for the detection of an SMBH
dating back to half billion years after the Big Bang).
40 CHAPTER 1. INTRODUCTION
10−1
100
Cosmic time [Gyr]
10−2
10−1
100
101
redshift z
0.00
0.02
0.04
0.06
0.08
0.10
0.12
SFR[Myr−1
Mpc−3
]
reionization
peakofstarformation
peakofSMBHactivity
SDSS-FIRST sample MgII QSOs
peakofSMBHactivity
AGN cycles, drop of SF, mergers
Exponential decay
Figure 1.20: Cosmic star-formation rate per comoving volume as a function of redshift
(cosmic time). The plot shows cosmic star-formation rate per comoving volume as a function
of redshift. Black thick line corresponds to the best-fit relation inferred from UV and IR
data according to Madau & Dickinson (2014). Orange-shaded area shows the epoch of
the reionization of neutral hydrogen (6 < z < 30), while the gray-shaded area depicts the
redshift range of the SDSS-FIRST sample analyzed in Section 2, and the magenta-shaded
area represents quasi-stellar objects or quasars (QSOs) with a broad MgII line analyzed in
Section 7.
2024). Quite surprisingly, the stellar mass derived from the JWST infrared data suggests
that it is comparable to the SMBH mass. The formation of such galaxies is consistent with
the direct-collapse scenario of the black-hole seed formation, in which the left-over material
is consumed by the formation of a compact, dense star cluster surrounding the black hole,
potentially resembling the NSC. In comparison with the conventional model of black-hole
seed formation from the remnant of a population III star, the direct-collapse scenario can
significantly speed up the black-hole growth by the formation of a much heavier seed, see also
Fig. 1.19 for comparison. In this picture, the quasar peak density at z ≈ 2.5 could represent
the SMBH growth phase to M• ∼ 108
− 109
M⊙ when there was enough cold material for both
star formation and the SMBH accretion since the star-formation activity also reached the peak
at a comparable time period in the evolution of the Universe (Madau & Dickinson 2014), see
also Fig. 1.20 for the redshift/cosmic-time dependency, which suggests a tight co-evolution
between the growth of SMBHs and star formation during galaxy evolution.
This co-evolution is indicated by several significant correlations between the SMBH
mass and large-scale galaxy properties. These include the SMBH mass - total galactic bulge
(spheroidal component) luminosity (M• − Lbulge) relation, which was fitted for the K-band
luminosity that is less affected by extinction (Marconi & Hunt 2003),
log (M•/M⊙) = (8.21 ± 0.07) + (1.13 ± 0.12)[log (LK,bulge/LK,⊙) − 10.9] , (1.24)
hence the slope is close to unity. A significant correlation is also present for the SMBH mass –
1.2. MAPPING DISTANT QUASARS 41
bulge mass (M•–Mbulge) where3
Mbulge ∝ Reσ2
e,
log (M•/M⊙) = (8.28 ± 0.06) + (0.96 ± 0.07)[log (Mbulge/M⊙) − 10.9] , (1.25)
which also has the slope close to unity and the rms scatter decreases to ∼ 0.25 dex. For the
slope set to unity, we get the Magorrian relation between the SMBH mass and the galaxy
bulge mass, M•/Mbulge ∼ 2.4 × 10−3
, see Magorrian et al. (1998) for the original study with
the mean ratio < M•/Mbulge >∼ 5 × 10−3
. In 2000, two studies (Ferrarese & Merritt 2000;
Gebhardt et al. 2000) were published that claimed a tight correlation between the SMBH mass
and the stellar velocity dispersion in the galactic spheroidal component (M• − σ⋆ relation),
which is either the galactic bulge or the whole elliptical galaxy. The M• − σ⋆ relation
qualitatively states that the more massive the SMBH is, the larger the velocity dispersion
in the galactic spheroid is. This result is quite profound and directly points towards the
co-evolution between the SMBH and its galactic host since the stellar velocity dispersion is
inferred on the large scales of kiloparsecs, hence on the length-scales that are at least one order
of magnitude larger than the gravitational sphere of influence of the SMBH, see Eq. (1.4).
Ferrarese & Merritt (2000) inferred the relation M• ∝ σ4.8±0.5
⋆ based on the measurements in
12 galaxies. In contrast, Gebhardt et al. (2000) found a slightly smaller slope of 3.75 ± 0.30
based on 26 galaxies. For elliptical galaxies, the Faber-Jackson relation (Faber & Jackson
1976) had been established earlier between the luminosity of the elliptical galaxy4
(spheroid)
and the stellar velocity dispersion, Lspheroid ∝ σ4
⋆. In combination with the Magorrian relation
(Magorrian et al. 1998), M• ∝ Lspheroid, we arrive at M• ∝ σ4
⋆ for elliptical galaxies. When
one takes into account a slightly different scaling between the bulge/spheroid mass and its
luminosity, Mspheroid ∝ L5/4
spheroid (Faber et al. 1987), then in combination with the Faber-Jackson
relation Lspheroid ∝ σ4
⋆ and the Magorrian relation M• ∝ Mspheroid, one arrives at M• ∝ σ5
⋆.
Hence, it is possible to recover the power-law slope between ∼ 4 and ∼ 5. Therefore, the
M• − σ⋆ relation as such had not been surprising, especially when one follows the simple
hypothesis that a larger mass concentration within the bulge/spheroid is expected to host a
more massive SMBH. It is, however, crucial to stress that the rms scatter of the M• − σ⋆
relation is smaller than for the M• − Lbulge relation, which implies that Mspheroid and Lspheroid
are not entirely necessary in the description. In other words, the SMBH mass–stellar velocity
dispersion relation is more fundamental. The physical cause behind the tight M• − σ⋆ relation
or the SMBH-spheroidal component co-evolution is likely the AGN energy and momentum
feedback, via which the SMBH can impact the host galaxy on large scales. It can proceed in
two basic modes (Alexander & Hickox 2012):
(i) quasar radiative mode: accretion disc outflows/winds and radiation expel cold gas
reservoir, which leads to the shut-off of star formation and SMBH rapid feeding;
(ii) radio-mechanical kinetic mode: radio jet impacts the surrounding cooling flow, which
leads to shocks that reheat the gas.
Hence, the SMBH activity (accretion/jet) is directly linked to the amount of cold gas that feeds
both star formation, which affects the stellar velocity dispersion via stellar mass distribution,
3
Re is the bulge effective radius, which contains half of its luminosity, and σe is the velocity dispersion at
Re.
4
An analogous relation exists for disc galaxies, Ldisc ∝ (∆V)4
, where ∆V is the rotation curve amplitude
(Tully-Fisher relation; Tully & Fisher 1977).
42 CHAPTER 1. INTRODUCTION
and accretion onto the SMBH, which contributes to the SMBH mass. There are also alternative
explanations. One of them is related to the galaxy hierarchical assembly via mergers, i.e. the
bottom-up structure formation. In the process of galaxy mergers, in which the masses of black
holes and spheroidal components are initially unrelated, central black holes of different masses
migrate to central regions via dynamical friction. After several mergers, the final black-hole
mass tends to correlate with the galaxy bulge/spheroid mass and its velocity dispersion (see
Jahnke & Macciò 2011, for this statistical, non-causal argumentation).
The negative AGN feedback can effectively work just considering pure energetics of
the involved processes. As the AGN accretes mass, it produces radiation that is capable of
driving an outflow that interacts with the ambient cold gas in the bulge/spheroid component.
Via shocks and fast radiative cooling, most of the energy associated with this interaction is
preserved in the bulk motion that is driving out ambient colder gas. The energy released via
the accretion onto the SMBH can be calculated as Eacc ≃ ηradM•c2
, while the binding energy
of the bulge is Ebulge ≈ GM2
bulge/Rbulge. The ratio of the total energy that is radiated away to
the gravitational binding energy is,
Eacc
Ebulge
≈
ηradM•c2
GM2
bulge
Rbulge
= ηrad
M•
Mbulge
c
σ⋆
2
∼ 225
ηrad
0.1
M•/Mbulge
10−3
σ⋆
200 km s−1
−2
≫ 1 , (1.26)
which proves at least qualitatively that the AGN activity can result in the expulsion of a
significant portion of the cold gas concentrated within the bulge.
The AGN feedback can recover the M• − σ⋆ relation not only qualitatively but also quantitatively
when one considers the momentum-driven nuclear outflows that become coupled
to cold gas and drive it out. Considering that the outflow with the rate ˙Mout and velocity
vout interacts with the optically thick gas, the momentum rate is comparable to the photon
momentum rate, assuming that the AGN shines at the Eddington limit,
˙Moutvout ≈
LEdd
c
, (1.27)
which for ˙Mout ∼ ˙MEdd implies vout ∼ ηradc. There are indeed detected nuclear outflows
moving at speeds of the fraction of the light speed, such as ultrafast outflows (UFOs; Pounds
et al. 2003; Tombesi et al. 2010) revealed by absorption lines in the X-ray spectra. When we
consider the mass shell m(r) (including both gas and stars) at the radius r and the gas fraction
fg, the equation of motion of the gas component can be expressed as follows,
d[ fgm(r)˙r]
dt
+
G fgm(r)[M• + m(r)]
r2
=
LEdd
c
d(r˙r)
dt
+
GM•
r
= −2σ2
⋆ 1 −
M•
Mσ
, (1.28)
where in the second equality, we applied m(r) ≈ 2σ2
⋆r/G, assuming the singular isothermal
sphere model. Mσ stands for the critical (minimum) SMBH mass that is capable of driving
out the gas shell since for M• > Mσ, ˙r2
→ σ2
⋆ for large r. For M• < Mσ, there is no outbound
solution and the outflow can be referred to as failed. The critical mass Mσ can be numerically
1.2. MAPPING DISTANT QUASARS 43
(a) Secular processes (b) Galaxy mergers (c) Cooling flows
in galaxy groups/clusters
jet
hot halo
Figure 1.21: Overview of the growth processes of supermassive black holes. In the left
panel (a), the SMBH grows via secular processes (galactic bar, galaxy interaction); in the
middle panel (b), the SMBH growth via galaxy mergers is depicted; in the right panel (c),
cooling flows in the hot halo gas of galaxy groups and clusters lead to the AGN trigger, whose
activity subsequently prevents the hot halo gas from further cooling.
evaluated as,
Mσ =
fgσT
πG2mp
σ4
⋆
≃ 2.3 × 108
fg
0.2
σ⋆
200 km s−1
4
M⊙ , (1.29)
where the gas fraction fg is scaled to the value close to the baryonic fraction of the Universe,
fg ∼ 0.16, which is the ratio of the baryonic matter to the total matter content. The derived
value for Mσ in Eq. (1.29) is very close to the current versions of the M• − σ⋆ relation, see for
instance Gültekin et al. (2009), who inferred M• ≃ 1.32 × 108
(σ⋆/200 km s−1
)4.24
M⊙. This
adds credibility to the model of AGN negative feedback as the driving physical cause behind
this tight correlation.
The SMBHs grow mostly via (a) the accretion of gas and dust channelled due to internal
and external secular processes, (b) via merger processes with other SMBHs as well as smaller
black holes and other compact objects, the third option is (c) the accretion of cooling flows in
galaxy groups and clusters (Alexander & Hickox 2012). The processes (a), (b), (c) trigger
an AGN activity, whose phases are relatively short (∼ 105
years) but they recur several times
during a more extended period of the SMBH growth whose duration is estimated to be between
44 CHAPTER 1. INTRODUCTION
∼ 107
and ∼ 109
years based on the Soltan argument (Schawinski et al. 2015). We illustrate
the SMBH growth processes in Fig 1.21. There are multiple signatures of the mergers of
two and more galaxies in the nearby Universe as well as in the earlier epochs of the galaxy
evolution. Moreover, several studies point towards the correlation between the merger process
and the AGN activity (Hernquist & Mihos 1995; Chiaberge et al. 2015). However, there are
more recent studies of cosmological simulations that show that the SMBH growth during
the whole galaxy evolution is mostly driven by secular (merger-free) processes (Martin et al.
2018; McAlpine et al. 2020; Smethurst et al. 2024), which include the angular momentum
redistribution by a galactic bar (internal secular processes) or a gravitational interaction within
the galactic group (external secular processes). In other words, mergers, are not the primary
cause behind the co-evolution of SMBHs and their host galaxies, though they can increase the
accretion rate in the galaxies undergoing a merger event (McAlpine et al. 2020) by a factor
of a few. Furthermore, Garland et al. (2024) showed that strongly barred disc-dominated
galaxies have a significantly larger fraction of AGN than weakly barred ones. The same
holds for the weakly barred versus unbarred galaxies. Hence, the galactic bar appears to play
a crucial role for the channelling of the cold gas towards the central regions of the galaxy.
Within the bar potential the orbital families x1 and x2 can provide a way to transport the gas
from the galactic disc to central regions of the galaxy, see Figs. 1.6 and 1.7 for the illustration
and the depiction of different structures. This can also address the formation of the 100-pc
molecular ring in our Galaxy and the associated structures of the Nuclear Stellar Disc and the
Nuclear Star Cluster, see Subsection 1.1 for the discussion. Eventually, an occasional infall of
a dense molecular cloud can trigger an enhanced activity of Sgr A*, potentially reaching the
level of a Seyfert galaxy every few million years, see also Subsection 1.3 for details.
Since the accreting gas has a certain angular momentum, it will circularize at the circularization
radius rcirc, see also Eq. (1.20), and form a rotating disc-like structure, generally
referred to as an accretion disc. Depending on the relative accretion rate, different types of accretion
flows can form. In the following subsection, we introduce the concept of reverberation
mapping of the circumnuclear environment, which has proven to be instrumental not only in
understanding kinematical and geometrical properties of the accreting gas and dust but also in
weighting SMBH masses and thus studying their growth processes during the cosmic history.
1.2.1 Reverberation mapping of accretion discs
Based on the spectral studies of AGN/quasars in the optical/UV domains, the presence of
prominent broad and narrow emission lines is one of the main characteristics of all active
galaxies. However, certain patterns and differences among AGN started to be discovered.
Those AGN that had both broad and narrow emission lines also exhibited a power-law
continuum component as well as the soft and sometimes hard X-ray emission. In comparison,
there were purely narrow-line AGN with the highly absorbed X-ray emission and a prominent
infrared bump in their SEDs. The sources with both broad and narrow components on the
top of the power-law continuum have been referred to as type I AGN, while the other ones
with just narrow components have been denoted as type II. There have also been intermediate
cases identified as well as AGN that change the type on relatively short timescales. The
current consensus is that the main factor affecting the AGN type is the viewing angle towards
the source: for type I sources we look close to the rotation axis, hence we can detect the
accretion-disc emission and the associated broad lines, while for type II, the geometrically
and optically thick dusty molecular torus obscures the view towards the center. This is a
1.2. MAPPING DISTANT QUASARS 45
so-called unified model of AGN (Antonucci 1993; Urry & Padovani 1995) that can also be
extended towards the radio domain where some of the differences can also be addressed by
the viewing angle with respect to the jet cone.
The accretion-disc models and their properties can be categorized based on the terms in
the energy equation (Frank et al. 2002; Kato et al. 2008), qadv = q+ + q−, where q+ is the
viscous heating rate per volume and q− is the radiative cooling rate per volume. The term
qadv expresses the net energy advection per volume and can be expressed as (in cylindrical
coordinates),
qadv = ρvRT
ds
dR
, (1.30)
where s is the specific entropy. Based on which terms dominate in the energy balance, the
accretion flow solutions are distinguished as follows:
• cooling-dominated flows: qadv ≪ q+ ≃ q−, viscous heating is balanced by radiative
cooling; standard Shakura-Sunyaev, Novikov-Thorne discs, and Shapiro, Lightman,
and Eardley solutions;
• advective flows: q− < q+ ≃ qadv, viscous heating is balanced by the advection of energy
through the event horizon; these solutions include the Advection-Dominated Accretion
Flows (ADAFs) for lower accretion rates and slim discs for high accretion rates close
to the Eddington rate and above;
• low-angular momentum flows: q+ ≪ q− ≃ −qadv; low angular-momentum settling
solutions and optically thin Bondi flows.
Specifically for AGN, we will focus on cooling-dominated and advective accretion discs.
The observational spectral properties of the accretion discs in AGN depend on their relative
accretion rates or Eddington ratios ˙m = ˙M/ ˙MEdd and the accretion solutions can be categorized
as (Kato et al. 2008),
(a) Advection-Dominated Accretion Flows (ADAFs) or sometimes referred to as radiatively
inefficient accretion flows that are optically thin and geometrically thick. They occur
for Eddington ratios of ˙m ≲ 0.01. They correspond to low/hard states of X-ray binaries
and SMBHs (Yuan & Narayan 2014).
(b) Standard accretion discs or sometimes referred to as Shakura-Sunyaev or NovikovThorne
solutions. They correspond to the relative accretion rates of 0.01 ≲ ˙m ≲ 0.1.
They are optically thick and geometrically thin. They correspond to high/soft states of
X-ray binaries and SMBHs (Shakura & Sunyaev 1973; Novikov & Thorne 1973).
(c) Slim discs correspond to the accretion rates very close to the Eddington rate or above it.
They are geometrically thicker than standard discs and they are optically thick. Because
of large densities, photons generated close to the mid-plane are trapped within the disc
and they are advected through the horizon without being radiated away. For this reason
slim discs are fainter than expected from their large accretion rates and therefore rather
radiatively inefficient (Abramowicz et al. 1988; Wang & Zhou 1999).
It is instructive to depict steady-state solutions of accretion discs on the local ( ˙m, Σ) plane,
i.e. for a fixed radius, see Fig. 1.22 for a schematic plot. In particular, we highlight the three
fundamental viscously and thermally stable solutions with a positive slope, d ˙m/dΣ > 0: an
46 CHAPTER 1. INTRODUCTION
advection
radiative cooling
log(Σ [gcm-2
])
log(Eddingtonratio)
α>1 α=
αcrit
α=α
crit
α>
αcrit
α<
αcrit
α>
α
crit
α=α
crit
advection
radiative
cooling
opticallythin
opticallythick
gas pressure
radiation pressure
α<
αcrit
ADAF
slim
disc
standardthindisc
Figure 1.22: Steady-state accretion solutions on a local ( ˙m, Σ) plot. For every radius, there
is a critical value of the α parameter (αcrit) that divides the plane into four types of solutions.
Above the thick dashed line, there are solutions with α > 1 that are considered nonphysical.
The dotted line divides the solutions dominated by advection and those dominated by radiative
cooling. The dashed line divides optically thin and thick solutions. Solutions dominated
by radiation pressure and gas pressure are divided by the dot-dashed line. In particular, we
highlight with a thick blue colour three stable steady-state solutions– ADAF (advectiondominated,
optically thin), a slim disc (advection-dominated, optically thick), and a standard
thin disc (radiative cooling, gas-pressure-dominated) - that are characterized by the positive
slope, i.e. d ˙m/dΣ > 0. The geometrical setup of these three solutions is depicted by the
illustrations to the left and the right of the vertical axes.
ADAF, a slim disc, and a standard thin disc. The solutions with a negative slope, for instance
a standard thin disc dominated by radiation pressure, are viscously and thermally unstable.
In an analogous manner as for X-ray binaries (Remillard & McClintock 2006), SMBHs
in galactic nuclei are expected to transition from low/hard state that is dominated by an
ADAF to high/soft state dominated by a standard accretion disc (Done & Gierli´nski 2005).
These spectral transitions, however, take place on longer timescales than for X-ray binaries in
proportion to the SMBH mass. There is an evidence for spectral state transitions in galactic
nuclei inferred from the study of a larger sample of galaxies (Svoboda et al. 2017). The main
parameter that determines spectral hardness/softness is the position of the truncation radius,
where the standard, radiation cooling-dominated disc transitions into advection-dominated
accretion flow (Yuan & Narayan 2014). The truncation radius is directly related to the relative
accretion rate (Eddington ratio) of the source, being larger for a lower relative accretion rate,
1.2. MAPPING DISTANT QUASARS 47
Advection - Dominated Accretion Flow (ADAF)
ADAF
relativeaccretionrate
high/so state
low/hard state
quiescent state
m ~ 0.1-1.0
m ~ 0.01
m < 0.01
.
.
.
standard disc
(radiation - cooling dominated, so thermal emission)
corona
(harder power-law emission)
jet
(radio emission)
Figure 1.23: Spectral states and the associated transitions between them in supermassive
black hole systems. On the right side of the illustrative figure, we show different spectral
states dominated by a standard accretion disc (top), an ADAF (bottom) or an intermediate
“mixed” stated (middle). On the left side, we depict the dependence of these states on the
relative accretion rate. With the change in the accretion rate, the transition of the spectral state
is induced.
which in the limit of quiescent nuclei, such as the Galactic center, leads to the disappearance
of the standard disc with a thermal SED and the complete spectral dominance of an ADAF.
Therefore, one of the best laboratories to detect state transitions in SMBH systems are tidal
disruption events (TDEs; Wevers 2020), in which the relative accretion rate evolves within
weeks to months from super-Eddington/Eddington values to sub-Eddington ones (see Gezari
2021, for a review as well as Subsection 1.2.3.) since the fall-back rate of the stellar debris
follows the power-law temporal evolution, ˙Mfb ∝ t−5/3
. There have also been detections of
spectral transitions within the luminosity-hardness plot for repeating partial TDEs AT 2018fyk
(Wevers et al. 2021) and eRASSt J045650.3-203750 (Liu et al. 2023). In all of the systems
where a state transition has been detected there is a common pattern – during the high/soft
state, the SED is dominated by soft thermal emission of an optically thick accretion disc,
while in the low/hard state a power-law component emerges due to hot corona. The transition
between the two states typically takes place around the Eddington ratio of a few 10−2
(Wevers
2020). We illustrate the spectral states and the transitions between them as a function of the
relative accretion rate in Fig. 1.23.
On a quantitative level, the truncation radius rtr depends on the mechanism that governs
the transition. Considering a so-called strong ADAF principle, i.e. whenever the ADAF
48 CHAPTER 1. INTRODUCTION
solution is possible, the flow proceeds as an ADAF, the truncation radius can be estimated as
(Abramowicz et al. 1995; Honma 1996; Kato & Nakamura 1998),
rADAF
tr ≃ 1600α4
0.1 ˙m−2
0.05 rg , (1.31)
where α is the viscosity parameter scaled to 0.1 and ˙m is the relative accretion rate (Eddington
ratio) scaled to 0.05. If, on the other hand, the transition occurs due to evaporation induced
by electron conduction between the standard disc and the hot two-temperature corona, the
truncation of the standard disc is expected at (Czerny et al. 2004),
revap
tr ≃ 191α0.8
0.1β−1.08
mag ˙m−0.53
0.05 rg , (1.32)
where βmag is the magnetization parameter and in this case it is defined as the ratio of the gas
pressure to the sum of the gas and the magnetic pressure (total pressure). When the magnetic
field is negligible, βmag ∼ 1, while for a stronger magnetic field, βmag becomes smaller and
the truncation radius increases. It is thus plausible that for the intermediate relative accretion
rates (0.01 ≲ ˙m < 1) the accretion flow has a “mixed” structure where the standard disc has
an inner hollow due to the transition into the ADAF (Štolc et al. 2023). This results in the
decrement of the thermal emission at shorter wavelengths, which has also been detected in
the UV spectra of some type I galactic nuclei (Dewangan et al. 2021; Kumar et al. 2023).
In the following, for studying the emission properties and variability of a nuclear region,
we will focus on standard thin disc solutions, which extend across the whole radial extent of
the accretion flow from the ISCO to the outer radius. Standard accretion discs can reproduce
well the power-law continuum of a large portion of type I quasars. It also seems that the
accretion disc can explain the general feature in SEDs of type I AGN in the optical/UV domain
called the Big Blue Bump (Czerny & Elvis 1987), especially for more realistic solutions
including opacity and inclination effects. The SED of a thin accretion disc represents, to the
first approximation, the sum of narrow rings whose black-body temperature falls off with the
distance as Tdisc ∝ r−3/4
, specifically (Frank et al. 2002),
Tdisc =
3GM•
˙M
8πr3σSB
1 −
risco
r
1/2 1/4
, (1.33)
where σSB is the Stefan-Boltzmann constant from the black-body radiation law. The AGN
accretion disc SED then can be constructed by summing the rings of infinitesimal width, each
having a corresponding black-body temperature Tdisc(r) and each viewed at the angle ι (Frank
et al. 2002),
νLν =
16π2
hν4
cos ι
c2
rout
risco
rdr
exp[hν/(kBTdisc(r))] −1
. (1.34)
where we neglected any disc atmosphere in the vertical direction. The monochromatic
luminosity νLnu was calculated by multiplying the monochromatic flux density νFν by 4πD2
L
where the luminosity distance DL can be calculated for the redshift z given the cosmological
model corresponding best to the observations of standard cosmological probes, such as the
cosmic microwave background radiation and its fluctuation spectrum (flat ΛCDM model
with Ωm0 ≃ 0.3; Planck Collaboration et al. 2020). The integration limits in Eq. (1.34) are
the innermost stable circular orbit rISCO and the outer radius of a disc rout. The outer radius
for quasars is expected to be of the order of ∼ 2000 rg, which corresponds to ∼ 12 days of
light-travel time in terms of maximum observed light echos (Lobban & King 2022) and also
1.2. MAPPING DISTANT QUASARS 49
4202468
log( [nm])
8 10 12 14 16 18 20 22
log( [Hz])
28
30
32
34
36
38
40
42
44
log(L[ergs1])
radio/mm FIR/MIR/NIR V UV X-ray -ray
ADAF (m=2×10 7, M =4×106 M )
standard disc (m=1, M =4×106 M )
Figure 1.24: Comparison of spectral energy distributions between the standard disc and
the advection-dominated accretion flow. The ADAF SED was calculated for the relative
accretion rate of ˙m = 2 × 10−7
and the SMBH mass of M• = 4 × 106
M⊙, which represent the
parameters of Sgr A*. The standard disc SED was evaluated for the same SMBH mass and
˙m = 1, i.e. the Eddington limit. We see that the shape of the SED as well as the frequency of
the peak luminosity are quite different. While for the standard disc, the peak luminosity is at
ν = 1015.93
Hz (λ = 35.2 nm), which corresponds to the far UV domain, the luminosity of the
ADAF peaks at ν = 1011.73
Hz (λ = 0.56 mm). Hence, the difference between the frequency
peaks is more than four orders of magnitude.
to the self-gravitating radius (Collin-Souffrin & Dumont 1990), where the disc is expected
to break up. The outer radius is expressed for M• = 108
M⊙, while for M• = 4 × 106
M⊙ we
obtain rout ∼ 5 × 104
rg. We compare the standard disc SED for Sgr A* with the ADAF SED
in Fig. 1.24. There is a clear difference in the SED shapes as well as the positions of the
SED peaks. While for the ADAF the SED peaks in the mm domain, at λ = 0.56 mm for the
case shown in Fig. 1.24, the luminosity peak for the standard disc is shifted to much shorter
wavelengths in the far-UV domain, λ = 35.2 nm. Hence, the difference is more than four
orders of magnitude in frequency.
The variability of type I quasars in different wavebands reflects the variability of the
accretion disc at different radii since Tdisc ∝ r−3/4
, see Eq. (1.33). In this regard, the variability
in the X-ray domain reflects the accretion processes close to the ISCO. A fraction of the
dissipated energy can power the hard X-ray emission of hot corona that is expected to illuminate
the disc at larger radii. As the material in the disc absorbs and reprocesses the harder
50 CHAPTER 1. INTRODUCTION
emission in more distant regions, we can in principle detect the delayed and blurred signal
at longer wavelengths. The time delay between shorter and longer wavelengths corresponds
approximately to the light-travel time, i.e. τ ≈ ∆r/c. Thus, by quasi-simultaneous monitoring
of an AGN at different wavelengths, we can effectively map the accretion disc and the associated
circumnuclear material by cross-correlating the light curves at given wavelengths, which
indicates the statistically best candidate time delay τ and thus the distance ∆r ≃ τc between
the regions in the accretion disc that emit at corresponding wavelengths. This technique is
known as reverberation mapping and it effectively trades the spatial resolution for temporal
resolution (see e.g. Cackett et al. 2021; Karas et al. 2021, for reviews). Mathematically, the reprocessed,
delayed variable electromagnetic signal ∆Fr(t) can be expressed as the convolution
of the driving variable radiation ∆Fd(t − τ) with the transfer function ψ(τ), which expresses
the geometry and the kinematics of the reprocessing medium,
∆Fr(t) =
τmax
0
ψ(τ)∆Fd(t − τ)dτ , (1.35)
where τmax is the time delay corresponding to the light-travel time τmax = ∆r/c between the
regions where the driving radiation originates and where it is reprocessed towards longer
wavelengths. In Fig. 1.25, we illustrate how the X-ray emission of the hot corona (assuming
the lamp-post geometry; Miniutti & Fabian 2004) is reprocessed further out in the disc and the
circumnuclear medium, including the geometrically thicker broad-line region (BLR) clouds
and the dusty molecular torus emitting in the infrared domain. Typically, to map out the
whole region, one needs to employ space-based X-ray satellites (hard X-ray detectors for
the corona and soft X-ray detectors for the innermost region of the accretion disc), UV and
optical telescopes, performing both photometric and spectroscopic measurements (to detect
reliably broad emission lines), and infrared telescopes to detect the emission of the more
distant dusty torus. To combine it with the variability studies of the jet in radio AGN, radio
telescopes join the multi-wavelength campaigns.
Reverberation mapping a crucial method in revealing the geometry, kinematics, and the
character of the accretion flow since there are just a few galactic nuclei whose inner engine
can be spatially resolved – see also Subsection 1.2.2 for more details. In particular, by
monitoring an AGN in several bands, including X-ray, UV, and optical bands, interband lags
can be determined. Let us denote the rest-frame time delay between the longer and shorter
wavelengths as ∆τ12. This time delay can be compared with the delay expected for an adopted
steady-state accretion-disc solution with the radial temperature dependence Tdisc ∝ r−b
. The
corresponding theoretical time delay for a specific band then is τ(λ) ∝ λ1/b
. For the standard
thin disc, the slope is b = 3/4 and the explicit form of the interband time lag between two
bands centered at the wavelengths λ1 and λ2, λ2 > λ1, is
∆τ12 = τ2(λ2) − τ1(λ1) ≃
3GM•
˙M
8πc3b4σSB
1/3
(λ4/3
2 − λ4/3
1 ) > 0 , (1.36)
where b = 0.29 cm K is the constant in the Wien’s displacement law that relates the (disc)
temperature to the wavelength where the black-body SED at a given radius peaks, λ =
b/Tdisc(r).
As it can be inferred from Eq. (1.36), ∆τ12 also depends on the SMBH mass and the
accretion rate as ∆τ12 ∝ (M•
˙M)1/3
, which leads to the differences among different AGN
and puts different requirements on the duration of the monitoring as well as on the cadence.
1.2. MAPPING DISTANT QUASARS 51
accretion disc
broad-line region
dusty torus
>105
rg
103
-105
rg
102
-104
rg
100
-101
rg
corona
X-ray RM
UV/optical RM
optical BLR RM
dust infrared RM
SMBH
hot flow
disc outflow
jet
different telescopes
Figure 1.25: Principle of the reverberation mapping of an AGN accretion disc and
the surrounding circumnuclear medium. The innermost region emits hard and soft Xray
emission that is further reprocessed in the regions more distant from the SMBH and is
detected at longer wavelengths from the UV, optical, to infrared domains. Below the accretion
disc/dusty torus, we indicate the typical length-scales (in gravitational radii) associated with
the X-ray, UV/optical, and infrared radiation.
In Fig. 1.26, we show the time delay ∆τ in days with respect to the U band (364 nm) as a
function of wavelength in nanometers for the cases with different SMBH masses and the
fixed relative accretion rate of ˙m = 0.1. The dashed lines correspond to the standard disc
prediction according to Eq. (1.36), while the more observationally motivated profiles 3 × ∆τ
(Fausnaugh et al. 2016) are represented with solid lines. In the left panel of Fig. 1.26, we
show the time delay for M• = 106
− 107
M⊙, while in the right panel, we depict the same for
M• = 108
− 109
M⊙.
While most of the multi-wavelength observational campaigns imply the qualitative consistency
of the wavelength-dependent time-delay with the theoretical predictions of the standard
disc ∆τ ∝ λ4/3
, see e.g. the results of the intense monitoring of the Seyfert 1 galaxy NGC 5548
(Edelson et al. 2015; Fausnaugh et al. 2016), a few discrepancies and systematic differences
have also appeared based on the studies of several AGN (see e.g. Cackett et al. 2021, for
discussion),
• the observed interband time lags tend to be ∼ 3 − 4 times larger than the lags expected
from the standard-disc model. In other words, the accretion discs appear to be larger
than predicted, see also Fig. 1.26 for comparison. This systematic effect could be
caused by an additional contribution of an extended medium, such as the BLR,
52 CHAPTER 1. INTRODUCTION
100 200 300 400 500 600 700
λ [nm]
−1.0
−0.5
0.0
0.5
1.0
1.5
∆τ[days]
U
V
M• = 106
M , ˙m = 0.1
M• = 107
M , ˙m = 0.1
100 200 300 400 500 600 700
λ [nm]
−20
−10
0
10
20
30
∆τ[days]
U
V
M• = 108
M , ˙m = 0.1
M• = 109
M , ˙m = 0.1
Figure 1.26: Expected time delay ∆τ (in days) with respect to the Johnson U band (364
nm) as a function of wavelength (in nanometers). In the left panel, we show the cases for
M• = 106
− 107
M⊙, considering the standard disc solution (dashed lines) and the time delay
that is three times longer (solid lines). The right panel is analogous to the left panel, except
that we consider M• = 108
− 109
M⊙. For all the cases, we adopt ˙m = 0.1. The dotted vertical
lines denote U (364 nm) and V (540 nm) bands.
• the U-band time delays are systematically above the best-fit relations ∆τ(λ), which can
be attributed to the contribution of the Balmer continuum originating in the BLR,
• the X-ray emission is less correlated with the UV/optical light curves (the correlation
coefficient is r < 0.5) in comparison with the correlation of UV and optical light curves
among themselves (r > 0.5). This implies that the X-ray emission originating close
to the ISCO in the hot corona may not be the main or rather the only driver of the
reprocessed emission at longer wavelengths.
The first two points related to the time delay or the accretion-disc size excess, which is also
confirmed by gravitational microlensing, can be explained by an additional reprocessing of
the photoionizing radiation within the diffuse gas of an extended nature, such as the BLR
(Cackett et al. 2018; Chelouche et al. 2019; Netzer 2022), which is supported by a large
time-delay excess around the Balmer jump (364.6 nm). Furthermore, the pure scattering of
photons by the ionized plasma within the BLR can also result in the prolonged time delays
(Jaiswal et al. 2023).
The contribution of the BLR to the reprocessed photons detected by the observer at a
given wavelength depends on its scale-height and the distance from the SMBH, i.e. on the
covering factor. Netzer (2022) constrain the covering factor to be ∼ 0.2, which means that
the broad-line region is consistent with being a flattened system of ionized cloudlets that
orbit the SMBH predominantly in a Keplerian manner. They are photoionized by the central
X-ray/far-UV source and kept at nearly the constant temperature of ∼ 10 000 − 20 000 K.
In combination with large velocities of BLR clouds, this gives rise to prominent broad
recombination emission lines of hydrogen (Hα, Hβ), a resonant line of magnesium (MgII), as
well as to higher-ionization broad lines of CIV and CIII].
The BLR can also be mapped using the reverberation mapping technique since the
emission-line variability correlates significantly with the AGN continuum light curves (Blandford
& McKee 1982). This allows the determination of the time lag τBLR between the BLR
line light curves and the photoionizing continuum. Already these observational properties
can be used to infer several BLR characteristics. A significant correlation implies that the
driving photoionizing power is given by the continuum emission and the clouds must be
1.2. MAPPING DISTANT QUASARS 53
optically thick to the central source of irradiation. The covering factor can be estimated based
on the equivalent widths of broad emission lines to be ∼ 20 − 30%. The scale-height of
the BLR is expected to be larger than the accretion-disc scale-height to effectively intercept
the continuum, though the structure should be flattened along the disc plane since the BLR
clouds are only rarely detected in absorption (Czerny 2019). The reverberation mapping of
the BLR using its broad emission-line variability can be applied to infer the following crucial
properties of AGN:
• the size estimate of the BLR by simply using the light-travel time τBLR, RBLR = cτBLR
(Netzer & Peterson 1997; Kaspi et al. 2000; Peterson et al. 2004; Mejía-Restrepo
et al. 2018). More precisely, depending on which line is monitored, the distance RBLR
corresponds to the mean radius of the given line-emitting material;
• by knowing the radius RBLR = cτBLR, one can also constrain the SMBH mass (Dibai
1977) by using the line width of the monitored broad line, ∆vFWHM (full width at half
maximum), which serves as a proxy for the Keplerian speed of the BLR material around
the SMBH. Since we view the system at a certain inclination and there are also effects
of the BLR geometry (scale-height), the full BLR velocity is related to the observed
FWHM velocity via a so-called virial factor fvir, vBLR = fvir∆vFWHM. Under the
assumption that the BLR clouds moving in the vicinity of the SMBH are virialized, the
virial SMBH mass can be inferred using,
Mvir =
RBLRv2
BLR
G
≃ fvir
cτBLR(∆vFWHM)2
G
. (1.37)
The virial factor fvir is of the order of unity and is related to the geometry, kinematics,
and line-of-sight properties of the BLR gas. Its value is mainly related to the inclination
ιBLR of the BLR plane with respect to the observer and the half-opening angle of the
BLR (HBLR/RBLR) with respect to the source of the photoionizing continuum. The value
of fvir is inversely proportional to the square sum of these terms (Collin et al. 2006;
Mejía-Restrepo et al. 2018; Panda et al. 2019),
fvir =
1
4[sin2
ιBLR + (HBLR/RBLR)2]
. (1.38)
In general, the virial factor fvir is a large source of uncertainty in the SMBH mass
determination and fixing its value to a specific value for single-epoch spectroscopic
measurements can result in the uncertainty by a factor of ∼ 2 − 3 (Woo et al. 2015).
By comparing the SMBH masses inferred from the accretion-disc continuum fitting of
AGN SEDs with those determined from the BLR reverberation mapping, see Eq. (1.37),
Mejía-Restrepo et al. (2018) found out that the virial factor is inversely proportional
to the line FWHM, fvir ∝ FWHM−1
. This can reflect the effect of the BLR inclination/viewing
angle according to Eq. (1.38) or it hints at the impact of radiation pressure
on the distribution of BLR clouds. A strong viewing-angle effect is expected for the
flattened geometry of the BLR, which is consistent with a “bird’s nest” BLR model
(Gaskell 2009), where higher-ionization lines originate closer to the SMBH and they
thus have larger FWHMs, while lower-ionization lines originate further away and as
a result, their FWHMs are smaller. Such a flattened geometry is likely related to disc
outflows, which can be launched due to radiation pressure (line-driven or dust-driven)
54 CHAPTER 1. INTRODUCTION
or they can also be magnetically driven (see Karas et al. 2021, for a detailed discussion).
In particular, the dust-driven outflow has been able to capture several basic BLR
characteristics simultaneously, including flattened geometry and kinematics dominated
by a Keplerian motion with a certain turbulent (outflow-inflow) component. The dusty
outflow is launched at the distance within the accretion disc where the dust can form
and survive, i.e. where the temperature of the disc drops below ∼ 1500 K (sublimation
radius). Dust grains increase opacity and radiation pressure acting on them can lift
the gaseous-dusty material above the disc plane. At the same time, as the cloudlets
rise, they are exposed to the direct, harder UV irradiation of the central source, which
leads to dust evaporation and a drop in radiation pressure support. The clouds then
fall back onto the disc surface. In this model, the dust-driven outflow is failed, only
a small fraction of the clouds can escape (Failed RAdiatively-driven Dusty Outflow –
FRADO; Czerny & Hryniewicz 2011; Czerny et al. 2017; Naddaf et al. 2021; Naddaf
& Czerny 2022). The FRADO model can address the origin of low-ionization BLR
lines (LIL) that have a lower ionization potential (<20 eV; Hα, Hβ, MgII, FeII, CII),
originate in the denser gas of the accretion disc, show no significant inflow-outflow
motion, and can thus be considered to be virialized. There is also a high ionization
line component (HIL), which has a higher ionization potential (>40 eV; Lyα, HeII,
CIV, NV), exhibits signs of an outflow, specifically via the presence of asymmetric line
shapes with a blue-ward tail and blue-shifted line centroids, and thus forms in the more
diluted outflowing gas. However, the HIL component is still located relatively close
to the SMBH since time delays can still be reliably measured (see Kaspi et al. 2021,
for CIV line time delays). The LIL and HIL components of the BLR are illustrated in
Fig. 1.27, which depicts the two-component BLR model proposed by Collin-Souffrin
et al. (1988);
• the radius-luminosity relation, RBLR − L, which has a power-law form, RBLR = KLα
. Initially,
for variable low-redshift sources, RBLR −L relation was confirmed and constrained
for the broad Hβ line (at 4861 Å) and the optical monochromatic luminosity at 5100 Å
with the power-law slope α = 0.67 ± 0.05 (Kaspi et al. 2005), which deviated from
α = 0.5 predicted by simple photoionization arguments. With the progressive addition
of more low-redshift sources (Bentz et al. 2006, 2009, 2013), and more importantly,
after accounting for the host-galaxy starlight, RHβ − L5100 was further refined and the
slope was constrained to be shallower and overall consistent with the expected value
close to 0.5. The best-fit RBLR − L relation for the Hβ line for 41 sources is Bentz et al.
(2013),
log
τHβ
1 day
= 1.527+0.031
−0.031 + 0.533+0.035
−0.035 log
L5100
1044 erg s−1
, (1.39)
which has the rms scatter of only σrms = 0.19 ± 0.02 dex. The theoretical slope of
0.5 comes from the definition of the ionization parameter Uion that relates the BLR
photoionization rate with the recombination rate,
Uion =
Q(H)
4πR2
BLRcne
, (1.40)
where ne is the electron number density that is related to the recombination rate. The
flux of photoionizing photons is evaluated as Q(H) =
+∞
νi
(Lν/hν)dν, where νi is the
frequency corresponding to the ionization energy, Eion = hνion. Under the assumption
1.2. MAPPING DISTANT QUASARS 55
(Balmer lines: Hα, Hβ, MgII, FeII, CII)
(Lyα, CIV, HeII, NV)
Figure 1.27: Two-component model of the Broad-line region. The low-ionization lines
(LILs) originate in the denser material of the accretion disc, while the high-ionization lines
(HILs) form in the more diluted outflowing gas. Figure was adopted from Collin-Souffrin
et al. (1988) with some modifications.
that for all AGN the ionization parameter and the BLR electron density are constants,
Uionne = const, we obtain RBLR ∝ Q(H)0.5
∝ L0.5
ν . As more Hβ quasars have been
monitored with accretion rates closer to the Eddington limit, the rms scatter of the
RBLR − L relation has substantially increased. Using 117 Hβ quasars at the redshift
0.002 < z < 0.9 and with the luminosity in the range 41.5 < log (L5100 [erg s−1
]) < 45.9,
Martínez-Aldama et al. (2019) showed that there is a positive correlation between
the departure from the best-fit RBLR − L relation and the relative accretion rate, i.e.
the higher the Eddington ratio, the shorter the rest-frame time delay with respect to
the expected one. This could be interpreted as the result of the transition towards
geometrically thicker slim discs at higher accretion rates that can block a fraction
of the photoionizing continuum. Using QSOs that were reverberation-mapped using
the broad MgII line (at 2798 Å) from low to intermediate redshifts, several studies
confirmed the existence of the MgII RBLR − L relation as more such sources were
available (Czerny et al. 2019; Zajaˇcek et al. 2020; Homayouni et al. 2020; Zajaˇcek et al.
2021; Yu et al. 2023; Zajaˇcek et al. 2024c). Zajaˇcek et al. (2020) confirmed analogous
correlation between the departure from the best-fit MgII radius-luminosity relation
and the relative accretion rate as for Hβ QSOs. Using 194 MgII QSOs, Zajaˇcek et al.
(2024c) constrained the MgII RBLR − L relation as follows,
log
τMgII
1 day
= 1.74+0.04
−0.04 + 0.32+0.04
−0.04 log
L3000
1044 erg s−1
, (1.41)
56 CHAPTER 1. INTRODUCTION
which has the substantial rms scatter of σ = 0.30+0.02
−0.02 dex. We see that the MgII
RBLR − L relation is significantly flatter than the Hβ RBLR − L relation, see Eq. (1.39).
The RBLR − L relation has even been confirmed for the HIL CIV line (at 1549 Å) (Kaspi
et al. 2021; Cao et al. 2022, 2024), which is perhaps a bit surprising because of its
presumed association with the unbound outflow. For 38 CIV QSOs, the best-fit RBLR −L
relation is (Cao et al. 2022),
log
τCIV
1 day
= 1.034+0.097
−0.087 + 0.441+0.044
−0.044 log
L1350
1044 erg s−1
, (1.42)
which has the rms scatter of 0.307+0.039
−0.056 dex comparable to the MgII RBLR − L relation.
Using the CIV line, one reaches quasars at the redshift of 3 and higher, whose CIV
emission is redshifted to the optical domain.
The importance of the RBLR − L relations for different broad emission lines is that they
allow the determination of the SMBH mass for one single-epoch spectrum. From such a
spectrum, one can determine the continuum monochromatic flux density and for a given
redshift, a monochromatic luminosity is determined. Combining this luminosity with the
RBLR − L relation, one can infer the time-delay for a given broad emission line. With the
determined FWHM of the line from the single-epoch spectrum, we can estimate the virial
SMBH mass using Eq. (1.37). Having many estimated SMBH masses at different redshifts
enables one to analyze the SMBH growth across the cosmic history. The power-law relation
τBLR ∝ Lα
can also be utilized for the standardization of quasars and thus for constraining
cosmological parameters, see Subsection 1.4 for more details.
1.2.2 Resolving spheres of influence of extragalactic nuclei
The Galactic center is the closest galactic nucleus to us. It is also the only nucleus where we
can resolve individual stars and study their proper motions and radial velocities. The sphere
of influence of Sgr A* is rSI ∼ 2.1 pc according to Eq. (1.4). In order to detect the presence of
a massive point mass, such as the SMBH at the center of a galaxy, one needs to able to resolve
at least the scale of one rSI. In reality, to reliably determine the SMBH mass, the Keplerian
rise of the stellar rms velocity along the line of sight vrms ∝ r−1/2
should be detected on the
scale of at least ∼ 0.1rSI (Merritt 2013). For the Galactic center distance of dSgrA∗ ∼ 8 kpc,
we can actually resolve the scales of l ∼ (λ/D)dSgrA∗ ∼ 454 AU ∼ 0.0022 pc, which is 10−3
rSI.
Therefore the gravitational potential of Sgr A* has been reliably probed by measuring the
stellar rms velocity inside rSI (e.g., Schödel et al. 2009). In addition to that, the presence of
the SMBH of M• ∼ 4 × 106
M⊙ has been independently confirmed by sampling several orbits
of S stars (i.e. astrometry studies, see e.g., Parsa et al. 2017).
The situation in extragalactic systems is generally much worse in terms of directly resolving
the sphere of the SMBH influence. The Galactic center is ∼ 112.5-times closer than M31
in the Local Group and ∼ 2062.5-times closer than the closest cluster of galaxies, the Virgo
cluster. It is thus possible to resolve the sphere of influence only for a few tens of galaxies.
The Keplerian rise of the stellar rms velocity was detected only for the Milky Way, M31
and its companion M32 in the Local Group. The central massive elliptical galaxy M87 in
the Virgo cluster exhibits only a very gradual rms velocity increase, flatter than the typical
Keplerian profile. This is most likely due to a core-like distribution of stars around the SMBH
M87* caused by previous mergers (Merritt 2013). When detecting the stellar integrated
1.2. MAPPING DISTANT QUASARS 57
light at different projected radii, more distant slower stars contribute more to the measured
line-of-sight rms velocity than the closer faster stars, which are fewer.
The stellar distribution in the nucleus of M31, the Andromeda galaxy, is asymmetric
(lopsided) with two apparent photometric centers P1-P2, one brighter (P1) than the other (P2).
This makes the interpretation of the Keplerian rise of the stellar rms velocity challenging, in
particular it makes the SMBH mass determination uncertain. The two nuclei are separated in
projection by about ∼ 1.5 pc, with the fainter one coinciding with the centroid of the bulge
(Lauer et al. 1993). There have been several interpretations of the Andromeda double-nucleus:
• it could be the result of the dust absorption, though this would require unusual dust
properties (Lauer et al. 1993);
• the brighter offset nucleus could be the remnant of another nucleus of the galaxy that
had previously merged with M31, potentially hosting another SMBH that would have
stabilized it against tidal disruption by M31* (Lauer et al. 1993);
• the double-nucleus structure is created by a single eccentric stellar disc orbiting around
M31* at the center of the bulge (Tremaine 1995; Kormendy & Bender 1999). The
brighter second “nucleus” is an apparent effect of the accumulation of stars close to their
apocenters where they move more slowly, and thus spend more time at the apocenter
orbital phase than at the pericenter closer to the SMBH. Bluer, younger stars orbit
around the true nucleus, close to the SMBH, which is analogous to the Galactic center
and suggests that there are dynamical processes close to the SMBH that tend to catalyze
star formation.
Instead of stellar kinematics, one can make use of gas motions that can more clearly trace
the SMBH potential if the gas orbits in one plane, i.e. there is a thinner gas disc close to the
SMBH. Then the gas velocity profile can be fitted with vgas = [G(M• + M⋆(< r))/r]1/2
with a
certain inclination of the gas disc with respect to the observer. The gas motion along the line
of sight is not so contaminated by the gas that is located further away, which is the case for
stellar kinematics. Macchetto et al. (1997) presented the rotation curve of an ionized gas ring
traced by [CII] emission close to M87* (∼ 5 pc), which led to the constraining of the SMBH
mass to a few 109
M⊙ (3.2 ± 0.9 × 109
M⊙). In special cases, the X-ray emission of an AGN
accretion disc can excite the molecular transitions in the orbiting material that lead to the
stimulated water maser emission (Greenhill 2002). An exemplary case is NGC 4258 where
the water maser emission at 22 GHz was resolved by the radio interferometry technique (Very
Long Baseline Array). At the resolution of milliarcseconds, which is 100-times better than
with optical telescopes, the molecular clouds were found to rotate within a thin, Keplerian disc
with the radius of ∼ 0.1 pc. This led to one of the most precise SMBH mass measurements of
M• = 3.9 × 107
M⊙ (Miyoshi et al. 1995).
Radio interferometry at millimeter wavelengths can reach sufficient angular resolution
to resolve event-horizon structures of M87* and Sgr A*, two SMBHs that have the largest
angular sizes on the sky, when a correlated signal is combined from several stations across the
whole globe. The basic condition for the imaging is the sufficient coverage of the interference
fringes (visibilities) across the uv-plane (expressed in baseline lengths) so that the Fourier
transform can be performed to produce an image on the sky (van Cittert-Zernike theorem). At
the same time, because of the low relative accretion rate, both SMBHs are embedded in the
geometrically thick ADAFs, whose SED becomes optically thin close to one millimeter, see
58 CHAPTER 1. INTRODUCTION
Fig. 1.14. These two factors have led to the attempt to observe M87* and Sgr A* using the
global millimeter Very Long Baseline Interferometry array (mm-VLBI). The project and the
collaboration utilizing mm-VLBI adopted the name Event Horizon Telescope (EHT)5
. With
the largest baseline of B ∼ 104
km and the observing wavelength of λ ∼ 1 mm, the smallest
angular separation that can be resolved is θEHT ∼ λ/B ∼ 21 µas. For a non-rotating SMBH,
the accretion flow of hot thermal plasma close to the ISCO produces synchrotron radiation.
Emitted photons can approach closest to the SMBH at the photon orbit and still return to
the place of their origin. This last photon orbit is seen by a distant observer at the radius of
3
√
3rg. It is expected to create a bright ring with a darker depression at the center – SMBH
silhouette or shadow (Falcke et al. 2000) – whose angular diameter is,
θshadow ≈
6
√
3GM•
c2dSMBH
→ 51.2
M•
4 × 106 M⊙
dSMBH
8 × 103 pc
−1
µas , (1.43)
which was estimated specifically for Sgr A*. For M87*, which is about thousand times heavier
and ∼ 2000 more distant, we get θshadow ∼ 25.6 µas. Thus, in both cases, since θEHT < θshadow,
the EHT should be able to resolve the SMBH shadow and produce its brightness distribution
if the uv-coverage of fringe visibilities in the baseline plane is sufficiently dense. Event
Horizon Telescope Collaboration et al. (2019) report the detection of the shadow of M87* and
subsequently, Event Horizon Telescope Collaboration et al. (2022) announce the detection
of the Sgr A* shadow (see Fig. 1.17 for the image reconstruction, including the polarized
signal). To capture the brightness distribution of Sgr A* has been more challenging since it is
variable on the timescales that are shorter than the observation duration at individual stations.
A typical orbital timescale close to the ISCO of Sgr A* (for a non-rotating case) is,
PSgrA∗ =
2πGM•
c3
r
rg
3/2
≃ 30
M•
4 × 106 M⊙
r
6 rg
3/2
min , (1.44)
while for M87*, we obtain a thousand times longer orbital timescale, PM87∗ ≃ 21 days, which
is much longer than the typical observing phase. In Fig. 1.28, we show the collection of
multi-wavelength images of M87 from the highest energies to the lowest, capturing this
elliptical galaxy with a prominent jet at the center of the Virgo cluster at all spatial scales.
The reverberation mapping of the BLR was the original and for a long time the only way
to spatially map the distances via the measured time delays. The near-infrared interferometry
applied to the Very Large Telescope at the European Southern observatory – the interferometer
GRAVITY (GRAVITY Collaboration et al. 2017) – enabled the spatial resolution of the region
for several AGN. The first resolved offset between red- and blue-photocenters of the broad
Paschenα line in 3C273 was detected by Gravity Collaboration et al. (2018). Similarly,
GRAVITY Collaboration et al. (2020a) spatially resolved Brγ line in IRAS 09149-6206
and the radius of the line-emitting region was consistent with the value expected from the
previously inferred radius-luminosity relation for the broad Hβ line. A spatially resolved Brγ
line was also reported for NGC3783 (GRAVITY Collaboration et al. 2021), where the BLR
geometry, as in the previous two sources, is consistent with a thick disc of cloudlets whose
density peaks at the inner radius. GRAVITY Collaboration et al. (2024) revealed near-infrared
VLTI/GRAVITY interferometric spectra for four more targets: Mrk509, PDS456, Mrk1239,
and IC4329A. Based on these sources and the three previously reported ones, GRAVITY
5
https://eventhorizontelescope.org/
1.2. MAPPING DISTANT QUASARS 59
Figure 1.28: Multi-wavelength view of M87, including the mm-Very Long Baseline
Interferometry image of the M87* shadow. The figure shows the composition of multiwavelength
images of M87 taken during the 2017 observing campaign when the first SMBH
“photo” was taken in April. There were 19 different instruments involved. From the left to
the right columns, there are mm/radio images (left; orange), UV/optical (middle; blue), and
X-ray/γ-ray images (right; green-red-yellow colours). The top row shows a series of three
images (from the left to the right: 1.3 mm, 251 nm, and 0.2-10 keV) with the spatial scale of
the order of 1000 light years that shows the core-jet structure, including the prominent knot A
in the forward-pointed jet. Credit for the image composition: J. C. Algaba (full credit is at the
bottom of the image).
Collaboration et al. (2024) constructed the RBLR − L relation independent of the previous
reverberation-mapping measurements. The best-fit relation is,
log
τNIR
1 day
= 1.69+0.23
−0.23 + 0.37+0.18
−0.17 log
L5100
1044 erg s−1
, (1.45)
which is flatter but within the uncertainties still consistent with the slope reported by Bentz
et al. (2013). GRAVITY Collaboration et al. (2024) found an indication for shorter time
delays for higher luminosity AGN, which is consistent with the trends of lag shortening for
higher Eddington ratios traced along the RBLR −L relation inferred from reverberation-mapped
data (Martínez-Aldama et al. 2019; Zajaˇcek et al. 2020). Overall, the spatially resolved BLRs
by the GRAVITY instrument have confirmed the robustness of reverberation mapping so far,
including the inferred virial SMBH masses and the previously determined radius-luminosity
relations. These tools can thus be further employed in the studies of the SMBH growth across
the cosmic history.
60 CHAPTER 1. INTRODUCTION
1.2.3 Signs of stellar-mass bodies close to extragalactic SMBHs
In the previous subsections we learned that characteristic broad and narrow optical and UV
emissions lines, the power-law continuum, the infrared bump as well as the analysis of the
polarized light led to the formulation of the unified model of AGN (Antonucci 1993; Urry &
Padovani 1995), in which observed spectral properties of AGN depend largely on the viewing
angle. For type I AGN that we observe close to the symmetry axis, i.e. we view an accreting
SMBH close to the face-on configuration, we can detect broad components of optical and UV
emission lines as well as the power-law continuum, including the X-ray emission, presumably
originating in the accretion disc. For type II sources, broad components are not visible and
the continuum emission has a profound infrared excess due to the emission of a more distant
dusty molecular torus. For type I sources, the continuum emission varies stochastically on the
timescales from days to months. Across different wavebands, these variations are more or
less correlated, including the emission of broad lines, which allows us to estimate the time
delays between different bands, and eventually determine the length-scales associated with
a particular circumnuclear medium – this is the so-called reverberation mapping technique,
see also Subsection 1.2.1. Although we have gained a basic understanding of geometrical,
spectral, and temporal properties of AGN, especially via reverberation mapping campaigns
(Czerny et al. 2023), some questions have still remained largely unanswered. One of them is
the effect of a large number of stars within the NSC on the accretion onto the SMBH and the
nuclear outflows. On the other hand, the AGN activity is expected to impact stars orbiting
around the SMBH. The questions like these have been challenging to tackle due to a lack of
information about orbiting stars in different galactic nuclei than the Galactic center. However,
some recent detections of repeating nuclear transients (RNT) seem to indicate that stars can
indeed affect noticeably the close surroundings of SMBHs.
In comparison with Sgr A* where a large number of stars within the NSC determine its
low level of activity (Quataert 2004; Shcherbakov & Baganoff 2010; Ressler et al. 2020),
there are several tens of detections of a rapid increase in the optical/UV luminosity by several
orders of magnitude of otherwise quiescent nuclei (Gezari 2021). These optical/UV flares
with the peak black-body luminosities of ∼ 1043
− 1044
erg s−1
and typical temperatures of
∼ 10 000 − 50 000 K are typically followed by a power-law decay. A standard interpretation
of these events is the tidal disruption of a star or a tidal disruption event (TDE). TDEs were
predicted before the actual discovery (Hills 1975; Rees 1988). A standard model picture is
that a star moving on a parabolic/hyperbolic orbit reaches the smallest distance to the SMBH,
the periapse, where the acceleration due to the tidal field of the SMBH is comparable to or
larger than the gravitational binding energy of the star. The critical distance for the star of
mass m⋆ and radius R⋆ is referred to as the tidal disruption radius rt,
rt ≈ R⋆
M•
m⋆
1/3
rt
rg
≈
c2
R⋆
GM2/3
• m1/3
⋆
∼ 18.7
R⋆
1 R⊙
M•
4 × 106 M⊙
−2/3
m⋆
1 M⊙
−1/3
, (1.46)
where the second expression is the ratio of the tidal radius of a star to the gravitational radius
of the SMBH. When the pericenter of the star is comparable to or smaller than rt, it will
be tidally perturbed. Subsequently, the debris stream forms, approximately half of which
escapes the SMBH altogether while the other half falls back and powers the emission. The
1.2. MAPPING DISTANT QUASARS 61
fall-back rate was found to evolve with time as a power-law, ˙Mfb ∝ (t − tp)−5/3
with respect to
the time of the peak luminosity tP, which is roughly consistent with many detections of TDEs
and their evolution with time (Gezari 2021). The ratio of the tidal disruption radius rt to the
pericenter distance of the star rp is referred to as the parameter β⋆ = rt/rp. For different types
of stars, there is a critical value of β⋆, below which the TDE is just partial. Specifically, for
main-sequence stars, βcrit ∼ 2−3 (Ryu et al. 2020), while for β < βcrit only the upper envelopes
of the star are tidally perturbed and the stellar core continues along the original orbit. When
the stellar orbit is bound, i.e. elliptic, this results in repeated partial TDEs or rpTDEs (see also
Suková et al. 2024, for discussion). There have been several rpTDEs detected so far with the
recurrence timescale or the orbital period between tens of days to about 30 years (Payne et al.
2022; Liu et al. 2023; Wevers et al. 2023). The repetition of the TDE flares is instrumental to
uncover the parameters of a given system, in particular the SMBH mass, spin, stellar type, the
pericenter distance, and the orbital evolution, since they all influence the flare shape, spectrum,
and the periodicity changes. The dynamics behind the orbits of rpTDEs is likely related to the
disruption of binaries on nearly parabolic orbits. This three-body interaction or the so-called
Hills mechanism (Hills 1988) leads to the binary disruption, where one component typically
escapes the system as a hypervelocity star while the other component becomes bound to the
SMBH and moves on orbits comparable to detected rpTDEs. Hence, rpTDEs probe not only
the accretion physics but also the dynamics of the whole (extragalactic) NSC, see Fig. 1.29
for the illustration.
A novel type of short-period repeating soft X-ray transients was discovered with the
recurrence timescale of a few hours to about one day (GSN069 was the first such a source;
Miniutti et al. 2019), therefore about two orders of magnitude less than rpTDEs. The eruption
amplitude reaches one to two orders of magnitude more than the quiescent emission. In other
wavebands, including optical, UV, and hard X-ray bands, there is no significant variability.
The duty cycle of the eruptions is of the order of ∼ 10% of the recurrence timescale. For these
reasons, such repeating nuclear transients (RNTs) were called QuasiPeriodic Erupters (QPEs;
Arcodia et al. 2021). Although there have been many theoretical models presented addressing
the QPEs, including accretion-disc instabilities (in particular the radiation-pressure instability;
Sniegowska et al. 2020; ´Sniegowska et al. 2023), star-disc and black hole-disc interactions
(see Suková et al. 2024, for a review), there is a preference towards models that explain the
repetitive soft X-ray eruptions as a result of a smaller body orbiting in the vicinity of the
SMBH. These models can be categorized into three groups according to the mechanism how
the X-ray emission peaks are produced:
• perturbations of the accretion rate due to inclined perturbers (Suková et al. 2021),
• ejection of shocked, adiabatically expanding clouds above the accretion disc as the
smaller body punches through the accretion disc surrounding the primary SMBH (Linial
& Metzger 2023; Franchini et al. 2023),
• a Roche-lobe overflow of the stellar-envelope material onto the SMBH, which resembles
rpTDEs, see Fig. 1.29, though Roche-lobe overflowing stars are expected to exhibit
orbits with only mild eccentricities due to the circularization via gravitational-wave
losses (Krolik & Linial 2022).
There is a preference for QPEs to be hosted by galaxies with lower-mass SMBHs (∼ 105
−
107
M⊙). Adopting M• = 106
M⊙ and assuming that the eruptions take place twice per
62 CHAPTER 1. INTRODUCTION
Star-SMBH interaction
inspiraling matter
tidally
distorted
envelope
star
Nuclear Star Cluster
colder gas �laments
out�ow region
SMBH
~10-6
pc~0.1 pc
scatteredbinary
Figure 1.29: Repeating partial tidal disruption event. The left panel shows the whole NSC
where two-body interactions result in the infall of binaries on nearly parabolic orbits. When
the binary approaches the SMBH, it disrupts, leaving one component tightly bound to the
SMBH. In the right panel, we show the tidal perturbation and stripping of such a star close to
the pericenter of its orbit. This leads to repeating nuclear flares on the orbital timescale.
perturber’s (mildly eccentric or nearly circular) orbit, Porb = 2Perupt, we obtain an estimate for
the semi-major axis of an orbiting body in gravitational radii for Perupt scaled to one hour,
a⋆
rg
=
c2
(πG)2/3
P2/3
eruptM−2/3
•
∼ 37.9
Perupt
1 hour
2/3
M•
106 M⊙
−2/3
. (1.47)
On the length-scales indicated by a⋆ gravitational radiation and the related energy losses may
be relevant depending on the secondary body’s mass. In order for the SMBH-secondary object
to merge within 10 years from now, the secondary-object mass should be at least (Peters
1964),
m2 ≃
5c5
256G3
a4
⋆
M2
•τmerge
≈ 634
M•
106 M⊙
2
a⋆
38rg
4
τmerge
10 years
−1
M⊙ , (1.48)
hence in the intermediate-mass black hole range (IMBH). For smaller periods of the eruptions
below half an hour, the mass of the secondary would be pushed down towards stellar-mass
1.2. MAPPING DISTANT QUASARS 63
black holes of ≲ 100 M⊙. Therefore, some of the current QPE sources or those detected in
the future could be electromagnetic counterparts of the extreme-mass/intermediate-mass ratio
inspiral (EMRI/IMRI) gravitational-wave sources to be detected by the Laser Interferometer
Space Antenna (Amaro-Seoane et al. 2023; Kejriwal et al. 2024).
Recently, the Swift J0230+28 source caught attention with the period of soft X-ray
eruptions of ∼ 22 days, which is intermediate between QPEs and rpTDEs (Evans et al. 2023;
Guolo et al. 2024). In addition to longer, regular flares, the source exhibits shorter rapid flares
with a comparable recurrence timescale (Pasham et al. 2024a). Moreover, after at most ∼ 536
days, the eruptions ceased to be detectable (Pasham et al. 2024a). The best interpretation is
either a rpTDE of a Jupiter-like planet or a double-EMRI system consisting of two co-orbiting
aligned stars. Another source – ASASSN-20qc – exhibited a TDE-like optical flare, followed
by a delayed X-ray emission. When the X-ray spectrum was analysed, Pasham et al. (2024c)
found the signature of an ultrafast outflow (UFO) that is periodically enhanced every 8.5
days. In contrast to the presence of the QuasiPeriodic ultrafast Outflow (QPOut), there is
no significant variability of the inflow rate. These properties are consistent with an orbiting
IMBH at the distance of ∼ 100 rg where the inclined IMBH pushes through the ADAF and
drags some matter along its orbit towards the outflow funnel where it is further accelerated by
the ordered magnetic field. At the same time, the ratio of the influence radius of the IMBH to
its distance is not large enough to cause significant perturbation of the inflow rate (Suková et al.
2021; Zajaˇcek et al. 2024e). Finally, the event AT2019qiz associated with the optical TDE
started to exhibit QPEs with the mean recurrence timescale of ∼ 48 hours as well as QPOuts
years after the TDE peak (Nicholl et al. 2024). The modeling of the detected X-ray, optical,
and UV emission of the accretion disc provides support for the perturber-disc interactions.
This source thus provides evidence that QPEs are associated with TDEs that eventually reveal
the presence of other bound secondary bodies in the vicinity of the SMBH thanks to the
supply of the fresh material that forms a new, denser accretion disc on the length-scale of
the tidal radius or larger. In summary, the high-cadence time-domain surveys provide new
evidence for repeating nuclear transients, many of which seem to be manifestations of the
star/compact remnant interaction with the circumnuclear medium of the SMBH.
Since most spiral and elliptical galaxies with the total stellar masses of ∼ 108
− 1010
M⊙
host dense and massive NSCs (Neumayer et al. 2020), the question arises if the SMBH feeding
by stars from the NSC cannot by itself address a large part of the SMBH growth during the
galaxy evolution. The SMBH can grow when a star passes through its event horizon or by
the accretion of the stellar debris after the TDE. In both cases, the critical length-scale that
determines whether the star is consumed or not is the loss-cone radius rlc (Merritt & Wang
2005). When the star approaches or goes below rlc, it will eventually be consumed by the
SMBH. When we approximate the NSC as a singular isothermal sphere, the stellar mass
accretion rate through the radius r is,
˙M⋆(r) ∼ 4πr2
σ⋆ρ⋆(r) ∼ 2
σ3
⋆
G
, (1.49)
where the stellar mass density is ρ⋆(r) ∼ σ2
⋆/(2πGr2
) for a given stellar velocity dispersion
σ⋆ within a singular isothermal sphere. The stellar-mass inflow rate through the loss cone is
(rlc/r) ˙M⋆(r). When we set r to the radius of the SMBH gravitational influence, see Eq. (1.4),
and rls ≈ 10rg, the loss-cone mass inflow rate can be evaluated as follows,
˙Mlc ≃
2σ3
⋆
G
rlc
rSI
≈ 20
σ5
⋆
Gc2
. (1.50)
64 CHAPTER 1. INTRODUCTION
When we assume that the “seed” black hole is fed mostly by disrupted or swallowed stars, the
resulting SMBH mass “now” after τgal ∼ 10 Gyr of the galaxy evolution is,
M• ∼ ˙Mlcτgal ≃ 20
σ5
⋆
Gc2
τgal
∼ 1.7 × 108 σ⋆
200 km s−1
5 τgal
10 Gyr
M⊙ , (1.51)
which is both qualitatively and quantitively consistent with the observed M• − σ⋆ relation
(Ferrarese & Merritt 2000), see Subsection 1.2 for the discussed relation to the AGN negative
feedback. The derived and evaluated relation in Eq. (1.51) implies that the SMBH “loss-cone”
feeding by stars can serve as an alternative or complementary pathway for the SMBH growth
and the associated feedback. The contribution of this process to the classical feeding pathways,
see Fig. 1.21 for the illustration, depends on the state of the stellar nuclear environment, in
particular the stellar density and the velocity dispersion of the NSC, which determine the
stellar mass inflow rate.
1.3 Synergies between the Galactic center and active
galactic nuclei
Currently, the Galactic center with the bolometric luminosity of Lacc ∼ 1036
− 1037
erg s−1
and
the accretion rate of ˙M ∼ 2 × 10−9
− 2 × 10−7
M⊙ yr−1
is extremely underluminous. With the
Eddington ratio of ˙m ∼ 10−7
, it is a typical representative of quiescent nuclei that host an
ADAF instead of a standard accretion disc. Therefore, the current SED with the peak close to
∼ 1 mm is much softer than the SED corresponding to the cooling-dominated standard disc
with the peak in far-UV domain, see Fig. 1.24. The question is how long Sgr A* has been in
such a low-luminosity state. Did it reach the Eddington rate during its past evolution? If yes,
for how long? Will it repeat again in the future?
Some aspects of the past evolution of Sgr A* can be inferred from its current accretion
rate and its mass. Taking the present accretion rate of ˙M ∼ 2 × 10−8
M⊙ yr−1
and extrapolating
it for the whole Galaxy lifetime of τgal ∼ 1010
yr implies that the SMBH would grow only
by ∆M• ∼ ˙Mτgal ∼ 200 M⊙, which is in contradiction with the mass of M• ≃ 4 × 106
M⊙.
This already points towards a more active past evolution unless Sgr A* was formed already
very massive via a direct-collapse scenario (see e. g. Natarajan et al. 2024). Assuming that at
certain epochs Sgr A* reached its Eddington luminosity, see Eq. (1.1), LEdd ∼ 5 × 1044
erg s−1
,
it should have had an accretion rate of,
˙MEdd =
4πGM•mp
ηradσTc
∼ 0.09
M•
4 × 106 M⊙
ηrad
0.1
−1
M⊙ yr−1
, (1.52)
where we adopted the radiative efficiency of ηrad ∼ 0.1. With the Eddington rate, the total
growth phase of Sgr A* would last τg ∼ M•/ ˙MEdd ∼ 4.4 × 107
years or only about ∼ 0.4% of
the total Galaxy lifetime would be enough to reach M• ∼ 4 × 106
M⊙ at the Eddington rate. In
case the individual active phase lasts τA ∼ 105
years (Schawinski et al. 2015), there should
have been about NA ∼ τg/τA ∼ 440 such active phases during the Milky Way evolution. Since
the number of non-active, quiescent phases should be comparable, NN ∼ NA, the quiescent
1.3. SYNERGIES BETWEEN THE GALACTIC CENTER AND ACTIVE GALACTIC
NUCLEI 65
phase is expected to last τN ∼ 22.6 × 106
years. Hence, on average, every 20 million years
Sgr A* is expected to reach the Eddington limit for ∼ 105
years.
Although these estimates are very rough, we can try to compare the recurrence timescale
of an active phase with the expected infall rate of a molecular material. An infalling/accreted
mass during one active phase ∆M• ∼ ˙MEddτA ∼ 104
M⊙ corresponds well to a smaller
molecular cloud. The closest reservoir of the molecular material in the vicinity of Sgr A*
is the Circum-Nuclear Disc (CND) with the total mass of 106
M⊙ (Christopher et al. 2005).
The CND consists of many clumps with the radius of rcl ∼ 0.1 pc. When they reach a gas
number density of ng ∼ 108
cm−3
, each has a mass of ∼ 104
M⊙. According to Hsieh et al.
(2021), there are about 16 sufficiently massive clumps within the radius of ∼ 2 pc and the
scale-height of ∼ 0.5, which yields the clump number density of ncl ∼ 2.5 pc−3
. For the
characteristic velocity dispersion of σcl ∼ 10 km s−1
, we obtain the clump-clump collisional
rate as Γcol ∼ nclσclS cl, where Scl ≈ πr2
cl is the typical clump cross-section. When we choose
one out of four final velocity directions after the collision (inwards/outwards, along/opposite
the CND rotation), the characteristic infall timescale is τinfall ∼ (0.25Γcol)−1
∼ 5 × 106
years,
which is within all the uncertainties comparable to the mean duration of the quiescent phase.
In fact, there are several indications for an increased mass supply as well as the putative
increased accretion/jet activity a few million years ago. The clockwise stellar disc of OB/WolfRayet
stars is likely a remnant of the massive star formation within a dense gaseous/accretion
disc (Levin & Beloborodov 2003). The detected large-scale γ-ray Fermi bubbles (Su et al.
2010) that extend ∼ 9 kpc above and below the Galactic plane seem to be associated with a
massive gas outflow associated with either the starburst activity and associated supernovae or
a collimated nuclear outflow-jet that took place a few million years ago. Based on the analysis
of ionization properties Bland-Hawthorn et al. (2019) favour a Seyfert-like enhanced accretion
activity over the mechanic outflow model. The relative accretion rate could have reached
˙m ∼ 0.1 − 1.0. On a slightly larger scales than the Fermi bubbles, eROSITA identified X-ray
eROSITA bubbles with a typical length-scale of 14 kpc (Predehl et al. 2020). In Fig. 1.30, we
show the superposition of both Fermi and eROSITA bubbles. Whether these structures were
all created during one event or there was a separate mechanism is still under investigation.
One of the main questions is whether we can still trace some fingerprints of the past
activity of Sgr A* in the central parsec. One of the obvious targets of the nuclear outflow
and the associated radiation could be the ionized and neutral/molecular gas in the sphere
of influence. However, the gaseous structures such as the CND or the minispiral are rather
short-lived, only of the order of ∼ 104
− 105
years. A more promising target is the stellar
population in the central parsec, especially late-type stars that must have existed during the
time of the potentially enhanced Sgr A* activity. In fact, in the central ∼ 0.5 pc, Sellgren et al.
(1990) identified a decrease in the CO-bandhead absorption feature that is indicative of the
surface-brightness of older red giants. It is still under investigation what could have caused
the preferential depletion of larger, brighter red giants while smaller, fainter ones seem to be
present and form a cusp-like distribution (Schödel et al. 2020). Two of the proposed scenarios
involve an enhanced accretion activity a few million years ago:
• red giant-accretion disc interaction: when red giants collided with denser clumps within
the self-gravitating outer disc, the outer envelopes of red giants were removed, which
effectively modified their observational properties as well as the subsequent stellar
evolution (Amaro-Seoane & Chen 2014; Amaro-Seoane et al. 2020);
66 CHAPTER 1. INTRODUCTION
Figure 1.30: Illustration of the size of the Fermi bubbles in the γ-ray domain in comparison
with the X-ray eROSITA bubbles. Fermi bubbles (FB) with the length-scale of ∼ 9 kpc
are more compact than eROSITA bubbles (EB) with the length-scale of ∼ 14 kpc. Illustration
credit: Max Planck Institute for Extraterrestrial physics.
• red giant-jet interaction, which can similarly ablate the outer layers of late-type stars.
This reveals deeper, warmer layers, and thus changes the photometric colour of late-type
stars and their luminosities, hence they are not classified as red giants any more, see
also Fig. 1.31 for illustration. Zajaˇcek et al. (2020) proposed the model and performed
the first analytical estimates of the mechanism. Subsequently, Kurfürst et al. (2024)
performed 3D hydrodynamical simulations of the jet-red giant interaction.
Even now Sgr A* exhibits order-of-magnitude near-infrared and X-ray flares lasting about
one hour on a daily basis Witzel et al. (2021). As we already discussed, this variability
may originate within the magnetically arrested disc, e.g. due to magnetic-reconnection
events. The observed variable X-ray emission of molecular clouds in the vicinity of Sgr A*
strongly indicates that there was a significantly enhanced emission in the Galactic center only
∼ 300 − 400 years ago. This event was first indicated by the detected iron-line at 6.7 keV
(Koyama et al. 1989). The fluorescent 6.4 keV iron line detected along the molecular cloud
Sgr B2 confirmed the illumination and the reprocessing of the central-source emission by a
molecular material in the CMZ (Sunyaev & Churazov 1998). This fluorescent iron line is
also variable (Inui et al. 2009) and because of the reflection of the central-source emission,
its X-ray emission was found to be significantly polarized (Marin et al. 2023). The variable
X-ray fluorescent emission across molecular clouds in the CMZ is thus overall consistent with
the reflection of the primary outburst in the direction of Sgr A*. The luminosity increase by
about five orders of magnitude a few hundred years ago could have been caused by a series
of discrete accretion events, for instance due to infalling compact gas clouds (Czerny et al.
2013).
1.4. GALACTIC NUCLEI AS STANDARDIZABLE CANDLES 67
jet
supermassive
black hole
red giant
modified giant
accretion disc
Ambient bow shock
loose, expanding atmosphere
dense core
detached
shocked
envelope
Figure 1.31: Potential effect of the jet during the period of enhanced activity of the
Galactic center on the surrounding population of red giants. During repetitive jet-star
collisions, the ram pressure of the jet plasma ablates the loose envelope of the red giant, which
leads to an enhanced mass loss (in addition to the stellar wind) and as a result, the red giant
has a higher photosphere temperature, which leads to the change in the appearance from the
“red” colour to a “bluer” colour in terms of photometry.
1.4 Galactic nuclei as standardizable candles
Active galactic nuclei (AGN) are found from the local Universe to the era of reionization
and even earlier when the first galaxies were just forming. It is therefore attractive to use
them for cosmological studies since they in principle provide a bridge between the local,
distance-ladder measurements (Cepheids, supernovae type Ia) and the early-Universe cosmic
microwave background (CMB) observations (see e.g. Czerny et al. 2023; Zajaˇcek et al. 2024b).
AGN as potential alternative cosmology probes with a large redshift range are especially
relevant for the resolution of current cosmological tensions between local and early-Universe
measurements, such as the Hubble tension, which has become more serious over the last
decade (Perivolaropoulos & Skara 2022; Abdalla et al. 2022). We illustrate the redshift ranges
for the CMB, local probes used for the distance ladder (cepheids, supernovae type Ia), and
for active galactic nuclei in Fig. 1.32. While the current expansion rate of the Universe (the
Hubble constant H0) determined using the local, late-Universe distance-ladder measurements
is H0 = 73.40 ± 1.04 km s−1
Mpc−1
(Riess et al. 2022), the value inferred from the CMB
anisotropies (power spectrum) assuming the flat ΛCDM model is H0 = 67.4±0.5 km s−1
Mpc−1
(Planck Collaboration et al. 2020). These two values currently differ by more than ∼ 5σ
(Riess et al. 2022), which can either be caused by hidden systematic errors in at least one
of the standard cosmological probes or the current standard model of cosmology (spatially
flat ΛCDM) is not valid, i.e. it can only serve as a good approximation of a more complex
68 CHAPTER 1. INTRODUCTION
cosmological model. That is why searching for alternative probes, such as quasars, that cover
a redshift range in between late and early Universe is needed to help reveal the cause of these
tensions.
It may seem challenging to standardize AGN, i.e. to use them as standardizable “candles”,
because of their more complicated geometry in comparison with stars, a large span of SMBH
masses as well as luminosities. Moreover, AGN are quite variable sources. However, two
established correlations of a power-law nature related to the inner accretion engine in principle
allow the determination of luminosity distances and the subsequent construction of the Hubble
diagram of quasars. These are:
• the BLR radius-luminosity relation (RBLR − L), which can further be written and
parametrized as log τ
day
= β + γ log νLν(z,p)
1044 erg s−1 , where νLν(z, p) = 4πDL(z, p)2
νFν
with DL(z, p) being the luminosity distance for a given QSO at the redshift z and p are
cosmological parameters of a given cosmological model;
• the relation between X-ray (2 keV) and UV (2500 Å) luminosities (LX −LUV), which can
also be expressed in the log-linear form as log LX
erg s−1Hz−1 = β′
+ γ′
log LUV
1029 erg s−1Hz−1 ,
where LX = 4πDL(z, p)2
FX and LUV = 4πDL(z, p)2
FUV.
We summarize both relations in Table 1.2, where we also specify the corresponding likelihood
functions that are used to infer both the parameters of the RBLR − L or LX − LUV relations and
cosmological parameters. It was shown in a series of works that quasars can be standardized
using the LX − LUV relation (Risaliti & Lusso 2019), with the indication of the deviation from
the standard flat ΛCDM model in the direction of a larger current relative matter content and
a dynamical dark energy. However, independent analyses showed that the same set of quasars
is not fully standardizable as the LX − LUV parameters depended on both the redshift and the
cosmological model (see e.g. Khadka & Ratra 2022).
Table 1.2: Basic methodology of the inference of cosmological parameters p for RBLR − L
and LX − LUV relations.
Relation Dependence on cosmology Likelihood function
log τ
day
= β + γ log νLν(z,p)
1044 erg s−1 log τ
day
= β + γ log
4πD2
LνFν
1044 erg s−1 ln(LF) = −1
2
N
i=1
[log(τobs
i )−log(τth
i )]2
s2
i
+ ln(2πs2
i )
log LX
erg s−1Hz−1 = β′
+ γ′
log LUV
1029 erg s−1Hz−1 log
4πD2
LFX
erg s−1Hz−1 = β′
+ γ′
log
4πD2
LFUV
1029 erg s−1Hz−1 ln(LF) = −1
2
N
i=1
[log(Fobs
X,i )−log(Fth
X,i)]2
s2
i
+ ln(2πs2
i )
Concerning RBLR − L relation, MgII and CIV QSOs were found to be standardizable
(Khadka et al. 2021, 2022b; Cao et al. 2022; Czerny et al. 2023; Cao et al. 2024), i.e. RBLR − L
relation parameters are independent of the cosmological model. These datasets provide only
weak cosmological constraints due to limited samples. The constraints are consistent with
the standard flat ΛCDM model; however, a moderate dark energy dynamics as well as a
small spatial curvature are also consistent with the studied QSO samples. Hβ QSOs were
also found to be standardizable, though those QSOs prefer a decelerated expansion of the
Universe and the cosmological constraints are in the 2σ tension with the standard flat ΛCDM
model (Khadka et al. 2022a).
It was possible to identify a sample of 58 X-ray detected, reverberation-mapped QSOs, for
which both the MgII RBLR − L and LX − LUV relations could be applied. Khadka et al. (2023)
found systematic differences between both relations: while the cosmological parameters
inferred using the MgII RBLR − L relation were consistent with the standard flat ΛCDM model,
1.4. GALACTIC NUCLEI AS STANDARDIZABLE CANDLES 69
Figure 1.32: Active galactic nuclei versus standard cosmological probes and the Hubble
tension. The illustration depicts the currently used standard cosmological probes – cosmic microwave
background (CMB) and local, distance-ladder measurements (cepheids, supernovae
of type Ia) – and their redshift range in the expanding Universe (top image; NASA/WMAP
Science Team). In contrast, we show quasars that can bridge the local measurements with
the distant CMB. Towards the bottom of the image, we show the values of the current expansion
rate of the Universe (H0, the Hubble constant) as inferred from the distance-ladder
measurements (orange colour; Riess et al. 2022) and the cosmic microwave background
power spectrum (magenta colour; Planck Collaboration et al. 2020). The bottom plot adopted
from Perivolaropoulos & Skara (2022) shows how the two Hubble constant values started
to significantly deviate from each other after 2013 and reached the difference of as much as
∼ 5σ around 2020 as the systematic errors decreased.
70 CHAPTER 1. INTRODUCTION
the LX −LUV relation preferred a larger value of the Ωm0 parameter. In addition, the distribution
of the luminosity-distance differences, ∆ log DL ≡ log DL,LX−LUV − log DL,R−L turned out to be
asymmetric with the peak shifted towards positive values. Zajaˇcek et al. (2024b) interpreted
this systematic difference between both methods using the extinction of both UV and X-ray
radiation, which affects more the LX − LUV relation since the X-ray and UV luminosities are
impacted differently. It is possible to show that extinction, or the optical depth difference
(τX − τUV), always contributes to the non-zero luminosity distance difference,
∆ log DL =
δ
β′
− γ′
η′
2(1 − γ′)
+
β − log τ
2γ
−
η
2
+ 7.518 +
log FUV,int − log FX,int
2(1 − γ′)
=0 for intrinsic quasar emission
+
(τX − τUV) log e
2(1 − γ′)
extinction contribution
.
(1.53)
In conclusion, the LX − LUV relation should not be used for the quasar standardization, while
the BLR radius-luminosity relation is less affected by extinction and is thus more promising in
terms of providing tighter cosmological constraints when larger reverberation-mapped quasar
datasets are available.
1.5 This Thesis
This Habilitation Thesis summarizes the research studies of galactic nuclei that span from the
nearest (Galactic Center) to distant galactic nuclei close to the peak of quasar activity. At the
same time, we study the circumnuclear environment of an extremely low-luminosity nucleus
at the center of the Milky Way as well as the properties of active galactic nuclei accreting
close to the Eddington limit. Thus we cover nearly nine orders of magnitude in the relative
accretion rate. In terms of the supermassive black hole mass, we cover about three orders of
magnitude. Therefore, we traverse a large portion of the parameter space, at least considering
the basic quantities, such as M•, ˙m, and the luminosity distance (redshift). Below we list
seven research papers, where the author of this thesis is the main author. Each of these papers
describes studied sources, the data, the applied methodology, and the main results in detail.
These works were published between 2019 and 2024,
• Paper 1: Radio-Optical Properties of Active Galaxies.
Description: We study a sample of SDSS-FIRST sources, specifically the distribution
of their radio spectral indices across narrow-line optical diagnostic diagrams. We find
that Seyfert galaxies are mostly associated with radio sources with a steeper radio
spectral index and a larger radio loudness. This is caused by the presence of larger and
older radio lobes and large-scale jet structures. On the other hand, low-ionization nuclear
emission region (LINER) sources have a tendency to exhibit a flat to an inverted radio
spectral index and a lower radio loudness. This could be interpreted by the renewed
radio activity in the optically thick core region. For more details, see Chapter 2.
Importance: We found a correlation between the radio spectral index distribution and
the ionization potential traced by optical line ratios. The lower ionization potential of
LINERs is associated with the radio activity of the core/compact jet.
• Paper 2: Reverberation Mapping of HE 0413-4031.
Description: In this paper, we perform the monitoring of an intermediate-redshift,
1.5. THIS THESIS 71
high-luminosity quasar denoted as HE 0413-4031 located at the redshift of z = 1.38. A
significant time delay of 302.6+28.7
−33.1 days is found between the variable broad line MgII
and the photoionizing continuum at 3000 Å in the rest frame. This measurement helps
to confirm the existence of the MgII RBLR − L relation as well as the shortening of BLR
time delays for high-accreting sources. For more details, see Chapter 3.
Importance: The high luminosity of HE 0413-4031 significantly contributes to constraining
the MgII radius-luminosity relation, which can further be applied to infer
SMBH masses from single-epoch spectra. A contribution to the MgII radius-luminosity
scatter based on the accretion rate of the sources is found, in particular, the higher the
accretion rate, the larger the deviation from the best-fit relation.
• Paper 3: Red-Giant Depletion in the Galactic Center.
Description: Bright red giants appear to be missing within the central 0.5 pc from
Sgr A*. In this study, we propose a novel mechanism for the depletion of red giants in
the inner half parsec from Sgr A*. An interaction of an evolved star with a powerful jet
with the luminosity of ∼ 1042
− 1044
erg s−1
is capable of ablating its upper layers and
increasing its effective temperature. Thus such a modified star will deviate from the
properties of typical red giants and will not be classified as a late-type star anymore.
The jet-induced mass ablation is also size-dependent, affecting more large red giants
located at closer separations from Sgr A*, which is consistent with the most recent
observations. For more details, see Chapter 4.
Importance: Missing red giants in the Galactic center can potentially be connected to
its increased activity in the past few million years.
• Paper 4: Reverberation-Mapping of HE 0435-4312.
Description: In this paper, we present a reverberation-mapping campaign of another
intermediate-redshift luminous quasar HE 0435-4312. A significant MgII delay of
296+13
−14 days in the rest frame is found using seven time-delay determination methodologies.
In combination with other 68 MgII reverberation-mapped quasars, we further
constrained the MgII RBLR − L relation, log (τ/1 day) = (1.67 ± 0.05) + (0.30 ±
0.05) log (L3000/1044
erg s−1
), which can be used for the SMBH mass determination using
single-epoch observations of intermediate-redshift quasars. Using a higher-accreting
subsample, we showed that the scatter along the RBLR − L relations decreases significantly.
We showed that the MgII RBLR − L relation can be applied for constraining
cosmological parameters. For more details, see Chapter 5.
Importance: We provide tighter constraints on the MgII radius-luminosity relation using
the reverberation-mapping of another high-luminosity quasar and other 68 sources.
The relation is found to be significantly flatter than the Hβ radius-luminosity relation.
A high-accreting subsample exhibits a radius-luminosity relation with a smaller scatter
and we demonstrate its application in cosmology.
• Paper 5: Enhanced Doppler Beaming.
Description: Stars orbiting the SMBH in the Galactic center within the inner S cluster
with the radius of ∼ 0.04 pc can reach velocities in excess of 1000 km s−1
. At such large
velocities, the Doppler boosting of their near-infrared flux density can reach detectable
values. In this manuscript, we study the effect of the continuum SED spectral index on
the relative flux density variability. In case the orbiting objects are dust-enshrouded,
colder or exhibit a significant inverted non-thermal spectrum, the Doppler boosting
72 CHAPTER 1. INTRODUCTION
of their light can be enhanced by as much as a factor of ∼ 4 to 10. For the objects
orbiting around Sgr A* with precisely measured trajectories, the amount of photometric
variations could be used to constrain their spectral type/nature. For more details, see
Chapter 6.
Importance: The amount of Doppler beaming depends on the SED continuum slope,
which can be used to quantify it for the sources of known nature in the Galactic center.
Subsequently, it can be subtracted from the overall variability. Alternatively, if the
trajectory of the unknown object is constrained, the detection of the Doppler beaming
along its orbit can be used to determine its nature.
• Paper 6: Effect of Extinction on Quasar Distances.
Description: Here we compare two methods used for turning quasars into standardizable
candles for the sample of X-ray detected reverberation mapped quasars. In
principle, both methods, RBLR − L and LX − LUV relations, should give a consistent
luminosity distance to the same quasar within the uncertainties. However, we find significant
systematic differences, specifically the distribution of the luminosity-distance
differences (∆ log DL = log DL,LX−LUV
−log DL,R−L) has a peak shifted from zero towards
positive values and it also deviates from the symmetric Gaussian distribution. We interpret
these effects using the model involving the extinction of quasar radiation by the
dust in host galaxies. Since dust extinction affects X-ray and UV radiation differently
and there are also variations among quasars, the LX − LUV relation is more affected and
should not be used for quasar standardization. For more details, see Chapter 7.
Importance: This work shows that the differences between cosmological constraints
given by the LX − LUV relation on one hand and the broad-line region R − L relation as
well as standard cosmological probes on the other hand are not really of a cosmological
nature, i.e. a different equation of state of dark energy, but rather they can be addressed
by the extinction of UV/X-ray radiation within AGN hosts.
• Paper 7: UV FeII Emission Model and BLR Time Delays.
Description: The stratification of the broad-line region material is an important aspect
of its geometry and distribution with respect to the SMBH. This is also related to the
spectral decomposition of the optical and UV domains in type I quasars. A particular
problem is the blending of the MgII broad line and the FeII pseudocontinuum in the
UV spectral domain in the rest frame of the source. The correct determination of the
MgII line flux depends on the way how the two overlapping emission components
are separated. To this goal, we revisit the intermediate-redshift luminous quasar HE
0413-4031. In addition to the eleven years of monitoring by South African Large
Telescope (SALT), a near-infrared spectrum was obtained using the SOAR telescope
that contained narrow emission lines of Hβ and [OIII]. This enabled us to obtain a
much more precise redshift determination of z = 1.39117 ± 0.00017, which led to a
different spectral decomposition of the MgII+FeII region than previously. Overall, the
MgII line properties and its time delay with respect to the continuum were not much
affected, which confirms that the MgII emission is a reliable SMBH mass estimator
and can additionally be applied for cosmological studies. On the other hand, the FeII
pseudocontinuum was more affected – for the best-fit FeII model, the FeII rest-frame
time delay of 251+9
−7 days was slightly longer than the MgII time delay of 224+21
−31 days,
which was consistent with the slightly smaller FeII FWHM of ∼ 4200 km s−1
, indicating
1.5. THIS THESIS 73
that the FeII line-emitting material is more distant than the MgII line-emitting material
by 27 light days (∼ 4700 AU). Moreover, the systematic blueshift of MgII became
much smaller (∼ −200/300 km s−1
) than for the previous decomposition and the FeII
template. This shows that a precise redshift determination in combination with the
more precise FeII emission model can significantly impact the overall assessment of
the BLR geometry and kinematics. For more details, see Chapter 8.
Importance: We obtained a better understanding of the MgII/FeII stratification within
the broad-line region. Specifically, the UV FeII line-emitting material is located a
bit further with respect to the MgII-emitting material. Although the FeII emission
properties are quite sensitive to the precise redshift determination and the spectral
decomposition of the MgII+FeII spectral complex, the MgII line properties and its time
delay are quite stable, which justifies its application for SMBH mass determination and
for cosmological studies.
Chapter
2
Paper 1: Radio-Optical Properties of
Active Galaxies
Supermassive black holes (SMBHs) at the centers of galaxies affect their host galaxies via
radiative and mechanical feedback. This is also supported by the correlations between the
SMBH mass and the large-scale properties of their hosts, especially the SMBH mass–stellar
velocity dispersion correlation (M• − σ⋆) and the relation between the SMBH mass and the
bulge–spheroid mass/luminosity.
To better understand the feedback cycle, we focused on the relation between the ionization
potential in host galaxies, which is traced by narrow emission-line ratios, and the radio
spectral index inferred between the pairs of the following frequencies: 1.4 GHz, 4.85 GHz,
and 10.45 GHz. We focused on the radio spectral index between the latter two frequencies
since the corresponding flux densities were measured using the Effelsberg telescope with the
comparable beam size.
Out of the initial sample of intermediate-redshift radio galaxies (F1.4GHz ≥ 10 mJy), we
determined the radio spectral index distribution (α4.85−10.45) in the optical diagnostic diagrams
for 209 sources. Considering how the sources are distributed in the narrow-line optical
diagnostic (BPT) diagrams based on their radio spectral index (F ∝ ν+α
), we found three
distinct groups: (i) sources with a steep radio spectral index (α < −0.7), with a high ionization
ratio, and a large radio loudness; (ii) sources with a flat radio spectral index (−0.7 < α < −0.4),
with a lower ionization ratio, and an intermediate radio loudness; and (iii) sources with an
inverted radio spectral index (α > −0.4), a low ionization ratio, and a small radio loudness.
These three groups – (i), (ii), and (iii) – are positioned along the transition zone between
the Seyfert and the low-ionization nuclear emission-line region (LINER) galaxies, with group
(i) distributed mostly within the Seyfert galaxies and group (iii) among the LINER sources.
We interpret these radio spectral index – ionization potential trends as a result of the recurrent
nuclear-jet activity with a characteristic timescale. Seyfert galaxies are characterized by an
older radio (jet) activity with optically thin large-scale radio structures (jet and lobes), while
among LINERs there are sources with the recently renewed jet activity dominated by the
compact, optically thick radio core.
Credit: Zajaˇcek et al. (2019a), A&A 630, A83. Reproduced with permission ©ESO.
75
A&A 630, A83 (2019)
https://doi.org/10.1051/0004-6361/201833388
c ESO 2019
Astronomy
&
Astrophysics
Radio spectral index distribution of SDSS-FIRST sources across
optical diagnostic diagrams
Michal Zajaˇcek1,2,3, Gerold Busch1, Mónica Valencia-S.1, Andreas Eckart1,2, Silke Britzen2, Lars Fuhrmann2,
Jana Schneeloch1, Nastaran Fazeli1, Kevin C. Harrington2,4, and J. Anton Zensus2
1
I. Physikalisches Institut der Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany
e-mail: zajacek@cft.edu.pl
2
Max-Planck-Institut für Radioastronomie (MPIfR), Auf dem Hügel 69, 53121 Bonn, Germany
3
Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland
4
Argelander Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
Received 8 May 2018 / Accepted 20 June 2019
ABSTRACT
Context. The empirical relations between supermassive black holes and their host spheroids point towards the crucial role of galactic
nuclei in affecting the properties of their hosts. A detailed understanding of how the activity of a galactic nucleus regulates the growth
of its host is still missing.
Aims. To understand the activity and the types of accretion of supermassive black holes in different hosts, it is essential to study the
radio-optical properties of a large sample of extragalactic sources. In particular, we aim to study the radio spectral index trends across
the optical emission line diagnostic diagrams to search for potential (anti)correlations.
Methods. To this goal, we combined flux densities from the radio FIRST survey at 1.4 GHz (with the flux density range
10 mJy ≤ F1.4 ≤ 100 mJy) for 396 SDSS sources at intermediate redshift (0.04 ≤ z ≤ 0.4) with the Effelsberg radiotelescope measurements
at 4.85 GHz and 10.45 GHz. The information about the optical emission-line ratios is obtained from the SDSS-DR7 catalogue.
Results. Using the Effelsberg data, we were able to infer the two-point radio spectral index distributions for star-forming galaxies,
composite galaxies (with a combined contribution to the line emission from the star formation and AGN activity), Seyferts, and low
ionization narrow emission region (LINER) galaxies.
Conclusions. While studying the distribution of steep, flat, and inverted sources across optical diagnostic diagrams, we found three
distinct classes of radio emitters for our sample: (i) sources with a steep radio index, high ionization ratio, and high radio loudness,
(ii) sources with a flat radio index, lower ionization ratio, and intermediate radio loudness, (iii) sources with an inverted radio index,
low ionization ratio, and low radio loudness. The classes (i), (ii), and (iii) cluster mainly along the transition from Seyfert to LINER
sources in the optical diagnostic (Baldwin, Phillips & Telervich; BPT) diagram. We interpret these groups as a result of the recurrent
nuclear-jet activity.
Key words. radio continuum: galaxies – methods: observational – techniques: spectroscopic – galaxies: active
1. Introduction
In previous decades, several correlations between the mass of
supermassive black holes (SMBH) and the properties of their
host spheroids (spheroidal mass, luminosity, stellar velocity dispersion)
point towards the co-evolution between SMBHs and
host galaxies (see Magorrian et al. 1998; Ferrarese & Merritt
2000; Gültekin et al. 2009; Kormendy & Ho 2013; Busch 2016,
and references therein). There are several observational studies
that point towards the relationship between black hole activity
and star-formation rate in the hosts of active galactic nuclei
(AGN, see e.g. Heckman & Kauffmann 2006).
In addition, the observed bimodality in the colours of local
galaxies (Strateva et al. 2001; Kauffmann et al. 2003; Baldry
et al. 2004; Balogh et al. 2004) points towards the correlation
between the star formation activity and the morphological type
of the galaxy. The more massive elliptical and lenticular galaxies
are preferentially located in the massive red cloud, while
less massive spiral and irregular galaxies are located in the blue
Table A.1 is also available at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.
u-strasbg.fr/viz-bin/cat/J/A+A/630/A83
cloud. The intermediate region, the so-called “green valley”, is
far less occupied (Faber et al. 2007) and the “green” sources
belong to mixed types, that is, red spirals. This implies that the
AGN are involved in the process of star formation quenching,
which is commonly referred to as AGN feedback in galaxy evolution
theories and simulations.
A useful tool for distinguishing the galaxies with different
prevailing photoionization sources is the Baldwin, Phillips,
and Terlevich diagram (BPT, Baldwin et al. 1981), in which
the source location is determined by a pair of low-ionization,
emission-line intensity ratios. A commonly used pair is the ratio
[N ii]/Hα and [O iii]/Hβ (see Fig. 1, right panel), but ratios of
other line intensities of a similar wavelength can be used as
well. BPT diagrams include forbidden lines, which are for AGN
sources associated with the narrow line region (NLR) and hence
type 2 AGN.
The emission-line ratios depend on the strength and shape
of the ionizing radiation field, as well as the physical properties
of the line-emitting gas including gas density, metal abundances,
dust, and cloud thickness (e.g. Veilleux & Osterbrock
1987; Komossa & Schulz 1997; Binette et al. 1997; Groves
et al. 2004a,b; Richardson et al. 2016). Systematic trends and
Article published by EDP Sciences A83, page 1 of 19
76 CHAPTER 2. PAPER 1: RADIO-OPTICAL PROPERTIES OF ACTIVE GALAXIES
A&A 630, A83 (2019)
correlations in different sections of the diagnostic diagrams have
been traced back to systematic changes in the ionization parameter,
the shape of the ionizing continuum, the fraction of matterbound
clouds, and/or the role of metal abundances.
According to a given set of ratios, four spectral classes of
galaxies are commonly distinguished. In star-forming galaxies
(SF), the ionizing flux is provided mostly by hot, massive,
young stars and associated supernovae that are surrounded by
HII regions. They have lower [OIII]/Hβ and [NII]/Hα ratios
than pure AGN sources (see also Figs. 1 and 2). In between
SF and AGN sources are composite (COMP) galaxies, with a
mixed contribution from star formation (HII regions) and AGN.
The AGN spectral class was further subdivided into Seyfert
2 sources (Sy) and low-ionization nuclear emission regions
(LINERs). LINERs are characterized by a lower [OIII]/Hβ
ratio in comparison with Seyfert 2 AGN sources and a higher
[NII]/Hα ratio with respect to star-forming sources (both SF and
COMP).
Systematic changes of line ratios across different regimes,
from the HII regime across the composite region and into
the AGN regime are seen in spatially-resolved spectroscopy
of nearby Seyfert galaxies (e.g. Bennert et al. 2006a,b;
Scharwächter et al. 2011), while Schulz & Fritsch (1994)
speculated about an ionization sequence from the AGN into
the LINER regime, based on systematic continuum-dilution
processes.
Radio galaxies are generally considered as active galaxies
that are luminous in radio bands. Strittmatter et al. (1980) argued
that the radio loudness of quasars, which is typically defined
as the ratio of the radio to the optical flux densities, shows
a certain degree of bimodality. Kellermann et al. (1989) confirmed
the bimodality in the radio loudness in the sense that
radio-quiet quasars are five to ten times more frequent than
radio-loud quasars, that is, they have radio emission comparable
to the optical emission. A similar result was also obtained by
Kellermann et al. (2016). Recent studies based on deep radio
studies, namely the FIRST (Faint Images of the Radio Sky at
Twenty centimeters) and the NVSS (National Radio Astronomy
Observatory Very Large Array Sky Survey; Becker et al. 1995;
Condon et al. 1998), in combination with sensitive optical surveys
SDSS (Sloan Digital Sky Survey) and 2dF (Two Degree
Field Survey; York et al. 2000; Croom et al. 2001) demonstrate
the large scatter in the radio loudness. They are, however, generally
inconclusive about the bimodal character of the distribution
(White et al. 2000; Ivezi´c et al. 2002; Cirasuolo et al. 2003a,b;
Laor 2003).
For a sample of galaxies, it was possible to determine the
estimates of black hole masses and hence study the dependence
of the radio loudness, R = FνR
/FνO
, on the Eddington ratio,
η ≡ LBol/LEdd, where FνR
and FνO
are monochromatic radio and
optical flux densities at frequencies νR and νO, respectively, and
LBol and LEdd are the bolometric luminosity and the Eddington
limit of the AGN. The general trend found is that the radio loudness
increases with a lower Eddington ratio, that is, there seems
to be an anti-correlation between R and η with a large scatter
(Ho 2002; Sikora et al. 2007). This trend is so far consistent
with the hardness-luminosity diagram for X-ray binaries (Fender
et al. 2004; Svoboda et al. 2017) and leads to the conclusion that
accretion at lower Eddington rates leads to smaller cooling rates,
and hence to hot, geometrically thick, and optically thin radiatively
inefficient accretion flows (RIAFs, Ichimaru 1977; Rees
et al. 1982). RIAFs are often modelled as advection-dominated
flows (ADAFs, Narayan & Yi 1995), which can launch jets
more effectively (Rees et al. 1982) than colder, optically thick,
Fig. 1. Distribution of the low-flux and high-flux samples in the
redshift-flux plane and in the BPT diagram. Top panel: two samples
of radio galaxies in the redshift-flux density plane: a high-flux sample
of 119 sources previously analysed by Vitale et al. (2015a) and a sample
extended towards lower radio flux densities at 1.4 GHz, 10 mJy ≤ F1.4 ≤
100 mJy (black points). The grey points represent a subset of the parent
sample in the redshift range of 0.04 ≤ z ≤ 0.4. Bottom panel: selected
radio galaxies for the Effelsberg observations in the [NII]-based BPT
diagnostic diagram (black points). The sample of radio galaxies with
F1.4 ≥ 100 mJy analysed by Vitale et al. (2015a) is denoted by green
crosses. The parent sample is colour coded depending on the density per
bin in the [OIII]–[NII] plane (bin size is set to 0.1 along both ratios).
and geometrically thin accretion discs that are associated with
larger Eddington ratios due to efficient cooling (e.g. Shakura
& Sunyaev 1973). This yields the trend of larger radio loudness
for sources with lower Eddington ratios. However, since
R ∝ 1/LO, where LO is the optical luminosity, and η ∝ LO, the
anti-correlation is generally expected and one should be careful
when interpreting the results. Moreover, optical emission as a
tracer of accretion rate only makes sense for type I AGN, since
for type II sources the optical emission is influenced by obscuration
and continuum dilution (Schulz & Fritsch 1994). Therefore,
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M. Zajaˇcek et al.: Radio spectral index distribution
Fig. 2. Low- and high-flux sample distribution in different optical diagnostic (BPT) diagrams. Left: [NII]-based diagnostic diagrams of the parent
(grey) and Effelsberg samples: a low-flux sample represented by black points and a high-flux sample denoted by green crosses. Demarcation lines
were derived by Kewley et al. (2001) to set an upper limit for the star-forming galaxies and by Kauffmann et al. (2003) to distinguish purely
star-forming galaxies. The dividing line between Seyferts and LINERs was derived by Schawinski et al. (2007). The new Effelsberg sample
(black points), extended towards lower radio fluxes, covers the whole diagnostic diagram. Middle: same samples as in the left panel in [SII]-based
diagnostic diagram. Right: high- and low-flux samples in [OI]-based diagram.
adding more parameters to the study of trends, such as spectral
slopes in the radio domain, may shed more light on the
radio-optical properties of galaxies and the physical processes
involved, namely the formation, acceleration, and collimation of
jets (Sikora et al. 2007) or the effect of mergers on the radio
loudness of the AGN (Chiaberge et al. 2015).
At frequencies 10 GHz, the radio-continuum spectra are
dominated by non-thermal synchrotron emission with the
characteristic power-law slope, Sν ∝ να
, while the thermal
bremsstrahlung (free-free) emission is negligible (Duric et al.
1988), contributing less than 10% at 10 GHz (Gioia et al. 1982),
and becomes more prominent towards mm-wavelengths. Concerning
the synchrotron spectral slope for radio galaxies with
jets, primary components (cores) are generally self-absorbed
with positive slopes of α ∼ 0.4, while secondary components
have negative spectral indices with mean values α ∼ −0.7 (Eckart
et al. 1986), which is consistent with optically thin synchrotron
emission. The integrated radio spectrum of radio jets is typically
associated with a flat spectral slope due to the superposition of
self-absorbed synchrotron spectra.
The role of radio galaxies in the galaxy evolution at low to
intermediate redshifts (z < 0.7) is unclear (Tadhunter 2016). In
general, the star formation activity in their hosts is expected to be
one order of magnitude smaller than for the peak of quasar and
star-formation activity at z ≈ 1.9 (Madau & Dickinson 2014).
However, the AGN in these radio galaxies are expected to come
through phases of intermittent accretion activity (Czerny et al.
2009), as well as mergers that influence the overall host properties,
and are expected to prevent the host gas reservoirs from
cooling and forming stars.
The contribution of different sources to the overall radio
luminosity of galaxies remains largely unclear. The value of the
radio spectral index α helps to distinguish between the prevalence
of optically thin and optically thick emission mechanisms.
Laor et al. (2019) made use of the high-resolution Very Large
Array (VLA) observations at 5 and 8.4 GHz of optically selected
radio-quiet (RQ) Palomar-Green (PG) quasars. They determined
the corresponding spectral slopes α5/8.4 for 25 RQ PG sources
and found a significant correlation between the slope value and
the Eddington ratio. Specifically, high Eddington-ratio quasars
(L/LEdd > 0.3) have steep spectral slopes, α5/8.4 < −0.5,
while lower Eddington-ratio sources (L/LEdd < 0.3) have flat
to inverted slopes, α5/8.4 > −0.5. A correlation is also found
with an Eigenvector I (EV1) set of properties (Fe ii/Hβ, Hβasym,
X-ray slope αX; see Boroson & Green 1992; Sulentic et al. 2000;
Marziani et al. 2001), where the flat to inverted RQ PG sources
have low Fe ii/Hβ and a flat soft X-ray slope. Laor et al. (2019)
found a dichotomy between radio-quiet PG quasars and 16 radioloud
(RL) PG quasars, which in contrast with RQ sources do not
exhibit the correlations with EV1 and the radio slope is instead
determined by the black hole mass, which implies a different
radiation mechanism for RL sources. These findings provide a
motivation for the investigation of further correlations between
radio slopes and optical emission-line properties for a larger
sample of radio galaxies.
Previously, we performed radio continuum observations of
intermediate redshift (0.04 ≤ z ≤ 0.4) SDSS-FIRST sources
at 4.85 GHz and 10.45 GHz to determine their spectral index
and curvature distributions (Vitale et al. 2015a). This sample
included star-forming, composite, Seyfert, and LINER galaxies
that obeyed the flux density cut of ≥100 mJy at 1.4 GHz (see
Fig. 1, green crosses). Vitale et al. (2015a) searched for the radio
spectral index trends in BPT diagnostic diagrams as well as for
the relation between optical and radio properties of the sources.
For the limited sample of 119 sources, they found a rather
weak trend of spectral index flattening in the [NII]-based diagnostic
diagram along the star-forming–composite–AGN Seyfert
branch.
The radio spectral index flattening trend triggered the motivation
to study more sources with lower radio continuum fluxes
at 1.4 GHz. The sample was extended by 381 additional sources
towards lower radio flux densities at 1.4 GHz, with integrated
flux densities 10 mJy ≤ F1.4 ≤ 100 mJy. Using the cross-scan
observations conducted by the 100-m Effelsberg radio telescope,
for point-like sources we determined flux densities at
two frequencies, 4.85 GHz and 10.45 GHz, which enabled us to
determine the spectral indices α[1.4−4.85] (for 298 sources) and
α[4.85−10.45] (for 90 sources).
In this paper, we present the findings based on the radiooptical
properties of the low-flux sample along with radiobrighter
sources previously reported in Vitale et al. (2015a).
We searched for any trends of the radio spectral slope in the
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A&A 630, A83 (2019)
low-ionization diagnostic diagrams. In other words, we were
interested in whether the changes in emission-line ratios across
the BPT diagram are systematically reflected in the radio spectral
index. Furthermore, the relation between the spectral index
and the radio loudness of the sources was unknown.
The paper is structured as follows. In Sect. 2 we introduce
the optical (SDSS survey) and radio (FIRST) samples used in
our study. Subsequently, in Sect. 3 we present the selection of
radio sources for follow-up observations with the Effelsberg 100m
telescope at two higher frequencies. The basic statistical properties
of spectral index distributions are presented in Sect. 4 in
combination with the optical properties of the sources. Subsequently,
we describe the fundamental trends of the radio spectral
slope in optical diagnostic diagrams as well as with respect to the
radio loudness in Sect. 5. We continue with the interpretation of
the results in Sect. 6. Finally, we summarize the main results in
Sect. 7. Additional materials, specifically radio flux densities for
new low-flux sources, are included in Appendix A.
2. Radio and optical samples
2.1. Sloan Digital Sky Survey
The Sloan Digital Sky Survey (SDSS) is a photometric and spectroscopic
survey of celestial sources that covers one quarter of
the north Galactic hemisphere (York et al. 2000; Stoughton et al.
2002). The spectra and magnitudes have been obtained by a
2.5-m wide field-of-view (FOV) telescope at Apache Point in
New Mexico, USA. The spectra have an instrumental resolution
of ∼65 km s−1
in the wavelength range of 380–920 nm. The identified
galaxies have a median redshift of 0.1. The spectra were
obtained by fibers with 3 diameter (the linear scale of 5.7 kpc
at z = 0.1), which makes the sample sensitive to aperture effects,
that is, low-redshift galaxies are dominated by nuclear emission
(see e.g. Tremou et al. 2015).
The seventh data release of SDSS (SDSS DR7, Abazajian
et al. 2009) contains parameters of ∼106
galaxies inferred from
the spectral properties based on the Max Planck Institute for
Astrophysics (MPIA) and Johns Hopkins University (JHU)
emission-line analysis. The stellar synthesis continuum spectra
(Bruzual & Charlot 2003) were applied for the continuum subtraction,
after which emission line characteristics were derived.
In particular, SDSS DR7 contains the emission-line characteristics
of low-ionization lines that are used to distinguish starforming
galaxies from AGN (Seyfert galaxies and LINERs or
high-excitation and low-excitation systems, respectively) in the
diagnostic diagrams. DR7 also contains the source images as well
as stellar masses inferred from the broad-band fitting of spectral
energy distributions by stellar population models.
2.2. Faint Images of the Radio Sky at Twenty-centimeters
Survey
The Faint Images of the Radio Sky at Twenty-centimeters Survey
(FIRST Becker et al. 1995) was performed by the VeryLarge-Array
(VLA) in its B-configuration at 1.4 GHz. The
FIRST survey covers ∼10 000 deg2
in the north Galactic cap,
partially overlapping the region mapped by SDSS. The sky
brightness was measured with a beam-size of 5.4 and an
rms sensitivity of ∼0.15 mJy beam−1
. At the sensitivity level
of ∼1 mJy, the FIRST survey contains ∼106
sources, of which
about a third are resolved with structures on the angular scale of
2 –30 (Ivezi´c et al. 2002). The survey contains both the peak
and the integrated flux densities, which allows us to distinguish
resolved and unresolved sources. The flux density measurements
have uncertainties smaller than 8%. The images for each source
are provided on the website.
2.3. SDSS-FIRST cross-identification
As described in Vitale et al. (2015a), we performed a crossidentification
of SDSS DR7 and FIRST source catalogues using
SDSS DR7 CasJobs, with a matching radius set to 1 (OMullane
et al. 2005). This results in a total of 37 488 radio-optical emitters
as a basis for further studies. This initial sample constitutes ∼4%
of SDSS sources and contains mostly active, metal-rich galaxies
(see also Vitale et al. 2012, for details).
As was already done in Vitale et al. (2015a) for a high-flux
sample, we apply the following selection criteria:
– the redshift limits, 0.04 ≤ z ≤ 0.4,
– the signal-to-noise lower limit of S/N > 3 on the equivalent
width EW of the emission lines used in the low-ionization
optical diagnostic diagrams.
The lower redshift limit of 0.04 is due to the fact that nearby
sources have angular sizes larger than the optical fiber used for
the SDSS survey. Hence they are dominated by their nuclear
emission (see e.g. Kewley et al. 2003). The upper redshift limit
is imposed to make sure that the emission-line diagnostics concerning
[N ii] and Hα lines is reliable, meaning that they fall into
the observable spectral window. By imposing the redshift constraints,
we obtain our parent sample with 9951 sources, which
are shown as grey points in the redshift-flux plot (see Fig. 1).
There is no evident dependency of the flux density on the redshift,
apart from the expected tendency of having more radio
galaxies towards lower radio flux densities.
Out of nearly 10 000 radio sources, only ∼1% of the sources
has the integrated flux density at 1.4 GHz above 100 mJy. The
combined radio-optical properties of these brightest sources
were investigated in Vitale et al. (2015a). By decreasing the
lower boundary of the flux density cut by one order of magnitude
to 10 mJy, the number of sources increases to 5.6%, that is,
by a factor of five.
Most of the sources of the parent sample, 93.5%, have flux
densities at 1.4 GHz below 10 mJy. Under the assumption that
many of these sources have steep to flat spectra, Sν ∝ να
, where
α ≤ 0, the detection of their flux density at frequencies larger
than 1.4 GHz would be beyond the detection limit of the Effelsberg
telescope, which is ∼5 mJy.
In Fig. 1, the subset of the parent sample in the redshift range
0.04 < z < 0.4 is plotted in the [N ii]-diagnostic diagram with
the aim of showing the source density in the [O iii]–[N ii] plane.
We see that most of the sources are located in the star-forming
composite branch, where AGN are supposed to turn on.
3. Effelsberg sample and observations
The aim of the previous study by Vitale et al. (2015a) was
to analyse the radio-optical properties across the parent sample.
The radio information was complemented by the radio flux
density measurements at two higher frequencies – 4.85 and
10.45 GHz – using the 100-m Effelsberg radio telescope. Vitale
et al. (2015a) selected the sources from the parent sample using
the lower limit for the integrated flux density of F1.4 ≥ 100 mJy
at 1.4 GHz. In total, 119 sources selected according to the criteria
above were observed by the Effelsberg radio telescope at
two additional frequencies. Thus, for these sources it was possible
to determine the spectral slopes α[1.4−4.85] and α[4.85−10.45].
This sample is denoted as a high-flux sample and the main
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79
M. Zajaˇcek et al.: Radio spectral index distribution
properties of the sources are summarized in Table A.1 of Vitale
et al. (2015a).
In Fig. 1, the sample occupies the upper part of the redshiftintegrated
flux plot. Due to the large radio flux, the sources are
dominated by galaxies with an AGN. In the [N ii]-based optical
diagnostic diagram (BPT diagram) the high-flux radio-optical
sample is dominated by composite sources, Seyfert, and LINER
galaxies (see green points in Fig. 1). There are only few metalrich
star-forming sources whose radio emission generally originates
in the shocks from supernovae and in (re)ignited AGN and
jet activity.
Therefore the high-flux sample is certainly not complete in a
statistical sense and the results published in Vitale et al. (2015a)
are not representative of the whole radio-optical parent sample.
This was the main motivation for the extension of the Effelsberg
sample towards lower radio flux densities; the integrated
radio flux density at 1.4 GHz was considered in the interval
10 mJy < F1.4 < 100 mJy, that is, we decreased the upper and
the lower flux limit of the high-flux sample by one order of magnitude.
As shown in Figs. 1 and 2, the low-flux sample (black
points) covers the whole [N ii]-based diagnostic diagram and its
coverage is also more uniform. It should therefore better represent
the radio-optical properties of the parent sample. However,
the bias towards the AGN and LINER sources is partially maintained,
as can be inferred from the [N ii]-, [S ii]-, and [O i]-based
diagrams in Fig. 2.
By imposing the redshift limits 0.04 ≤ z ≤ 0.4, as well as the
signal-to-noise criterion on the equivalent width of the optical
emission lines, S/N > 3, the low-flux sample initially consisted
of 381 galaxies with the integrated flux densities 10 mJy ≤ F1.4 ≤
100 mJy. These sources were first observed at 4.85 GHz with
the 100-m telescope in Effelsberg. Observations were performed
between April 2014 and June 2015. The receiver at 4.85 GHz
is mounted on the secondary focus of the Effelsberg antenna. It
has multi-feed capabilities with two horns, which allow real-time
sky subtraction in every subscan measurement. The total intensity
of each source was determined via scans in the azimuth and
the elevation. According to the brightness of the source, several
subscans were used, ranging from 6 up to 24. In the data reduction
process, subscans were averaged to produce final subscans
used for further processing. Each scan had a length equal to 3.5
of that of the beam size at the corresponding frequency to ensure
the correct subtraction of linear baselines.
Before combining the subscans, we checked each for possible
radio interference, bad weather effects, or detector instabilities.
During each observational run, we observed standard bright
calibration sources, such as 3C286, 3C295, and NGC 7027,
which were used for correcting gain instabilities and elevationdependent
antenna sensitivity. Finally, we used these sources for
the absolute flux calibration. The whole data reduction was performed
using a set of Python and Fortran scripts. The flux density
was obtained by fitting Gaussian functions to the signal in
the averaged single-dish cross scans. Further details on the data
reduction can be found in Vitale et al. (2015a), who applied the
same routines for brighter sources.
From 381 sources, we managed to determine the reliable
flux density at 4.85 GHz for 298 sources. The flux densities
range between 350 mJy and 4 mJy with the mean and median
values of 30 mJy and 17 mJy, respectively. Other sources were
too faint or extended at least in one direction and therefore it
was not possible to reliably determine an integrated flux density.
For 10.45 GHz observations, 256 sources out of 298 were
scheduled for observing based on the extrapolated flux density
based on the non-simultaneous 1.4 GHz and 4.85 GHz flux densities.
At 10.45 GHz some sources were too faint, were extended
at least in one direction, or the reliable flux density determination
was not possible due to a higher sensitivity to weather effects at
10.45 GHz. In the end, we obtained flux densities at 10.45 GHz
for 90 sources. The maximum and minimum flux densities are
206 mJy and 6 mJy, respectively. The mean and median values
are 32 mJy and 19 mJy, respectively. The three non-simultaneous
flux densities for 90 sources in the low-flux sample, F1.4, F4.85,
and F10.45, are listed in Table A.1, along with the radio spectra
for each source as well as the mean radio spectrum for each
galaxy spectral class (star-forming, composite, AGN Seyfert,
and LINER galaxies).
In the following analysis, unless otherwise stated, we use
the low-flux sample in combination with the high-flux sample of
Vitale et al. (2015a). For the study of radio continuum properties
between 1.4 and 4.85 GHz, we have 298 low-flux sources and
119 high-flux sources available. Between 4.85 and 10.45 GHz,
there are 90 low-flux and 119 high-flux sources.
4. Spectral index properties
4.1. General properties of radio spectral index distributions
We present the radio flux densities at 1.4 (FIRST), 4.85,
and 10.45 GHz (both Effelsberg) for 90 low-flux sources in
Table A.1. The flux densities at 1.4 GHz (FIRST) and 4.85 GHz
(Effelsberg) are non-simultaneous (more than one year apart
from each other), while the Effelsberg observations at 4.85 GHz
and 10.45 GHz were performed within one year of each other.
For high-flux sources, the analysis as well as the optical and
the radio images were presented in Vitale et al. (2015a). The
catalogue of the high-flux sources is available in Vitale et al.
(2015b), where the (quasi)-simultaneous flux densities (obtained
during a single observing session) are listed.
For the flux density in the radio domain, we assume
the power-law dependency on frequency, using the notation
F(ν) ∝ ν+α
, where α is the spectral index. Based on the nonsimultaneous
measurements of flux densities F1.4 (FIRST) and
F4.85 (Effelsberg), we calculated the spectral index α[1.4−4.85]
using
α[1.4−4.85] =
log (F1.4/F4.85)
log (1.4/4.85)
· (1)
We note that there is a large beam-size difference between
the VLA in the B-configuration and the Effelsberg telescope at
4.85 GHz: the half-power beam-width (HPBW) at 20 cm for the
VLA is θ1.4
HPBW ≈ 4.3 , whereas for the Effelsberg telescope at
4.85 GHz, θ4.85
HPBW ≈ 2.4 . This could have led to the exclusion
of extended structures for the VLA measurements for approximately
one third of the sources that are clearly extended on the
scales of 2 −30 (Ivezi´c et al. 2002) and thus, for such extended
sources, it influences the integrated flux densities and spectral
indices α[1.4−4.85] as well. Moreover, the observations were more
than one year apart from each other, thus possibly contaminated
by the variability of the sources. We include the distribution of
α[1.4−4.85] for completeness, however, due to the potential beamsize
effect, we exclude it from further analysis.
For the spectral index at higher frequencies, α[4.85−10.45],
which is determined analogously to Eq. (1) as
α[4.85−10.45] =
log (F4.85/F10.45)
log (4.85/10.45)
, (2)
the effect of excluding extended structures is largely diminished,
since for the analysis in this paper we considered only point
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A&A 630, A83 (2019)
2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5
0
10
20
30
40
50
60
spectral index 1.4-4.85 GHz
2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5
0
5
10
15
20
25
30
35
spectral index 4.85-10.45 GHz
Fig. 3. Distributions of spectral indices α[1.4−4.85] and α[4.85−10.45]. Left panel: a two-point spectral index (α[1.4−4.85]) distribution for the combined
low-flux and high-flux sample (in total 417 sources). Right panel: a two-point spectral index (α[4.85−10.45]) distribution for the combined low-flux
and high-flux sample (in total 209 sources).
sources that were consistent with HPBWs of 2.4 and 1.1 at
4.85 GHz and 10.45 GHz, respectively. Moreover, the observations
at 4.85 GHz and 10.45 GHz were performed within one
year of each other, hence the spectral index α[4.85−10.45] captures
the integrated radio continuum better than the spectral index
α[1.4−4.85], which can be influenced by the core emission due to
the small VLA beam width.
The uncertainty of the spectral index σα was calculated by
propagating the measurement errors of flux densities at the corresponding
frequencies,
σα =
1
| log (4.85/10.45)|
(σ4.85/F4.85)2 + (σ10.45/F10.45)2, (3)
where σ4.85 and σ10.45 are the measurement uncertainties of flux
densities at the corresponding frequencies. We show exemplary
error bars in Fig. 4. The median value of σα at higher frequencies
for the joint sample is σα = 0.1.
The distributions of spectral indices α[1.4−4.85] and α[4.85−10.45]
for all observed sources are plotted in Fig. 3 in the left and the
right panel, respectively. For the lower frequencies, the mean
spectral index is α[1.4−4.85] = −0.25 ± 0.54 (median −0.36). For
the higher frequencies, the mean spectral index is α[4.85−10.45] =
−0.51 ± 0.63 (median −0.58). The two-dimensional distribution
of spectral indices at both lower and higher frequencies is in
Fig. 4.
For the general classification of radio spectra with the powerlaw
shape F(ν) ∝ ν+α
, we use the following categories based on
the spectral slope α:
(i) α < −0.7, for short denoted as steep, which are typical for
optically thin synchrotron structures, where electrons have
cooled off, such as radio lobes;
(ii) −0.7 ≤ α ≤ −0.4, denoted as flat, with the mixed contribution
of optically thin and self-absorbed synchrotron emission,
typical for jet emission;
(iii) α > −0.4, denoted as inverted, which are characteristic for
sources where synchrotron self-absorption becomes important,
such as in AGN core components.
This division reflects the distributions of the spectral index for
lower and higher frequencies as found for samples of radio-loud
galaxies, such as in the S5 polar-cap sample (Eckart et al. 1986).
We adopt it for all the histograms of the radio spectral index,
from Fig. 3 onwards.
The mean and median radio spectra calculated for different
spectral classes according to the BPT diagram – star-forming,
2.0 1.5 1.0 0.5 0.0 0.5 1.0
Spectral index [1.4 4.85GHz]
2.0
1.5
1.0
0.5
0.0
0.5
1.0
Spectralindex[4.8510.45GHz]
Fig. 4. Two-dimensional distribution of spectral indices at lower
(x-axis) and higher frequencies (y-axis). The green points mark the
high-flux sources, while the red crosses depict the low-flux sample.
Some of the sources have error bars for α[4.85−10.45] to show typical
uncertainties of the spectral index.
composites, Seyferts, LINERs – are scaled for comparison
in Fig. 5. The values of spectral indices for mean
spectra are 0.37, 0.28, 0.39, −0.01 at smaller frequencies
1.4 GHz−4.85 GHz and −0.71, −0.41, −0.81, −0.23 at higher
frequencies 4.85 GHz−10.45 GHz for star-forming, composite,
Seyfert, and LINER sources, respectively. Spectral indices for
median spectra, which were calculated from the spectra of
individual sources after the normalization with respect to the
mid-frequency, are 0.46, −0.22, −0.19, 0.02 at smaller frequencies
1.4 GHz−4.85 GHz and −0.88, 0.0, −0.59, 0.13 at higher
frequencies 4.85 GHz−10.45 GHz for star-forming, composite,
Seyfert, and LINER sources, respectively.
The distribution of spectral indices is very reminiscent of
the distribution that one finds for higher redshift quasars. The
S5-survey (Kuehr et al. 1981; Gregorini et al. 1984) shows
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M. Zajaˇcek et al.: Radio spectral index distribution
Fig. 5. Median and mean spectra for different spectral classes scaled for
the common value at the mid-frequency of 4.85 GHz.
the transition between the lobe and jet-dominated structures,
which are more prominent at lower radio frequencies, and the
flat to inverted cores that are dominant at higher radio frequencies.
Unfortunately, the spectral slope expected from the synchrotron
emission of supernova remnants, which are a clear
tracer of high-mass star formation, has a similar slope as the
radio lobe-jet structures. The radio emission from star-forming
regions can be expected to be relevant for objects on the division
lines between star-forming and Seyfert/LINER objects. In
the Seyfert/LINER domain of the diagnostic diagrams, objects
with starburst-AGN mixing can be found (e.g. Kewley et al.
2006; Davies et al. 2016). However, a detailed and sensitive
structural investigation at high angular resolution is required
to differentiate between the presumably extended radio contribution
from star formation and that of the core-jet-nucleus
structure of a radio-active AGN. This will be possible with
instruments dedicated for low-surface brightness investigations
like the Square Kilometer Array (SKA; see e.g. Agudo et al.
2015).
4.2. Radio spectral index between 1.4 and 4.85 GHz
The mean and median values of the spectral index α[1.4−4.85]
for the whole low-flux and high-flux sample are in Table 1.
LINER sources have the flattest median and mean radio spectral
indices in comparison with galaxies in other spectral classes.
This is also apparent in the histogram in Fig. 6 (left panel),
where we plot the two-point spectral index distribution for
each spectral class. Another way of representing this trend is
shown in the plot in Fig. 6 (right panel), which combines the
radio classification (steep, flat, inverted) and the optical spectral
classification of galaxies (SF, Comp, Sy, LINER). While
among the composites 50.5% are inverted sources and among
the Seyferts 44.5% are inverted sources, most of the LINERS
(58.8%) have inverted spectra. The fraction of steep sources
(α < −0.7) among LINER sources is only 17.6%, which is
comparable to composite sources (17.8%). The fraction of steep
Seyferts is 28.2%. In terms of the mean and median spectral
slopes, LINERs have the flattest index α[1.4−4.85] with a mean
of −0.22 and a median of −0.24, followed by the composites
with a mean and median of −0.25 and −0.40, respectively, and
the Seyferts with mean and median values of −0.31 and −0.49,
respectively.
Table 1. Mean, standard deviation, median, 16%-, and 84%-values of
the radio spectral index α[1.4−4.85], respectively, for each optical spectral
class of galaxies and the overall sample.
Spectral class Mean α[1.4−4.85] σ Median α[1.4−4.85] 16% P 84% P
SF −0.25 0.45 −0.33 −0.66 0.24
COMP −0.25 0.54 −0.40 −0.73 0.22
SY −0.31 0.61 −0.49 −0.83 0.21
LINER −0.22 0.50 −0.24 −0.72 0.26
Total −0.25 0.54 −0.36 −0.76 0.24
4.3. Radio spectral index between 4.85 and 10.45 GHz
In an analogous way to frequencies 1.4−4.85 GHz, we determine
the spectral index α[4.85−10.45] between the non-simultaneous
Effelsberg measurements at 4.85 GHz and 10.45 GHz, with the
mean and median values listed in Table 2. In this case, the
primary beam size is comparable, hence the resolution effects
should not be so significant as for 1.4 GHz obtained from
the FIRST survey. Those sources whose emission profiles in
cross-scans were clearly extended were excluded from further
analysis.
The distribution of the spectral index α[4.85−10.45] for each
optical spectral class is in Fig. 7 (left panel). The fractions of
three radio classes – steep, flat, and inverted – are calculated for
each spectral class in the right panel of Fig. 7, where composites
have the largest fraction of inverted sources (α > −0.4), 42.9%,
followed by LINERs, 37.9%. In terms of the overall fraction of
sources with a spectral index larger than α > −0.7 (non-steep
spectra), composites have the largest fraction with 73.9%, followed
by LINERs (66.3%) and Seyferts (58.3%). In the higher
frequency range 4.85−10.45 GHz, the composite sources have
the flattest spectral slope α[4.85−10.45], with a mean of −0.42
and a median of −0.43, followed by LINERs with mean and
median values of −0.46 and −0.59, respectively, and Seyferts
with a mean and median spectral slope of −0.63 and −0.64,
respectively.
The spectral-index distributions for the high-flux density
sample are dominated by sources with low spectral indices as
can be seen in the left column of Fig. 8 where we denote highflux
sources as HF and low-flux sources as LF. The α1.4/4.85 index
distribution has a median of −0.53 and a median width of 0.501
.
Towards higher frequencies the index even drops and the distribution
becomes narrower. The α4.85/10.45 index has a median of
−0.67 and a median width of 0.20. However, the distributions
have weak tails towards flatter spectra, indicating that several
sources contain flat spectrum components at a flux density level
lower than the fluxes for the steep components.
Therefore, the situation changes for the low-flux density
sample. The flux densities are lower now and for more sources
they are close to the typical fluxes of the flat components. Hence,
the portion of the sources with flat spectral index increases leading
to a more prominent shoulder towards the flat side of the
distributions (see the middle and right columns of Fig. 8). This
is very pronounced for the α1.4/4.85 index. For about 2/3 of the
sources (i.e. 89 out of 289) the 10.45 GHz flux drops below
the detection limit. Correspondingly, the α4.85/10.45 distribution
is biased towards flat-spectrum sources. For the low-flux density
sample, the α1.4/4.85 index distribution has a median of −0.26
and a median width of 0.33. The distribution is highly skewed
to the steep side and has a peak at −0.6. The α4.85/10.45 index
1
For the uncertainty in the median we quote the median deviation from
the median or twice the value if we refer to it as the width.
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0
5
SF
0
25
Comp
0
20
Sy
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
spectral index 1.4-4.85 GHz
0
25
LINER
SF Comp Sy LINER
steep
flat
inverted
4
7
13
18
(17.8%)
32
(31.7%)
51
(50.5%)
31
(28.2%)
30
(27.3%)
49
(44.5%)
32
(17.6%)
43
(23.6%)
107
(58.8%)
radio spectral index [1.4-4.85 GHz]
Fig. 6. Distribution of the spectral slope α[1.4−4.85] at lower frequencies among different spectral classes of galaxies. Left: two-point spectral index
distribution α[1.4−4.85] for different optical spectral classes of galaxies (SF, composites, Seyferts, and LINERs). The mean and median values are
listed in Table 1. Right: fractional distribution of steep, flat, and inverted sources among star-forming, composite, Seyfert, and LINER galaxies.
0
2
SF
0
5
Comp
0
10
Sy
2.0
1.5
1.0
0.5
0.0
0.5
1.0
1.5
spectral index 4.85-10.45 GHz
0
20
LINER
SF Comp Sy LINER
steep
flat
inverted
5
3
4
11
(26.2%)
13
(31.0%)
18
(42.9%)
25
(41.7%)
21
(35.0%)
14
(23.3%)
32
(33.7%)
27
(28.4%)
36
(37.9%)
radio spectral index [4.85-10.45 GHz]
Fig. 7. Distribution of the spectral slope α[4.85−10.45] at higher frequencies among different spectral classes of galaxies. Left: two-point spectral index
distribution α[4.85−10.45] for different optical spectral classes of galaxies (SF, composites, Seyferts, and LINERs). The mean and median values are
listed in Table 1. Right: fractional distribution of steep, flat, and inverted sources among star-forming, composite, Seyfert, and LINER galaxies.
distribution has median of −0.25 and a width of 0.86, with a
similar but more pronounced 0.3 wide secondary peak around
α4.85/10.45 = −0.10. Separate plots of the α1.4/4.85 index for the
sources with (median −0.11, median width 0.38) and without
(median −0.36, width 0.31) a 10.45 GHz measurement show
that the low-spectral index α1.4/4.85 of the 10.45 GHz detected
sources is also flatter by about 0.25.
The dropout in sources with α4.85/10.45 measurements in our
low-flux sample is predominantly an effect of the flux sensitivity
we reached. From the uncertainties in Table A.1 we estimate
a 3σ flux density limit of 12 mJy. We find that about 70% of
all sources without α4.85/10.45 measurements indeed fall below
this flux density limit if one uses their low-frequency spectral
index combined with the 4.85 GHz flux density to predict
their 10.45 GHz flux density. A stronger spectral steeping
towards 10.45 GHz and the effect of radio-source angular extension
may account for the remaining 30%. For the observations
at 4.85 GHz, 64 sources out of the original 381 (16.8%) were
extended at least in one direction of cross-scans (larger than the
HPBW at 4.85 GHz ∼ 144 ). For the subsequent observations at
10.45 GHz of 256 selected sources, we had 50 sources (19.5%)
broader than the HPBW of 66 at least in one direction. We
excluded the extended sources from further analysis due to the
fact that it was not possible to determine flux densities by Gaussian
fitting to the combined cross-scan intensity profiles.
In terms of properties in the diagnostic diagrams, the sources
with and without α4.85/10.45 measurements do not differ significantly.
There, median log([O iii]/Hβ) and log([N ii]/Hα) values
of 0.23 ± 0.19 and −0.03 ± 0.11 and values of 0.22 ± 0.22
and −0.09 ± 0.14 are reached, respectively. However, as in
the high-flux density sample, the trend that the sources with
flat-spectrum components show a higher excitation remains:
for the sources with α4.85/10.45 measurements, we find median
log([O iii]/Hβ) and log([N ii]/Hα) values of 0.26 ± 0.19 and
−0.03 ± 0.11, and for the sources without α4.85/10.45 measurements,
we find log([O iii]/Hβ) and log([N ii]/Hα) values of
0.19 ± 0.26 and −0.10 ± 0.15, respectively.
5. Trends of the spectral index in optical diagnostic
diagrams
While in the previous section we looked for trends in the radio
spectral index between different activity classes as traced by
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M. Zajaˇcek et al.: Radio spectral index distribution
0
2
4
6
8
10
12
14
16
18 HF sample, α1.4/4.85
2 1 0 1 2
0
5
10
15
20
25 HF sample, α4.85/10.45
0
5
10
15
20
25
30
35 LF sample, α1.4/4.85
2 1 0 1 2
0
1
2
3
4
5
6
7
8
9 LF sample, α4.85/10.45
0
5
10
15
20
25
30 without 10.45 GHz
detections
LF sample, α1.4/4.85
2 1 0 1 2
0
1
2
3
4
5
6
7
8
9 with 10.45 GHz
detections
LF sample, α1.4/4.85
Fig. 8. Low-flux density sample experiences an increasing influence of flat-spectrum sources. Top and bottom left: α1.4/4.85 and α4.85/10.45 index
distribution for the high-flux density sample (HF). Top and bottom middle: α1.4/4.85 and α4.85/10.45 index distribution for the low-flux density sample
(LF) (two sources – not shown here – have a α4.85/10.45 below −3). Top and bottom right: α1.4/4.85 index distribution for the low-flux sources (LF)
without and with 10.45 GHz measurements.
the optical diagnostic diagram, we will pursue the reverse way
and investigate how different radio spectral indices are reflected
in the optical diagnostic diagram. Considering the radio luminosity
of the sources at 1.4 GHz, L1.4 GHz
2
, expressed in erg s−1
(which traces better the radio-core emission due to a smaller
beam size of the VLA), in the parent sample the general trend
is that the radio luminosity increases from the star-forming,
through the composites, LINERs, and up to the Seyfert sources
(Fig. 9, top row). The distribution of radio luminosities implies
that our source selection lacks metal-rich star-forming galaxies
with radio luminosities below log(L1.4 GHz/erg s−1
) < 40.5,
and as redshift increases, systematically fainter sources in all
luminosity bins. Hence, our radio measurements and analysis
mostly trace nearby luminous, active galaxies in the composite–
LINER–Seyfert regions. This is demonstrated in Fig. 9, where
we first show the subsample of the parent sample with the
2
The integrated flux at ν0 = 1.4 GHz in Jansky is derived from the
FIRST survey. We derive the luminosity distance, DL, from the redshift,
using a standard cosmology with H0 = 70 km s−1
Mpc−1
, Ωm = 0.3 and
ΩΛ = 0.7. The luminosity is then given by L1.4 GHz = 4πD2
L ν0 fν0
.
Table 2. Mean, standard deviation, median, 16%-, and 84%- values of
the spectral index α[4.85−10.45], respectively, for each optical spectral class
of galaxies and the overall sample.
Spectral class Mean α[4.85−10.45] σ Median α[4.85−10.45] 16% P 84% P
SF −0.61 0.65 −0.65 −1.02 0.05
COMP −0.42 0.80 −0.43 −0.90 0.19
SY −0.63 0.52 −0.64 −0.89 −0.29
LINER −0.46 0.59 −0.59 −0.95 0.02
Total −0.51 0.63 −0.58 −0.92 0.00
integrated flux density at 1.4 GHz greater than 10 mJy and
less than 1000 mJy (middle row). For the sources detected at
4.85 GHz as well as 10.45 GHz (low + high sample, 209 sources;
see the bottom row), we see distribution peaks in the SeyfertLINER
part of the optical diagram as for the flux-limited subsample
for all luminosity bins, with the apparent loss of radio
sources in the composite and star-forming parts in the lowest
luminosity bin, log (L1.4 GHz) < 40.5, due to source drop-outs.
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A&A 630, A83 (2019)
1.0 0.5 0.0 0.5
log([NII]/H )
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
SF comp
LINER
Seyfert
log(L1.4GHz)<40.5
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
40.5<log(L1.4GHz)<41.2
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
log(L1.4GHz)>41.2
1.0 0.5 0.0 0.5
log([NII]/H )
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
SF comp
LINER
Seyfert
10mJy F1.4 1000mJy
log(L1.4GHz)<40.5
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
10mJy F1.4 1000mJy
40.5<log(L1.4GHz)<41.2
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
10mJy F1.4 1000mJy
log(L1.4GHz)>41.2
1.0 0.5 0.0 0.5
log([NII]/H )
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
SF comp
LINER
Seyfert
log(L1.4GHz)<40.5
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
40.5<log(L1.4GHz)<41.2
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
log(L1.4GHz)>41.2
Fig. 9. Distribution of the radio luminosity at 1.4 GHz, L1.4 GHz, in optical diagnostic diagrams. Top row: distribution of the radio luminosity L1.4 GHz
for the parent sample. The contours correspond to the distribution of the sources for the luminosity bins, log (L1.4 GHz) < 40.5, 40.5 < log (L1.4 GHz) <
41.2, and log (L1.4 GHz) > 41.2, with the increasing radio luminosity from left to right. Middle row: distribution of the radio luminosity L1.4 GHz as
in the top row but for a flux-limited subsample of the parent sample, 10 mJy ≤ 1.4 GHz ≤ 1000 mJy. The luminosity bins are the same as in the top
row. Bottom row: distribution of the radio luminosity L1.4 GHz for the Effelsberg sample only (low + high flux sources). The luminosity bins are the
same as in the top row.
Figure 10 shows the position of the sources in all three classical
optical diagnostic diagrams, binned by the radio spectral
index. Using the previous definitions, we distinguish between
steep (α[4.85−10.45] > −0.7), flat (−0.7 < α[4.85−10.45] < −0.4), and
inverted radio spectra (α[4.85−10.45] < −0.4). The plots show that
when going from steep via flat to inverted spectra, the optical
line ratios, in particular the ratio log([O iii]/Hβ), decrease. This
indicates that the ionization potential of sources with inverted
A83, page 10 of 19
85
M. Zajaˇcek et al.: Radio spectral index distribution
1.0 0.5 0.0 0.5
log([NII]/H )
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
SF comp
LINER
Seyfert
steep: [4.85 10.45] < 0.7
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
flat: 0.7< [4.85 10.45] < 0.4
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
inverted: [4.85 10.45] > 0.4
1.0 0.5 0.0 0.5
log([SII]/H )
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
SF
LINER
Seyfert
steep: [4.85 10.45] < 0.7
1.0 0.5 0.0 0.5
log([SII]/H )
SF
LINER
Seyfert
flat: 0.7< [4.85 10.45] < 0.4
1.0 0.5 0.0 0.5
log([SII]/H )
SF
LINER
Seyfert
inverted: [4.85 10.45] > 0.4
2.0 1.5 1.0 0.5 0.0
log([OI]/H )
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
SF LINER
Seyfert
steep: [4.85 10.45] < 0.7
2.0 1.5 1.0 0.5 0.0
log([OI]/H )
SF LINER
Seyfert
flat: 0.7< [4.85 10.45] < 0.4
2.0 1.5 1.0 0.5 0.0
log([OI]/H )
SF LINER
Seyfert
inverted: [4.85 10.45] > 0.4
Fig. 10. Spectral index trends in the optical diagnostic diagrams. From top to bottom panels: [NII]-, [SII]-, and [OI]-based diagrams, respectively,
with the progressively increasing spectral index from the left to the right panels: α[4.85−10.45] < −0.7, −0.7 ≤ α[4.85−10.45] ≤ −0.4, and α[4.85−10.45] >
−0.4, respectively. Contours indicate Gaussian kernel density estimates.
radio spectra is weaker than that of sources with a steep radio
spectrum.
Since this vertical movement in the optical diagnostic diagram
follows the same direction as the usual division line
between Seyfert and LINER galaxies (Kewley et al. 2006;
Schawinski et al. 2007), this trend will lead to the previously
discussed increase of radio spectral index towards LINER
sources, namely that steeper sources tend to fall into the Seyfert
and more inverted into the LINER category. Since we select
brighter radio emitters with optical counterparts, it is quite possible
that all our sources have a contribution from an AGN to some
extent.
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A&A 630, A83 (2019)
0 1 2 3 4 5
radio loudness Rg
1.5
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
steep
flat
inverted
Fig. 11. Clustering of the radio sources in the radio loudness–ionization
ratio plane. The galaxies are grouped with respect to the spectral index
in the following categories: α[4.85−10.45] < −0.7, −0.7 ≤ α[4.85−10.45] ≤
−0.4, and α[4.85−10.45] > −0.4.
In the further search for general trends, we added another
parameter, radio loudness, which can directly trace the energetics
of AGN and their hosts rather than the purely astronomical
division into low- and high-flux sources. Using the flux density at
20 cm from FIRST, F1.4, we converted the radio flux density into
the ABν-radio magnitude system of Oke & Gunn (1983) according
to Ivezi´c et al. (2002),
m1.4 = −2.5 log
F1.4
3631 Jy
, (4)
in which the zero point 3631 Jy does not depend on the wavelength.
Subsequently, the radio loudness can be calculated as the
ratio of the radio flux density to the optical flux density,
Rg ≡ log
Fradio
Foptical
= 0.4(g − m1.4), (5)
where we use the optical g-band for each source from the SDSSDR7
catalogue.
Here we note that the optical flux density is related to the host
galaxy and not to the AGN, since our sample is radio selected.
An inspection of the optical spectra also shows that only a handful
of sources display the typical power-law continuum shape
that is associated to the accretion disk. Hence, the radio loudness
derived in this way expresses the ratio between the radio power
of the AGN to the optical emission of the host galaxy and can be
taken as an upper limit of the intrinsic AGN radio loudness.
Figure 11 shows the location of the three radio classes, with
steep, flat, and inverted radio spectra in the Rg – log([O iii]/Hβ)
plane where the radio loudness Rg is along the x-axis and the
low-ionization ratio log([O iii]/Hβ) is along the y-axis. We show
that sources cluster in well-discriminated regions.
To justify these spectral-index categories, we fit a Gaussian
mixture model (GMM), which is an unsupervised machine learning
algorithm. For this, we consider the quantities radio loudness,
Rg, low-ionization ratio, log([O iii]/Hβ), and radio spectral
index, α[4.85−10.45], as a three-dimensional space; this means
every galaxy is represented by a vector
x =


Rg
log([O iii]/Hβ)
α[4.85−10.45]

 . (6)
The GMM assumes that the data points can be described
by a superposition of a finite number of multivariate Gaussian
distributions with unknown parameters in this parameter space.
The model is the probability density function represented as a
weighted sum of the Gaussian component densities. Using the
model, we can then give probabilities for data points belonging
to one of these classes. For the fit, we assume three components
and use the expectation maximization technique implemented in
the Python library Scikit-Learn (Pedregosa et al. 2011).
In Fig. 12, we show the three classes in the Rg –
log([O iii]/Hβ) plane and, to represent the third dimension, we
show histograms of the radio spectral index α[4.85−10.45]. In accordance
with our results based on a manual cut in radio spectral
index (Fig. 11), we find three distinct classes:
(1) associated with a steep radio index, high ionization ratio, and
high radio loudness;
(2) associated with a flat radio index, lower ionization ratio, and
intermediate radio loudness;
(3) associated with an inverted radio index, low ionization ratio,
and low radio loudness.
6. Interpretation of the results
6.1. General trends in radio-optical properties
By measuring flux densities with the Effelsberg radio telescope,
calculating spectral indices, and analysing their distributions
in the optical diagnostic diagrams, we can recover these basic
trends in the radio-optical properties of our selected sources,
(a) the radio luminosity increases in the direction of increasing
low-ionization ratio [O iii]/Hβ (see Fig. 9) with the exception
of the LINERs, which show lower radio luminosities and low
ionization ratios (plus higher stellar masses) compared to the
Seyferts with high radio luminosities;
(b) there is a trend of the radio spectral index steepening in the
direction of increasing [O iii]/Hβ (see Fig. 10);
(c) the radio loudness increases in the same direction, as shown
by Fig. 12.
Our results are representative for the nearby luminous, active
SDSS-FIRST sources, which are predominantly located in the
AGN (Seyfert-LINER) region of the optical diagnostic diagram.
In comparison with previous studies, the determination of spectral
indices allows us to connect the radio luminosity and radioloudness
trends (Kellermann et al. 1989; Sikora et al. 2007) with
the radio-morphological structures, such as the activity of radio
primary components (cores), jet components, and radio lobes, as
is known from the studies of quasar and blazar studies (Eckart
et al. 1986).
Considering the bolometric luminosities of AGN sources,
for which the luminosity of the emission line [O iii] serves as
a proxy, there is a trend of less radio-luminous galaxies being
located towards lower L[O iii] and these sources have progressively
flatter to inverted radio spectra (see the top row of Fig. 13,
left panel). On the other hand, more radio-luminous sources have
larger L[O iii] and steeper spectra.
To analyse the trends (a), (b), and (c) in relation with the
accretion rate ˙Macc, we calculate the Eddington ratio, defined as
η ≡ Lbol/LEdd, where the bolometric luminosity is derived from
the [O iii] luminosity using Lbol = 3500 L[O iii] (Heckman et al.
2004) and the Eddington luminosity is LEdd = 4πGM•mpc/σT =
1.3 × 1038
(M•/M ) erg s−1
. The black-hole masses for SDSSFIRST
sources can be estimated from the black-hole mass–
velocity dispersion M• −σ correlation, using the relation found
by Gültekin et al. (2009),
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M. Zajaˇcek et al.: Radio spectral index distribution
0 1 2 3 4 5
radio loudness Rg
1.5
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
Gaussian mixture model
class 1
class 2
class 3 0
10
20
30
class 1
0
10
20
30
class 2
1.5 1.0 0.5 0.0 0.5 1.0
spectral index [4.85 10.45GHz]
0
10
20
30
class 3
Fig. 12. Results of the Gaussian mixture model. Left panel: radio sources in the radio loudness–ionization ratio plane according to the spectral
index divisions as found from the Gaussian fitting. Right panel: spectral-index histogram with three basic groups that are very similar to the manual
cut with these limits: α[4.85−10.45] < −0.7, −0.7 ≤ α[4.85−10.45] ≤ −0.4, and α[4.85−10.45] > −0.4.
log (M•/M ) = 8.12 + 4.24 log (σ /200 km s−1
). (7)
In the bottom row of Fig. 13 (left panel), we depict the distribution
of the spectral index α[4.85−10.45] with respect to the radio
luminosity L1.4 GHz and the Eddington ratio η. All sources irrespective
of their radio spectral index have very similar Eddington
ratios, with 2/3 of them within log η ∼ [−3, −2]. This similarity
in accretion rates is driven by the strong dependency of η on
the stellar-velocity dispersion (η ∝ σ4
) and the characteristics
of our sample: the brightest radio galaxies with optical counterparts
(dominated by the stellar emission) on the sky are – mostly
– very massive, M ∼ 1011−12
M , have a large velocity dispersion,
σ ∼ 180−320 km s−1
, and thereby have a heavy SMBH
with log(M•/M ) ∼ 8.5.
6.2. Relation between radio emission and Eddington ratio
Our results seem to be at odds with previous findings that the
radio loudness anti-correlates with the Eddington ratio (Sikora
et al. 2007; Broderick & Fender 2011). Since the ionization ratio
log([O iii]/Hβ) is proportional to the hardness of the ionization
field, which in turn depends on the accretion efficiency expressed
by the Eddington ratio, we find that sources with a lower radio
loudness correspond to those with lower ionization ratio and
their radio spectral indices are inverted, which is indicative of
self-absorbed synchrotron emission (see Fig. 12). On the other
hand, the radio-louder sources are associated with larger ionization
ratio and their spectral indices demonstrate optically thin
synchrotron emission.
Although our sample spans shorter ranges in L1.4 GHz and
log η when compared with extended samples like that of Sikora
et al. (2007), it displays similar luminosities to their broad line
radio galaxies (BLRGs) and radio loud quasars (RLQs) when
using only core radio powers (see Broderick & Fender 2011)
indicating that our sample might represent the narrow line optical
counterpart of those objects.
To estimate how our radio-loudness definition and sample
selection bias our results, we study integral quantities and compare
the sources selected for the Effelsberg observations to the
parent sample. One main source of discrepancy could be the
use of the host-galaxy optical luminosity in the radio-loudness
calculation (see Eq. (5))3
. However, galaxy hosts of Effelsberg
sources seem to be quite similar; 90% of them have elliptical
morphologies spanning only around 0.5 dex in g-band luminosities.
Therefore we conclude that the main trend of decreasing
radio spectral index with radio loudness is caused by the variations
in the core radio luminosities.
The basic explanation of the trend of decreasing spectral
indices α[4.85−10.45] with the increasing ionization ratio [O iii]/Hβ,
which corresponds to the LINER–Seyfert transition in the optical
diagnostic diagrams, might be the renewal of AGN activity
in the past ∼105
–107
years (Tadhunter 2016; Padovani et al.
2017). At least one third of the sources that have larger [O iii]/Hβ
and steeper radio spectral indices have extended jet structures,
that is, radio emission is dominated by older radio lobes, where
electrons cooled down. Since the timescales for the formation
of the radio extended structures and the optical narrow-line
region brightening are quite different, the observed trend can be
explained by two scenarios: objects in the Seyfert region must
have been optically-active for a long enough period for the radio
lobes to develop, or the radio structures formed in the past and
their activity has been re-triggered some decades ago.
On the other hand, only 1/8 of the sources with lower ionization
ratios display jet-like structures. They might have started (or
re-started)theirnuclearactivityveryrecently,whichcouldexplain
inverted spectral indices corresponding to compact self-absorbed
core emission. Since they did not have enough time to develop
extended radio lobes, their radio luminosities are also smaller.
Visual inspection of FIRST images and literature research
for each object in the Effelsberg sample allowed us to classify
them as jetted or non-jetted sources. We find that 2/3 of flat and
steep radio spectrum objects do not show extended structures
that could be related to jet emission. Thus, we do not confirm the
one-to-one relation between morphologies and spectral indices
(compact/extended versus inverted/flat-steep) found by Massardi
et al. (2011).
Our results seem to be in accordance with the correlations
found for radio-quiet Palomar-Green quasars by Laor et al.
(2019). They found an increase in the line ratio Fe ii/Hβ from
3
We refrain from using L[O iii] to estimate the optical AGN emission
to avoid obtaining an artificial trend by comparing R ∝ 1/L[O iii] with
η ∝ L[O iii].
A83, page 13 of 19
88 CHAPTER 2. PAPER 1: RADIO-OPTICAL PROPERTIES OF ACTIVE GALAXIES
A&A 630, A83 (2019)
39 40 41 42
log(L[OIII]/erg s 1)
38.5
39.0
39.5
40.0
40.5
41.0
41.5
42.0
42.5
log(L1.4GHz/ergs1)
steep
flat
inverted
38 40 42
log(L[OIII]/erg s 1)
37
38
39
40
41
42
43
log(L1.4GHz/ergs1)
5 4 3 2 1 0
log( )
39
40
41
42
log(L1.4GHz/ergs1)
steep
flat
inverted
5 4 3 2 1 0
log( )
37
38
39
40
41
42
43
log(L1.4GHz/ergs1)
Fig. 13. Distribution of the Effelsberg sources with respect to the radio luminosity, luminosity of [O iii] line, and the Eddington ratio. Top row–left
panel: distribution of the radio spectral index α[4.85−10.45] with respect to the radio luminosity L1.4 GHz and the luminosity of [O iii] line. Right panel:
localization of the Effelsberg sources (low + high flux; orange points) in the plane of L1.4 GHz and L[O iii] with respect to the parent sample (grey
points). Bottom row–left panel: distribution of steep, flat, and inverted radio spectral indices with respect to the radio luminosity L1.4 GHz and the
Eddington ratio η. Right panel: distribution of the Effelsberg sources (orange points) in the same plane as in the left figure with respect to the
parent sample (grey points).
inverted, through flat, up to steep radio spectral indices, in the
same way as we found for [O iii]/Hβ. They interpret the correlations
of the radio spectral index with the Eigenvector 1 parameters
using the nuclear-outflow interpretation, which at least
partially can be used for our findings as well. Higher excitation
for steep sources, which are also radio louder (see Fig. 11)
could be indicative of a large-scale nuclear outflow, which is a
source of optically thin synchrotron emission. On the other hand,
sources with lower [O iii]/Hβ with flat to inverted radio slopes,
which are radio weaker, could lack an outflow and the dominant
source of radio emission would be the compact nucleus (coronal
emission) that emits optically thick synchrotron emission.
6.3. Flat and inverted spectral index towards LINERs:
Implications for their character
The interpretation and the nature of LINERs remains still unclear
and several recent studies have attempted to shed more light on
their characteristics and the potential effect of the environment
(Singh et al. 2013; Coldwell et al. 2017, 2018). The fact that
50% of LINERS in both frequency ranges have flat to inverted
spectral indices points to the activity of the nucleus and the dominant
contribution of the core and the jet radio emission to the
overall radio emission of LINER galaxies.
In our study of the radio-optical properties of SDSS-FIRST
sources, LINERs are characterized by a lower ionization ratio
[O iii]/Hβ in comparison with Seyfert AGN sources. Keeping in
mind the colour-stellar mass sequence (Schawinski 2009), LINERs
have the largest stellar and black hole masses (see Fig. 14
for the distribution of stellar and black hole masses across the
parent sample and Fig. 15 for the distribution of the average stellar
mass across both the parent and the low+high flux sample). In
addition, they are associated with redder colours and smaller star
formation rates than other optical spectral classes (SF, COMP,
Seyfert; Leslie et al. 2016).
The optical low-ionization emission could be explained
by the presence of the extended population of hot and old
post-asymptotic giant branch (AGB) stars, as is indicated by
A83, page 14 of 19
89
M. Zajaˇcek et al.: Radio spectral index distribution
Fig. 14. Distribution of stellar and black-hole masses for the SDSS-FIRST parent sample. Left panel: SDSS-FIRST distribution of stellar masses
in the optical BPT diagram. The colour bar indicates the logarithm of the stellar masses in units of solar masses. Right panel: distribution of the
black hole masses inferred from the measurement of the stellar velocity dispersion in the SDSS-FIRST sources.
studying the radial brightness distribution by Singh et al. (2013),
which is consistent with a spatially extended ionizing source
(stars) rather than a point source (nucleus). However, in the radio
domain, the mean spectral indices α[1.4−4.85] and α[4.85−10.45] indicate
the increase in the mean radio spectral slope in comparison
with Seyferts (see also the trend of the increasing spectral index
in Fig. 10). This trend can be explained by the dominant contribution
of the jet emission (the overall flat radio spectrum due
to the collective contribution of self-absorbed structures) and the
nuclear activity (inverted, optically thick synchrotron source).
Therefore, we cannot support the claim of Singh et al. (2013)
that LINERs are defined by the lack of AGN activity, at least
not for our subsample of radio-emitting LINERs. The AGN ionizing
field is likely not dominant in the optical domain, but
according to our statistical study, the nuclear and jet activity
must be present. This is also in agreement with the studies of
Coldwell et al. (2017, 2018) where they find that LINERs are
redder and older than the control sample of galaxies in environments
of different density. They also show that LINERs are
likely to populate low-density regions in spite of their elliptical
morphology, that is, their occurrence in low-density galaxy
groups is two times higher than the occurrence of the control,
non-LINER galaxies. The fact that LINERs are more likely to
be found in low-density regions points towards nuclear activity,
since active galaxies typically do not follow the morphologydensity
relation (Popesso & Biviano 2006; Coldwell et al. 2009,
2014; Padilla et al. 2010). This also indicates the relevance of
major mergers in the galaxy evolution, since the low-density
galaxy groups favour major mergers due to lower velocity dispersion
among members. Major mergers can restart the nucleus
as has been found in several studies (Popesso & Biviano
2006; Coldwell et al. 2009; Alonso et al. 2007). In addition,
Chiaberge et al. (2015) found that major mergers are a trigger
for radio-loud AGN and the launching of relativistic jets.
Using the luminosity-hardness diagram, which is applied to stellar
black hole binaries, Nagar et al. (2005) argue that LINERs
seem to occupy a “low/hard” state (geometrically thick and optically
thin, hot accretion flows, low Eddington ratio, launching
collimated jets), while low-luminosity Seyfert sources are in a
“high” state (geometrically thin and optically thick, cold accretion
discs, high Eddington ratios, incapable of launching collimated
jets). In this picture, LINERs would be characterized by
radiatively inefficient flows with recently (re)started nuclear and
jet activity, which could explain their overall lower [OIII]/Hβ
ratio in the optical diagnostic diagrams and the increasing spectral
index on the transition between Seyfert and LINER sources.
7. Summary
We studied the radio-optical properties of selected crossmatched
SDSS-FIRST sources, with a particular focus on the
spectral index trends in the optical diagnostic diagrams. Combining
the high-flux sample (S1.4 ≥ 100 mJy; Vitale et al. 2015a)
and the low-flux sample presented in this paper (10 mJy ≤ S1.4 ≤
100 mJy), we cover a total of 417 star-forming, composite,
Seyfert, and LINER sources based on the standard spectral
classification using the emission-line ratios. For a total of
209 sources (90 from the low-flux sample and 119 from the highflux
sample) we have flux density measurements at 10.45 GHz.
First, we searched for potential trends of the radial spectral
index between the classical optical spectral classes of galaxies.
Second, we looked at how the different ranges of the radio
spectral index are positioned in the optical diagnostic diagrams.
While the first approach yielded basic statistics, the second
approach turned out to be more appropriate for our sample in
the context of radio-optical trends.
We find a scenario that is largely consistent with models in
which the source population shows a dichotomy that reflects a
switch between radiatively efficient and radiatively inefficient
accretion modes at similarly (compared to QSOs and quasars)
low accretion rates. The location of radio sources in the narrow
emission-line diagnostic (BPT) diagrams shifts with the increasing
importance of a radio-loud AGN away from galaxies dominated
by radio emission powered by star formation. Hence, the
radio weakness dominates the radio loudness over stellar mass
estimate (for the stellar mass, see Fig. 15) and leads to a clear
separation from the radio-loud objects. This is seen in the diagnostic
diagrams in this paper and has also been put forward by
similar investigations (e.g. Fig. A.1 by Best & Heckman 2012).
Comparing the α1.4/4.85 values of all the sources in the
low-flux density sample with each other, one finds that while
the high-flux density sources are dominated by the steep spectral
index components and steepen towards higher frequencies,
the low-flux density sample is significantly influenced by the
A83, page 15 of 19
90 CHAPTER 2. PAPER 1: RADIO-OPTICAL PROPERTIES OF ACTIVE GALAXIES
A&A 630, A83 (2019)
1.0 0.5 0.0 0.5
log([NII]/H )
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
SF comp
LINER
Seyfert
log(Msun)<11.25
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
11.25<log(Msun)<11.5
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
log(Msun)>11.5
1.0 0.5 0.0 0.5
log([NII]/H )
1.0
0.5
0.0
0.5
1.0
1.5
log([OIII]/H)
SF comp
LINER
Seyfert
log(Msun)<11.25
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
11.25<log(Msun)<11.5
1.0 0.5 0.0 0.5
log([NII]/H )
SF comp
LINER
Seyfert
log(Msun)>11.5
Fig. 15. Distribution of the average stellar mass across the parent and the low + high flux sample. Top panel: SDSS-FIRST distribution of stellar
masses in the optical BPT diagram for the whole parent sample. From the left to the right figures: galaxies with the average stellar mass in the
range log(M [M ]) < 11.25, 11.25 < log(M [M ]) < 11.5, log(M [M ]) > 11.5, respectively, are represented with density contours. Bottom
panel: distribution of the average stellar mass across the BPT diagram for the same mass bins as in the top panel, but for the combined low + high
flux sample.
increasing presence of flat-spectrum components. A detailed
investigation of the spectral-index distributions of the high and
low-flux density samples shows that in both samples the presence
of flat-spectrum components implies a higher excitation in
the optical diagnostic diagrams. In particular, the fainter sources
that contain a significant contribution by a compact flat-spectrum
component can be investigated through the present low-flux density
sample.
If we turn to the sources from both samples that have
10.45 GHz measurements and hence a known α[4.85−10.45] value,
we find the following: considering steep (α[4.85−10.45] > −0.7),
flat (−0.7 < α[4.85−10.45] < −0.4), and inverted radio spectra
(α[4.85−10.45] < −0.4), we recovered three basic classes with
respect to the radio loudness and ionization ratio [O iii]/Hβ:
(1) sources with a steep radio index, high ionization ratio, and
high radio loudness;
(2) sources with a flat radio index, lower ionization ratio, and
intermediate radio loudness;
(3) sources with an inverted radio index, low ionization ratio,
and low radio loudness.
In the optical diagnostic diagrams, these three classes correspond
to the transition from Seyfert to LINER classification in
terms of the ionization line ratios. Seyfert sources with higher
ionization ratio are dominated by older, optically thin radio
emission. Towards the lower ionization ratio, LINERs exhibit
a flat to inverted radio spectral index, which is indicative of the
compact, self-absorbed core and the jet emission. In the local
Universe, these trends may result from re-triggered nuclear and
jet activity.
Acknowledgements. We are grateful to the referee, Brent Groves, for very
constructive comments that helped to improve the manuscript. We thank Stefanie
Komossa (MPIfR), Pavel Kroupa (University of Bonn), Thomas Krichbaum
(MPIfR), Madeleine Yttergren (University of Cologne), Bozena Czerny
(CFT PAN), Mary Loli Martinez-Aldama (CFT PAN), and Swayamtrupta Panda
(CFT PAN) for very helpful discussions and input. This work was done with
the financial support of SFB956 – “Conditions and Impact of Star Formation:
Astrophysics, Instrumentation and Laboratory Research” at the Universities of
Cologne and Bonn and MPIfR, in which M.Z., G.B., A.E., N.F., S.B., J.-A.Z.,
K.H. are members of sub-group A2 – “Conditions for Star Formation in Nearby
AGN and QSO Hosts” and A1 – “Understanding Galaxy Assembly”, with M.V.
and L.F. being its former members. Michal Zajaˇcek acknowledges the financial
support by National Science Centre, Poland, grant No. 2017/26/A/ST9/00756
(Maestro 9).
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A&A 630, A83 (2019)
Appendix A: Table of the basic radio-optical
properties
Here we summarize the information on 90 sources of the
low-flux sample, for which we obtained radio flux densities
at 4.85 GHz and 10.45 GHz using the 100-m Effelsberg radio
telescope. In combination with the integrated flux of these
sources at 1.4 GHz, we determined the corresponding spectral
slopes.
In Table A.1, we include the redshift z, right ascension RA,
declination Dec, integrated flux density at 1.4 GHz as adopted
from the FIRST survey catalogue, the measured flux densities at
4.85 GHz and 10.45 GHz, and the corresponding errors. The final
column denoted as [NII]d is the galaxy spectral type according
to the [NII]-based optical diagnostic diagram (BPT diagram): SF
denotes star-forming galaxies, COMP composites, SEY Seyfert
AGN sources, and LIN stands for LINERs (see also Fig. A.1 for
corresponding positions in the [N ii]-based BPT diagram).
Table A.1. Sources with the flux densities 10 mJy F1.4 100 mJy with measured flux densities at two higher frequencies, 4.85 GHz and
10.45 GHz.
z RA Dec F1.4 [mJy] F4.85 [mJy] Err [mJy] F10.45 [mJy] Err [mJy] [NII]d
0.054 37.92 −1.1677 14.250 27.5 1.3 30.8 3.3 COMP
0.062 116.18 38.6531 19.570 14.9 0.1 10.7 5.1 COMP
0.133 119.36 40.9047 12.800 10.8 0.2 13.0 2.4 COMP
0.095 129.18 53.5757 17.870 26.2 2.5 22.6 4.6 LIN
0.136 130.40 51.9057 40.580 56.5 18.0 17.3 4.2 LIN
0.127 137.97 56.9317 15.100 7.7 0.6 14.6 5.0 LIN
0.216 119.03 38.5669 63.950 20.0 0.9 12.1 2.9 LIN
0.066 119.49 39.9934 99.200 23.0 0.8 13.5 7.9 SEY
0.098 135.66 52.1874 38.440 18.3 0.8 18.2 4.6 SEY
0.069 235.62 52.9975 28.580 33.6 2.7 64.5 6.3 LIN
0.052 234.90 55.5044 31.490 16.9 1.5 17.5 3.3 COMP
0.108 242.15 53.6394 40.340 16.9 0.9 14.5 3.7 COMP
0.199 243.92 47.1866 98.080 182.0 1.9 119.9 7.5 COMP
0.195 246.83 48.5241 23.590 54.6 1.4 44.4 5.2 LIN
0.191 246.58 50.0678 15.670 9.9 1.0 18.6 5.5 LIN
0.055 10.46 −9.3032 40.200 50.2 2.8 15.9 5.5 LIN
0.077 13.03 −9.4912 29.930 51.6 12.3 18.9 3.3 LIN
0.143 20.94 −9.3843 74.240 31.8 0.4 133.1 6.7 LIN
0.103 20.99 −9.6855 14.700 43.4 3.5 12.0 2.8 LIN
0.049 21.32 −8.8737 11.570 135.9 20.4 7.8 2.8 COMP
0.049 21.87 −8.5543 24.250 44.0 5.8 9.2 2.3 SF
0.146 22.93 −8.4370 64.300 32.6 0.8 15.7 3.3 LIN
0.271 23.31 −9.5340 21.170 17.1 1.1 8.7 3.2 SF
0.136 33.21 −9.7125 47.020 22.8 1.3 13.8 2.8 LIN
0.166 31.57 −9.9549 18.720 26.0 1.4 24.9 3.4 LIN
0.081 343.62 −9.2759 27.930 16.2 1.5 14.9 4.1 LIN
0.059 185.77 63.2223 16.500 15.0 1.8 10.9 3.2 COMP
0.131 198.60 62.3294 64.520 181.7 10.3 94.8 7.9 LIN
0.099 250.46 37.3093 22.510 27.5 1.6 25.3 3.9 LIN
0.099 130.52 40.8460 24.430 20.7 1.0 30.3 4.0 LIN
0.236 126.72 39.8121 13.870 38.8 1.1 23.3 3.9 LIN
0.147 127.32 40.0373 10.850 14.2 1.0 16.3 3.8 COMP
0.167 136.84 46.3384 35.100 23.3 0.9 13.6 3.2 SEY
0.192 139.76 47.4986 13.470 7.7 0.9 18.6 4.6 COMP
0.207 145.02 51.0727 16.270 78.2 1.3 58.2 5.9 SEY
0.159 170.12 58.9371 84.050 45.6 3.5 34.1 3.4 SEY
0.234 322.42 0.0892 23.820 12.8 4.8 11.8 5.0 COMP
0.074 326.71 0.3542 10.440 18.4 2.6 6.0 2.3 SF
0.133 151.79 50.3990 30.640 24.3 0.8 25.0 5.1 LIN
0.166 157.93 52.4264 83.670 360.8 3.5 178.0 7.0 SEY
0.055 175.82 55.2777 11.720 18.8 2.8 19.1 2.8 LIN
0.091 196.40 54.0284 23.140 34.6 7.4 15.5 3.2 LIN
0.140 200.69 53.0299 22.790 106.1 74.7 8.2 3.2 SEY
0.137 232.51 43.0404 22.650 16.5 0.8 23.6 15.9 SEY
0.119 234.96 41.7237 19.630 24.0 1.0 22.6 5.0 LIN
0.066 241.43 37.1791 28.190 9.8 0.8 14.5 4.1 SEY
0.110 235.44 47.4652 83.380 68.3 1.3 37.1 5.4 SEY
Notes. Using the symbol [NII]d, we denote the diagnostics according to the [NII]-based optical diagnostics diagram, where SF stands for starforming
galaxies, COMP composites, SEY represents Seyfert AGN, and LIN denotes LINER sources.
A83, page 18 of 19
93
M. Zajaˇcek et al.: Radio spectral index distribution
Table A.1. continued.
z RA Dec F1.4 [mJy] F4.85 [mJy] Err [mJy] F10.45 [mJy] Err [mJy] [NII]d
0.042 239.97 44.7090 58.810 26.1 0.7 11.6 4.7 LIN
0.173 188.57 50.9069 52.400 57.9 0.7 45.0 4.3 SEY
0.181 173.13 57.5192 35.560 25.4 1.4 22.3 3.3 SEY
0.117 179.04 56.7764 19.940 25.9 9.9 16.3 3.2 LIN
0.047 218.30 52.9631 15.190 11.6 0.9 15.0 3.7 COMP
0.150 243.84 39.9390 28.440 33.1 10.7 12.0 3.3 COMP
0.075 252.55 29.2934 10.220 13.9 1.2 13.2 5.5 LIN
0.168 211.91 40.8988 61.280 23.2 2.2 24.0 4.7 LIN
0.173 219.51 39.5710 17.760 19.7 0.9 33.2 4.8 LIN
0.237 231.28 35.5338 17.740 17.8 1.0 12.7 3.2 COMP
0.055 231.75 35.9770 13.060 12.3 1.1 15.4 3.7 COMP
0.154 239.21 32.9769 18.030 21.1 2.8 7.7 3.2 LIN
0.226 242.04 29.7541 48.500 37.4 6.6 19.5 3.7 SEY
0.112 166.28 46.8885 56.180 45.6 1.2 28.7 3.8 SEY
0.065 205.15 44.8048 82.200 86.0 48.7 43.5 4.5 SEY
0.058 245.20 24.0142 28.520 12.9 1.0 15.0 9.5 COMP
0.050 242.09 28.4787 78.160 120.9 0.2 83.9 4.5 LIN
0.201 233.72 29.1555 44.420 32.8 2.3 20.0 8.4 COMP
0.108 211.83 50.4603 58.400 29.0 1.4 18.7 3.7 SEY
0.040 229.53 42.7459 30.370 20.2 0.8 18.1 4.6 COMP
0.088 113.98 42.2034 17.720 11.0 0.2 6.5 2.3 LIN
0.052 118.18 45.9493 50.150 276.2 27.2 93.7 10.7 SEY
0.044 129.10 56.5974 10.870 17.7 2.3 21.9 4.2 SF
0.084 229.95 27.7727 15.670 28.7 1.1 31.5 8.4 LIN
0.118 238.43 23.8071 64.950 250.5 5.8 168.5 9.3 SEY
0.084 119.20 53.2156 38.980 18.8 0.3 11.1 3.3 LIN
0.122 132.05 60.7737 19.980 34.9 6.5 32.4 3.2 LIN
0.191 137.83 63.1578 13.910 68.4 11.5 11.1 2.8 COMP
0.139 208.31 35.1470 42.090 36.5 1.0 30.1 3.9 LIN
0.115 213.01 29.4671 36.970 31.6 1.4 32.4 5.7 LIN
0.126 213.75 26.8312 22.280 12.2 1.3 21.7 4.7 LIN
0.165 222.05 28.8887 42.410 15.7 1.1 26.8 6.5 LIN
0.069 226.00 24.1049 17.260 12.5 1.2 34.5 5.7 COMP
0.101 237.75 19.2783 30.570 37.8 1.5 36.8 5.2 LIN
0.110 240.91 15.9007 93.750 199.9 2.5 206.0 9.0 COMP
0.229 235.33 14.3696 11.180 26.7 1.0 26.3 4.6 SF
0.149 225.46 16.6183 32.240 26.4 1.4 19.5 4.6 LIN
0.139 214.84 21.6037 20.920 14.8 2.4 18.1 3.7 COMP
0.138 214.04 22.4760 25.650 14.0 0.9 22.7 6.0 LIN
0.151 225.88 19.6523 91.950 86.7 2.4 76.7 5.4 LIN
0.150 230.43 18.2440 93.270 40.2 4.1 13.7 4.6 LIN
0.057 245.57 50.3720 15.660 7.8 0.8 7.8 3.7 COMP
0.104 249.69 27.9109 40.920 26.5 1.4 24.6 4.2 LIN
Fig. A.1. Location of the sources from Table A.1 in [NII]-based
diagnostic diagram.
A83, page 19 of 19
94 CHAPTER 2. PAPER 1: RADIO-OPTICAL PROPERTIES OF ACTIVE GALAXIES
Chapter
3
Paper 2: Reverberation-Mapping of
HE 0413-4031
For low-redshift quasars and Seyfert galaxies, the broad-line region (BLR) radius-luminosity
(RBLR − L) relation was established for the broad Hβ line (486.135 nm in the rest frame). As
expected from the simple photoionization theory, the RBLR − L relation has a power-law form,
RBLR ∝ Lγ
, with γ ∼ 0.5. This relation can be used for the estimation of the supermassive
black hole masses using just one single-epoch spectrum, hence the RBLR − L relation has
relevance for the understanding of the supermassive black hole growth across the cosmic
history.
For higher-redshift quasars, the UV line of MgII is redshifted to the visible portion of
the spectrum and can be used for reverberation mapping using optical telescopes. Czerny
et al. (2019) established the existence of the MgII RBLR − L relation using the high-luminosity
source CTS C30.10 and nine other sources with lower luminosities.
In this paper, we investigated another high luminosity source – quasar HE 0413-4031
(z = 1.38) with the monochromatic luminosity of log (L3000 [erg s−1
]) = 46.754+0.028
−0.132. The
source was monitored for six years using the South African Large Telescope (SALT). Using
seven different methods, we established the rest-frame MgII time delay of 302.6+28.7
−33.1
days. Using 11 quasars, we could fit the rest-frame time delay of the MgII line versus the
monochromatic luminosity at 300 nm, with the result of log (τ/lt. days) = (1.45 ± 0.08) +
(0.42 ± 0.05) log (L3000/1044
erg s−1
). Hence, the MgII R − L relation appears to be slightly
flatter than the Hβ relation. The MgII time delay of HE 0413-4031 lies below the best-fit
relation, which is in agreement with the found correlation between the rest-frame time delay
difference and the Eddington ratio – since HE 0413-4031 is a highly accreting quasar, it leads
to the shortening of the BLR time delay.
In addition, we also fitted the broad-band spectral energy distribution of HE 0413-4031
using the relativistic thin accretion disc model. The inferred supermassive black hole mass,
MSED
• = 1.5 × 109
− 3.5 × 109
M⊙, is in agreement with the virial estimate based on the
reverberation mapping, MRM
• ( fvir = 1) ≃ 1.1 × 109
M⊙, which provides an independent check
of the reverberation-mapping analysis.
Credit: Zajaˇcek et al. (2020), ApJ 896, 146. Reproduced with permission ©AAS.
95
Time-delay Measurement of MgII Broad-line Response for the Highly Accreting Quasar
HE 0413-4031: Implications for the MgII–based Radius–Luminosity Relation
Michal Zajaček1
, Bożena Czerny1
, Mary Loli Martinez–Aldama1
, Mateusz Rałowski1
, Aleksandra Olejak1
,
Swayamtrupta Panda1,2
, Krzysztof Hryniewicz2
, Marzena Śniegowska1
, Mohammad-Hassan Naddaf1
, Wojtek Pych2
,
Grzegorz Pietrzyński2
, C. Sobrino Figaredo3
, Martin Haas3
, Justyna Średzińska2
, Magdalena Krupa4
, Agnieszka Kurcz4
,
Andrzej Udalski5
, Marek Gorski6
, and Marek Sarna2
1
Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland; zajacek@cft.edu.pl
2
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland
3
Astronomisches Institut—Ruhr Universitaet Bochum, Germany
4
Astronomical Observatory of the Jagiellonian University, Orla 171, 30-244 Cracow, Poland
5
Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warsaw, Poland
6
Departamento de Astronomia, Universidad de Concepcion, Casilla 160-C, Chile
Received 2019 October 29; revised 2020 May 17; accepted 2020 May 17; published 2020 June 23
Abstract
We present the monitoring of the active galactic nuclei continuum and Mg II broad-line emission for the quasar HE
0413-4031 (z=1.38) based on the six-year monitoring by the South African Large Telescope (SALT). We
manage to estimate a time-delay of -
+
302.6 33.1
28.7
days in the rest frame of the source using seven different methods:
interpolated cross-correlation function, discrete correlation function (DCF), z-transformed DCF, JAVELIN, two
estimators of data regularity (Von Neumann, Bartels), and χ2
method. This time-delay is below the value expected
from the standard radius–luminosity relation. However, based on the monochromatic luminosity of the source and
the spectral energy distribution modeling, we interpret this departure as the shortening of the time-delay due to the
higher accretion rate of the source, with the inferred Eddington ratio of ∼0.4. The Mg II line luminosity of HE
0413-4031 responds to the continuum variability as µ 
L Lline cont
0.43 0.10
, which is consistent with the light-travel
distance of the location of Mg II emission at Rout∼1018
cm. Using the data of 10 other quasars, we confirm the
radius–luminosity relation for the broad Mg II line, which was previously determined for the broad Hβ line for
lower-redshift sources. In addition, we detect a general departure of higher-accreting quasars from this relation in
analogy to the Hβ sample. After the accretion-rate correction of the light-travel distance, the Mg II–based radius–
luminosity relation has a small scatter of only 0.10 dex.
Unified Astronomy Thesaurus concepts: Accretion (14); Active galaxies (17); Quasars (1319); Radio-loud quasars
(1349); Supermassive black holes (1663); Quasars (1319); Spectroscopy (1558)
1. Introduction
Reverberation mapping (RM) of active galactic nuclei
(AGNs) is a leading method to study the spatial scale as well
as the structure of the broad-line region (hereafter BLR; see
Blandford & McKee 1982; Peterson & Horne 2004; Gaskell
2009; Czerny 2019). The method is very time consuming
because it requires tens or even hundreds of spectra, covering
well the characteristic timescales in a given object. Collected
data allow for the measurement of the time-delay of a chosen
emission line with respect to the continuum. Assuming lighttravel
time of light propagation, we thus obtain the characteristic
size of the BLR. Subsequent discovery of the relation
between the size of the BLR and the source of absolute
monochromatic luminosity (Kaspi et al. 2000; Peterson et al.
2004; Bentz et al. 2013) opened a way to measure black hole
masses in large quasar samples using just a single-epoch
spectrum (e.g., Collin et al. 2006; Vestergaard & Peterson 2006;
Shen et al. 2011; Mejía-Restrepo et al. 2018).
The radius–luminosity relation based on the monitoring of
the broad Hβ component is relatively well studied in the case of
lower-redshift sources, including nearby quasars (below ∼0.9;
Kaspi et al. 2000; Bentz et al. 2013; Grier et al. 2017). For
larger redshifts, Hβ moves to the infrared bands, and in the
optical band, the spectrum is dominated by UV emission lines.
Sources with redshifts in the range of ∼0.4–1.5, when the
spectrum is observed in the optical band, become dominated by
the Mg II line, and at higher redshifts C IV moves into the
optical band. Thus, the single-spectrum methods are used to
scale the Hβ and the other line properties (mostly systematic
differences in the line widths) to be able to cover a large
spectral range. Direct reverberation measurements in other lines
than Hβ are still rare. In the current paper, we show a new
reverberation measurement done in the Mg II line for the
redshift larger than one.
The Mg II line seems to be suitable for the black hole mass
measurements because, together with Hβ, it belongs to the lowionization
lines (Collin-Souffrin et al. 1988), and thus should
originate close to the accretion disk, where the motion of the
emitting material is largely influenced by the potential of the
central black hole. Therefore the motion of the Mg II-emitting
material is expected to be quasi-Keplerian, i.e., the velocity
field is dominantly Keplerian with a certain turbulent
component. In analogy to the Hβ broad component, the Mg II
line is virialized (Marziani et al. 2013), while high-ionization
lines exhibit clear line profile asymmetries that imply the
outflowing motion and the importance of the radiation force.
On the other hand, monitoring of Mg II is more difficult
because the line in many sources has very low variability
amplitude (Goad et al. 1999; Woo 2008; Zhu et al. 2017; Guo
et al. 2020) and/or the timescales at larger redshifts and for
more massive (and luminous) quasars are considerably longer.
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 https://doi.org/10.3847/1538-4357/ab94ae
© 2020. The American Astronomical Society. All rights reserved.
1
96 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
Also the width of the Mg II line is narrower than the Hβ broad
component, which indicates the position at larger light-travel
distances (Marziani et al. 2013). In addition, the Mg II lineemitting
gas is evidenced to respond to nonthermal radiation
from jets, which may further complicate the RM for radio-loud
and γ-ray emitting sources (León-Tavares et al. 2013;
Chavushyan et al. 2020).
Successful determination of the line time-delay has been
achieved only for 10 sources so far (Metzroth et al. 2006; Shen
et al. 2016; Grier et al. 2017; Lira et al. 2018; Czerny et al.
2019), but it nevertheless allowed for the preliminary
construction of the radius–luminosity relation based on the
Mg II line (Czerny et al. 2019) with the slope close to R∝L0.5
(Panda et al. 2019b) being consistent with the relation for the
Hβ line (Bentz et al. 2013). The key measurement toward
larger luminosities came from the bright quasar CTS C30.10
(z=0.90052, [ ( )] =-Llog erg s 46.0233000
1 ) monitored for
6 yr with the South African Large Telescope (SALT). The
source CT252, for which the RM was also performed in Mg II
line (Lira et al. 2018), alongside CIII] and C IV monitoring, so
far had the largest redshift of z=1.890 among Mg II sources.
In this paper, we show the results for the quasar HE 0413-
4031 also monitored with the SALT, but brighter
( [ ( )] =-Llog erg s 46.7413000
1 ) and located at the redshift of
z=1.389 (according to NED7
). This quasar was found as part
of the Hamburg/ESO survey for bright QSOs (Wisotzki et al.
2000). Apart from the quasar spectrum, the source is also radioloud
and belongs to the flat-spectrum radio quasars (FSRQ)—
blazars (Mao et al. 2016). In fact, according to the NED
database, the radio spectral slope at lower radio frequencies
between 0.843 GHz and 5 GHz is inverted with α = 0.68,8
which indicates a compact self-absorbed radio core. From this,
we estimate the flux density at 1.4 GHz, F1.4 ≈ 21 mJy, which
implies the monochromatic luminosity per frequency of
L1.4 ≈ 2.5 × 1026
W Hz−1
> 1024
W Hz−1
, based on which
HE 0413-4031 can be classified as radio-loud AGN
(Tadhunter 2016).
In the analysis, we determine the rest-frame time-delay of the
Mg II line using different statistically robust methods—
interpolated cross-correlation function (ICCF), discrete correlation
function (DCF), z-transformed DCF, JAVELIN, two
estimators of data regularity (Von Neumann, Bartels), and χ2
method. The determined rest-frame time-delay of ∼303 days
turns out to be smaller than the time-delay predicted from the
expected radius–luminosity relation, where the radius of the
BLR is proportional to the square root of the monochromatic
luminosity. Because HE 0413-4031 is a quasar with the
accretion rate close to the Eddington limit, which is inferred
from the detailed spectral energy distribution (SED) fitting, we
demonstrate that the shortening of the measured time-delay is
due to the accretion-rate effect in analogy to the Hβ-based
radius–luminosity relation (Martínez-Aldama et al. 2019).
The paper is structured as follows. In Section 2, we present
the observational analysis including both spectroscopy and
photometry. Subsequently, in Section 3, we analyze the mean
spectrum, rms spectrum, spectral fits of individual observations,
and the variability properties of lightcurves. The focus of
the paper is on the time-delay determination of the Mg II broadline
emission with respect to the continuum using different
statistical methods, which is presented in detail in Section 4. In
Section 5, we present the preliminary virial black hole mass
and Eddington ratio, and using other measurements of Mg II
time-delay, we construct a Mg II–based radius–luminosity
relation and demonstrate that the departure of the sources
depends on their accretion rate, which leads to the significant
time-delay shortening for the highly accreting quasar HE 0413-
4031. In the discussion part in Section 6, we discuss the nature
of Mg II emission in terms of the source classification along the
quasar main sequence, taking into account its radio properties.
In addition, we analyze the response of the Mg II line with
respect to the continuum variability, which is related to the
intrinsic Baldwin effect, and we perform the SED fitting to
obtain independently the black hole mass and other parameters
related to accretion. Finally, we summarize the main conclusions
in Section 7.
2. Observations
The quasar HE 0413-4031, located at redshift z=1.389
according to the NED database, is a very bright source: VéronCetty
& Véron (2001) report the V magnitude of
MV=16.5 mag. Its position on the sky (04h
15m
14s
; −40°
23′ 41″) made it a very good target for the spectroscopic
monitoring with the SALT. The source was monitored from
2013 January 21 until 2019 August 8. The spectroscopic and
photometric data are summarized in Section A in
Tables A1–A3.
2.1. Spectroscopy
The quasar was observed using the Robert Stobie
Spectrograph on SALT (RSS; Burgh et al. 2003; Kobulnicky
et al. 2003; Smith et al. 2006). A slit spectroscopy mode was
used, with the slit width of 2″. Adopted medium resolution
grating PG1300 and the grating angle of 28.625, with the filter
PC04600, gave a configuration of a spectral resolution of 1523
at 7370 Å. The same configuration has been used in all 25
observations, covering more than six years. A single exposure
usually lasted about 820 s, and two exposures were taken
during each observation. All observations were performed in
service mode. The observation dates are given in Table A1.
The basic reduction of the raw data was done by the SALT
staff by applying a semiautomatic pipeline that was a part of the
SALT PyRAF package. At the next stage the two images were
combined with the aim to remove the cosmic rays as well as to
increase the signal-to-noise ratio. The wavelength calibration
was performed using the calibration lamp exposures taken after
the source observation. In most observations argon lamp was
used. Additionally, we checked the calibration using the OI sky
line 6863.955 Åbecause in our observations of another quasar
with SALT, the lamp calibration was not very accurate at early
years of monitoring. However, for HE 0413-4031 the
differences between the lamp calibration and the sky line
position were at a level of a fraction of an Angstroem.
Due to the specific design of the SALT, correcting for
vignetting is an important issue. For that purpose we used an
ESO standard star LTT 4364 (white dwarf, with practically no
spectral features in the interesting spectral range), which was
observed with SALT in the same configuration as the quasar.
Through analytic parameterization of the ratio of ESO and
SALT spectrum of the star, we obtained a correction to the
spectral shape of a quasar in the observed wavelength range
from 6342 to 6969 Åin the observed frame. Formally, the part
7
https://ned.ipac.caltech.edu/
8
We use the flux-frequency convention Fν∝ν+ α
.
2
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
97
of the spectrum up to 8600 Åis available, apart from two gaps,
but the correction of the spectral shape by the comparison star
is not satisfactory in this spectral range. Absolute calibration of
the SALT spectra was performed using the supplementary
photometry.
2.2. Photometry
Spectroscopic observations were accompanied by denser
photometric monitoring. For a significant part of our campaign,
high-quality data were collected as part of the OGLE-IV survey
done with the 1.3 m Warsaw telescope at the Las Campanas
Observatory, Chile. Monitoring was performed in the V band,
with the exposure time 240 s, and the typical error was about
0.005 mag.
We also obtained photometric measurements from the SALT
on the same night as the spectroscopic observations were
performed, whenever the instrument SALTICAM was available.
We used the images obtained in g band; usually two
exposures were made, with the exposure time 45 s. Because the
SALT instrument is not suitable for highly accurate photometric
observations, the typical error of this photometry is of
the order of 0.012 mag. Because SALTICAM data were
collected in a different band from OGLE, we allowed for a
grayshift of the SALTICAM set using the periods when the two
monitorings overlapped.
Finally, in the period between 2017 December 3 and 2019
March 24, we also performed short, denser monitoring with the
40 cm Bochum Monitoring Telescope (BMT), based at the
Universitaetssternwarte Bochum, near Cerro Armazones in
Chile.9
This monitoring was done in two bands, B and V, but
for the purpose of this work only V-band lightcurve has been
used. This data set is not entirely consistent with the OGLE +
SALTICAM data; there appears to be a slight offset by
0.171 mag, when comparing the earliest BMT point with the
last OGLE point. We corrected the magnitude of all the BMT
points by this offset, i.e., increasing their magnitudes by
0.171 mag to match the first BMT point with the nearest OGLE
point. For comparison, we performed time-delay measurements
with this data subset included or not included in the
photometric lightcurve. The photometric data points are listed
in Tables A2 and A3.
2.3. Spectroscopic Data Fitting
We use the same approach to the modeling of the Mg II
region as in Czerny et al. (2019). Because of the potential
problems with the remaining vignetting effect, we concentrate
only on the relatively narrow spectral band, from 2700 to
2900 Å, in the quasar rest frame. We allow for the following
components: (i) power-law component of arbitrary slope and
normalization, representing the continuum emission from the
accretion disk; (ii) Fe II pseudo-continuum modeled using
theoretical templates of Bruhweiler & Verner (2008), folded
with a Gaussian of the width representing the kinematic
velocity of the Fe II emitter; and (iii) the Mg II line itself. We
also test other Fe II templates for completeness, but we discuss
this issue separately, in Appendix C.
In our model, the Mg II line is parametrized in general by
two separate kinematic components, each modeled assuming a
Gaussian or a Lorentzian shape. The amplitudes, the width, and
the separation are the model parameters. Each kinematic
component in turn is modeled as a doublet, and the ratio within
the doublet components (varying from 1 to 2) depends on the
optical depth of the emitting cloud.
The additional parameter is the source redshift, because the
determination of the redshift in the NED database is not
accurate enough for our data. Because we do not have an
independent measure of the redshift from narrow emission
lines, we assume that Fe II and one of the Mg II components
represent the source rest frame.
All model parameters are fitted together; we do not first fit
the continuum, because in the presence of the Fe II pseudocontinuum
there is no clear continuum-dominated region and
fitting all components at the same time is more appropriate.
However, we differentiate between the global parameters and
the parameters when modeling individual spectra. We first
created a composite spectrum by averaging all observations; for
such an average spectrum we determined the redshift, the best
Fe II template and the Fe II smearing velocity, and the best
value of the doublet ratio, and these values were later kept fixed
when individual data sets were modeled.
We calculate the equivalent width (EW) of the lines with
respect to the power-law component, within the limits where
the model was applied (i.e., integrating between 2700 and
2900 Å). Calculation is done from the model, by numerical
integration, and EW(Mg II) contains both kinematic and
doublet components.
The reported errors of the fit parameters, including the errors
of EWs of Mg II and Fe II, were determined by construction of
the error contours—that is, computations for an adopted range
of the parameter of interest, with all other parameters allowed
to vary. This leads in general to asymmetric errors around the
best-fit value. For the requested accuracy, we adopted the χ2
increase by 2.706, appropriate for one parameter of interest,
which represents a 90% confidence level (statistical significance
0.1).10
2.4. Spectroscopic Flux Calibration and Mg II Absolute
Luminosity
The approach to data fitting outlined in Section 2.3 allows
only for deriving EW of the Mg II and Fe II lines. However,
computations of time-delay require the knowledge of the
continuum lightcurve and the line luminosity lightcurve.
A continuum lightcurve is provided by the photometric
monitoring, and we use this photometry to calibrate the SALT
spectra and to determine the Mg II line flux.
Because we have three instruments providing us with the
photometry, and they are of a different quality, as explained in
Section 2.2, we first perform the interpolation of the
photometry data points at the epochs for which the EW of
Mg II is available using the weighted least-squares linear
B-spline interpolation, using the inverse of photometry
uncertainties as the corresponding weights in the spline
interpolation algorithm.
Having established the photometric flux at the time of the
spectroscopic measurements still does not allow us to obtain
the calibrated spectrum easily. The V band does not overlap
with the wavelength covered by our spectroscopy (see
Section 2.1), and the redshift of our source (z=1.389)
corresponds to the rest-frame wavelength of 2304 Å. Therefore,
9
http://www.astro.ruhr-uni-bochum.de/astro/oca
10
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98 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
we have to interpolate between the V band and the median of
our fitting band, 2800 Årest frame. Because the measurement
of the continuum slope in our narrow wavelength range is not
very precise, and the slope changes between observations, the
use of this slope could introduce an unnecessary scatter into the
line flux calibration. Therefore we decided to use the broadband
quasar continuum spectrum of Zheng et al. (1997) 11
as a
template, and we assumed that the ratio between the flux at
2304 Å(corresponding to the V band in our quasar) and a
continuum at 2800 Åin HE 0413-4031 is always the same as in
the template.
This gave us a relation between the V magnitude and the
2800 Åcontinuum νFν flux at 2800 Å, F2800:
[ ] ( )= - - - -F Vlog 0.4 8.234 erg s cm 12800
1 2
This is of course an approximation, but the amplitude of the
flux variations in our source is not very large so the issue of a
spectrum becoming bluer when the quasar is brighter (see, e.g.,
Ulrich et al. 1997; Wilhite et al. 2005; Kokubo 2015, and the
references therein) should not be critical.
3. Results: Spectroscopy
3.1. Mean Spectrum
We first combined the SALT spectra in order to establish the
global source parameters, which will be fixed later in the
analysis of all 25 spectra.
The mean spectrum is shown in Figure 1 (top panel). For
comparison, in Figure 1 (middle panel) we also show the
spectrum in the early epoch (#5), when the quasar was close to
the minimum flux density, as well as the spectrum from the
later epoch close to the maximum flux density (#20, bottom
panel). The Mg II line shape in this quasar looks simple,
immediately suggesting that HE 0413-4031 belongs to class A
quasars (Sulentic et al. 2000). We checked that assuming just a
single kinematic component of Lorentzian shape for Mg II is
sufficient, and adding the second component does not improve
the χ2
significantly. The best fit for a 2-component model
allows for 0.2% contribution from the second kinematic
component, which is very broad (11,140 km s−1
), and the total
χ2
for such a fit is better than in a single-component fit only by
1.0. The source is thus a typical representative of class A
sources. We also checked that a Lorentzian shape offers much
better representation of the line shape than the Gaussian. If we
assume a single kinematic component with a Gaussian shape,
the reduced χ2
of the best fit is 16.0 per degree of freedom. If
we allow for 2 Gaussian kinematic components, one with no
shift with respect to Fe II and the second one at arbitrary
position, the fit improves (reduced χ2
=7.7) but still does not
match the one with a single Lorentzian shape, despite the
higher number of parameters. We note that in the case of the
2-Gaussian fit, the component bound to Fe II dominates
(contains 57% of the line flux), which happened at the expense
of the overall Fe II contribution, which dropped down by a
factor of 3 in comparison with a single Lorentzian fit. However,
such a fit is not favored by the data. The single-component
Lorentzian profile typical of population A sources (Sulentic
et al. 2000) arises due to the turbulence in the line-emitting
clouds, and the broadening of the line is due to the rotation
(Kollatschny & Zetzl 2011; Goad et al. 2012; Kollatschny &
Zetzl 2013a, 2013b).
Because in our full model one of the kinetic components was
set at zero rest-frame velocity, together with Fe II, while the
second kinematic component has an arbitrary shift in velocity
space with respect to them, we eliminated the first kinematic
component, leaving the second one, which allows for the
flexibility of the shift between Mg II and Fe II. This model is
also later used to fit individual spectra.
We tested several templates of the Fe II from Bruhweiler &
Verner (2008), and the best fit was provided by the d12-m20-
20-5.dat model, which assumes the cloud number density
1012
cm−3
, the turbulent velocity 20 km s−1
, and the hydrogen
ionizing photon flux 10−20.5
cm−2
s−1
. The same template was
favored for the quasar CTS C30.10 also monitored by SALT
(Czerny et al. 2019). It is not surprising, because recent
modeling of the quasar main sequence also suggest values of
that order for the local BLR cloud density and the turbulent
Figure 1. Top:flux-calibrated mean spectrum of HE 0413-4031. Data are
shown with a red line, and the black line gives the best-fit model. Remaining
lines show the spectral components: power law (green dashed line), Fe II
pseudo-continuum (blue dotted line), and Mg II total flux (two doublet
components, magenta dotted line). The lower panel shows the residua, which
are noticeable only close to 2900 Å, where the sky line contamination was the
strongest and the background subtraction did not fully correct for this effect.
Middle:flux-calibrated spectrum of HE 0413-4031 for the minimum phase
(epoch 5). The lines represent the same spectral components as in the top panel.
Bottom:flux-calibrated spectrum of HE 0413-4031 for the maximum phase
(epoch 20). The lines represent the same spectral components as in the top
panel. The epochs are listed in Table A1.
11
Downloaded fromhttps://archive.stsci.edu/prepds/composite_quasar/.
4
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
99
velocity (Panda et al. 2018, 2019a). The best-fit half-width of
the Gaussian used for template convolution was 1200 km s−1
.
We calculated a grid of models for different redshift and
different ratio of the doublet, and these two quantities are
strongly coupled. We determined the best-fit redshift as
z=1.37648, and the doublet ratio as 1.9. This is a value
quite close to the optically thin case, 2:1 ratio.
These parameters—the choice of the Fe II template, template
smearing velocity, redshift, and doublet ratio—were later
assumed to be the same in all fits of the individual spectra,
while the Fe II amplitude, Mg II amplitude, line width and line
shift, and power-law parameters were allowed to vary from
observation to observation.
The best-fit FWHM of the Mg II line in the mean spectrum is
-
+
4380 15
14
km s−1
, formally just above the line dividing the class
A and class B source (Sulentic et al. 2000; Marziani et al.
2018). However, some trend with the mass in this division is
expected, because for Seyfert galaxies the dividing line
between Narrow Line Seyfert 1 galaxies and Seyfert galaxies
is at 2000 km s−1
(Osterbrock & Pogge 1985), instead of at
4000 km s−1
, as in quasars. HE 0413-4031 is still more massive
and brighter than most quasars in Sloan Digital Sky Survey
(SDSS) catalogs (Shen et al. 2011; Pâris et al. 2017). Because
we fit the single Lorentzian shape, we cannot derive the line
dispersion σ from the fit, because the Lorentzian shape
corresponds to the limit of FWHM/s  0. We can, however,
determine the line dispersion numerically because the FWHM/
σ ratio is an important parameter (Collin et al. 2006).
Therefore, we subtracted the fitted Fe II and the remaining
underlying continuum, and integrated the line profile. We
obtained σ=2849 km s−1
, and FWHM/σ=1.54, which
confirms that the source belongs to Population 2 of Collin et al.
(2006), or class A of Sulentic et al. (2000).
In the mean spectrum, the EW(Mg II) is -
+
27.45 0.10
0.12
Å, a bit
below the average value for the Mg II from Large Bright
Quasar Sample (42 Å, Forster et al. 2001).
The most interesting part is the shift we detect between the
Mg II line and the Fe II pseudo-continuum. This shift is by
15.1 Å, or equivalently, 1620 km s−1
, and the Mg II line is
redshifted with respect to Fe II. It may also be that Fe II is
blueshifted with respect to Mg II; however, we cannot
distinguish between these cases. Kovačević-Dojčinović &
Popović (2015) in their study observed redshifts, not blueshifts
of the Fe II. In addition, the conclusion about the relative shift
strongly depends on the combination of the Fe II template used
and the adopted redshift, as we discuss in Appendix C.
Unfortunately, we are unable to establish the proper position
of the rest frame for our SALT observation. We failed to
identify the narrow [NeV]3426.85 Å line, which is relatively
strong in the quasar spectra,12
but this search did not yield a
reliable identification.
3.2. Determination of the Mean and RMS Spectra
For constructing the mean and the rms spectra, we follow the
standard procedure as explained by Peterson et al. (2004). The
mean spectrum is calculated using the following relation
( ) ( ) ( )ål l=
=
F
N
F
1
, 2
i
N
i
1
where Fi(λ) are individual spectra. For studying variability
phenomena, we also construct an rms spectrum using
⎧
⎨
⎩
⎫
⎬
⎭
( ) [ ( ) ( )] ( )ål l l=
-
-
=
S
N
F F
1
1
. 3
i
N
i
1
2
1 2
The flux-calibrated mean and rms spectra are shown in the
top panels of Figures 1 and 2, respectively. For the flux
calibration we used the composite quasar spectra created by
Vanden Berk et al. (2001). For the continuum, they proposed a
power law with an index of αλ=−1.56. This continuum was
normalized for each spectrum according to the V magnitudes
reported in Table A2, which were simply converted to flux
units in order to get the flux normalization.
The rms spectrum was estimated following Equation (3).
Mean and rms profiles look similar, but to check this more
quantitatively, we fitted the rms spectrum in the same way we
fitted the mean spectrum. The result is shown in Figure 2, upper
panel. The line is still well fitted when we use a single
Lorentzian model. The FWHM in rms spectrum is 4337 km
s−1
, only marginally narrower than the FWHM of the mean
spectrum (4380 km s−1
). When the mean and rms spectra are
compared at the zero-flux level, i.e., with the continuum
subtracted, we see that the core of Mg II is most variable, with
Figure 2. Decomposition of the flux-calibrated rms spectrum (top panel) and
the comparison of the rms (red) and mean (black) spectra at the zero-flux level
(represented by a dashed green line), first with the continuum subtracted (Mg II
+Fe II; middle panel), and subsequently with the Fe II emission subtracted
(Mg II; bottom panel). From the rms spectra it is clear that the core of Mg II line
is the most variable, with a much smaller variability in the wings.
12
http://classic.sdss.org/dr6/algorithms/linestable.html
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The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
100 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
the wings having a much smaller variability, which could be
attributed to Fe II emission (see the central panel of Figure 2). If
we subtract the Fe II pseudo-continuum from the rms and mean
spectra, the only variable part of the Mg II emission is at the
core of the line (see the bottom panel of Figure 2). The
EW(Mg II) if measured in the rms spectrum is 21.01 Å, lower
than in the mean spectrum (27.45 Å), and EW(Fe II) is lower
than in the mean spectrum (8.32 Å instead of 10.13 Å), which
results from the enhanced role of the continuum power law.
The consistency of the rms and the mean spectra fits also
supports the single-component Lorentzian fit of the line shape.
3.3. Spectral Fits of Individual Observations
For each of the spectra, the EW(Mg II), FWHM(Mg II),
EW(Fe II), shift between Mg II and Fe II, and power spectrum
parameters were determined. The results are given in Table A1,
and Figure 3 visually shows the evolution of these properties
with time.
The mean shift of the Mg II and Fe II lines, calculated from the
individual spectra, is 1582 km s−1
, somewhat smaller than
obtained from the mean spectrum. Variations from one spectrum
to the other are at the level of 82 km s−1
(dispersion), larger than
individual errors. If we fit a linear trend, we see a systematic
increase of the Mg II and Fe II separation by 109 km s−1
in six
years, but it is not much larger than the dispersion in the
measurements; however, it seems formally significant if we use
the individual measurement errors given in Table A1. The
corresponding acceleration 18 km s−1
yr−1
is much smaller than
the large value of 104±14 km s−1
yr−1
found for the quasar HE
0435-4312 also using the SALT instrument (Średzińska et al.
2017).
The averaged FWHM is 4390.8 km s−1
; the dispersion is
200 km s−1
, again slightly larger than typical measurement
error, but no interesting trends could be noticed. Thus, we
observe some small variations in the line shape, but they are
indeed marginal, consistent with the fact that rms spectrum is
similar to the mean shape of the line.
3.4. Lightcurves: Variability and Linear Trends
The continuum photometric lightcurve and the Mg II lightcurve
are presented in Figure 3. The continuum shows a mostly
slow but noticeable variation. A single brightening trend
dominates for most of the monitoring period, replaced with
some dimming during the last 1.5 yr. The overall variability
level of the continuum is Fvar=13.0%, if BMT telescope is
included, and 10.4%, if these data are not taken into account.
Here we use the standard definition of the excess variance,
( )
( )å
d
=
- -
=
F
x x x
Nx
, 4
i
N
i i
var
1
2 2
2
where x is the average value, and δxi is the individual
measurement error. Because this linear trend seems suggestive,
we also checked the shorter timescale variability by first fitting
a linear trend to the lightcurve in the log space (i.e., when using
magnitudes), and then subtracting this trend from the original
lightcurve. We did this only for the data without BMT. The Fvar
dropped from 10.4% down to 7.4%.
The Mg II line variability is lower, Fvar=7.2%, and
Fvar=7.1%, depending on whether BMT telescope data were
or were not used for Mg II calibration, respectively. It is
interesting to note, however, that the levels of variability in
Mg II and the continuum are comparable if the long-term trend
was subtracted from the data.
We also determine Fe II lightcurve, and the variability level
of Fe II seems higher, at the level of 14.7% if BMT data are
neglected, and 14.9% if the BMT data are included. However,
the measurement errors are large due to the coupling between
the continuum and Fe II pseudo-continuum.
Figure 3. Temporal evolution of photometric and spectroscopic characteristics
from the monitoring of the quasar HE 0413-4031. From the top to the bottom
panels: photometric lightcurve (V-band magnitude) from OGLE, SALT, and
BMT (color-coded; BMT data were shifted by 0.171 mag up to correct for the
systematic offset with respect to the OGLE data); Mg II line-emission
lightcurve (in erg s−1
cm−2
); the equivalent width of the Mg II line in Å; the
velocity shift of the Mg II line with respect to the Fe II line in km s−1
; the
equivalent width of Fe II line in Å. The time is expressed in JD-2450000.
6
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
101
The mean monochromatic luminosity at 3000 Å can be
derived from the V-band magnitude of 16.5, using the
extinction reported in NED with a value of 0.034, source
redshift of 1.389, and standard cosmological parameters for the
flat universe (H0=70 km s−1
Mpc−1
, Ωm=0.28, and
ΩΛ=0.72, see Kozłowski 2015, for details). We obtain
=Llog 46.7543000 . The uncertainty of the monochromatic
luminosity can be estimated from the minimum and the
maximum points along the photometric lightcurve, 16.429 mag
and 16.830 mag, respectively, which implies =Llog 3000
max
46.782 and =Llog 46.6223000
min
. Hence, for the further analysis,
we consider = -
+
Llog 46.7543000 0.132
0.028
.
As already pointed out, the linear trend is present in both
continuum and Mg II line emission lightcurves. In Figure 4, we
show the fit of a linear function to both lightcurves, considering
the case with and without BMT data in the left and right panels,
respectively. The linear trend is toward smaller magnitudes, i.e.,
the continuum and line-emission flux densities increase during the
observational run. The slope of the linear trend is larger for
the continuum than for the line-emission lightcurves. The
continuum slope is sc=0.057 mag yr−1
and the line slope is
sl=0.024 mag yr−1
with the BMT data included; without BMT
data, the continuum increase drops a little, sc=0.051 mag yr−1
,
while the line-emission slope is comparable, sl=0.023 mag yr−1
.
In other words, the decrease in the continuum magnitude is 2.38
and 2.17 larger than the decrease for the line-emission magnitude
with and without BMT data, respectively.
4. Results: Time-delay Determination
As for the intermediate-redshift quasar CTS C30.10
(z=0.90052) (Czerny et al. 2019), we apply several methods
to determine the time-delay between the continuum V band and
Mg II line emission. Apart from the standard interpolated crosscorrelation
function, we apply several statistically robust
methods suitable for unevenly sampled, heterogeneous pairs
of lightcurves (see Zajaček et al. 2019b, for an overview),
namely the discrete correlation function, z-transformed discrete
correlation function, JAVELIN, χ2
method, Von Neumann,
and Bartels estimator. For all seven methods, we consider the
two pairs of lightcurves, those with and without magnitudeshifted
BMT data. The detailed description of the time-delay
analysis is in the Appendix in Section B, with subsections B.1–
B.6 describing individual methods including the corresponding
plots and the tables.
4.1. Final Time-delay for Mg II Line
Due to the systematic offset of the BMT data in the
continuum lightcurve, we decided to distinguish two cases for
all time-delay analysis techniques. For a matter of completeness,
below we summarize in Table 1 the main results for all
the methods, including the cases with and without magnitudeshifted
BMT data. The most prominent peak in the time-delay
distributions is the peak close to 700 days in the observer’s
frame. This peak is generally present in all seven methods.
However, the ICCF analysis generally gives longer time-delays
of 900–1000 days, which could be caused by the interpolation
and hence by adding new points to the analysis. A noticeable
difference is also for the JAVELIN method, where the timedelay
peak is close to 1050 days. Because JAVELIN uses the
damped random walk for fitting the continuum lightcurve,
which is then smoothed and time-delayed to reproduce the
Mg II line-emission lightcurve, extra points are introduced to
the lightcurves in a similar way as for the ICCF. This can lead
to biases and artifacts, especially for irregular and sparse data
sets. This is why we decided to prefer the peak around
700 days, which is the most prominent for all discrete methods
that do not require interpolation and are model-independent
(DCF, zDCF, Von Neumann). The detected time-delay of
-
+
498.9 125.9
170.9
days for the Von Neumann estimator with shifted
BMT data is most likely an artifact because it is an excess
given by only one point; see Figure B6 (left panel). The second
minimum of the Von Neumann estimator around 700 days is
then more pronounced and clearly given by more points. In
addition, the minimum around 500 days is not present for the
case without BMT data; see Figure B6 (right panel).
Given the arguments above, we focus on the observed timedelay
around 700 days. Concerning the average value, we
obtain the rest-frame time-delay of t = -
+
302.21 61.4
43.3
days for the
case with the shifted BMT data, and t = -
+
303.02 24.5
37.8
days for
the case without them. The final average value then is
Figure 4. Linear-trend fit to both continuum and line-emission lightcurves in the log space. Left panel: the linear trend fits with BMT data included. The BMT data
were shifted by 0.171 mag to correct for the systematic shift with respect to the OGLE data. The legend includes the best-fit parameters for both the continuum and the
line-emission lightcurves. The fit statistics are χ2
=7121.4 and c = 84.8red
2
for the continuum and χ2
=177.9 and c = 7.7red
2
for the line lightcurve. Right panel: as
in the left panel, but without BMT data. The fit statistics are χ2
=5609.2 and c = 79.0red
2
for the continuum and χ2
=172.9 and c = 7.5red
2
for the line lightcurve.
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The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
102 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
t = -
+
302.6 33.1
28.7
days, which corresponds to the light-travel
distance of t= = ~-
+
R c 0.254 pc 10 cmMg II 0.028
0.024 17.9 . The
inferred value of the light-travel distance RMg II is larger than
typical BLR length-scales inferred from other RM campaigns
with time-delays of the order 10–100 light days for AGN with a
broad range of black hole masses (Korista & Goad 2000, 2004;
Shen et al. 2016). The length-scale of the BLR has implications
for the line variability, as was shown by Guo et al. (2020), and
we will specifically discuss the Mg II line–continuum variability
relation in Section 6.2.
The results provided by the ICCF and the JAVELIN
analyses provide a time-delay that we treat as secondary for
the reasons of interpolation and the model-dependence. In the
rest frame, this secondary time-delay is -
+
428.8 48.1
29.4
days for the
case with the shifted BMT data and -
+
433.2 45.0
29.9
days for the case
without the BMT data. The average rest-frame value is
-
+
431.0 32.9
21.0
days. This secondary time-delay peak should be
reevaluated when more continuum and line-emission data are
available to assess if it is just an artifact of data sampling
irregularity.
5. Results: Mg II–based Radius–Luminosity Relation
5.1. Preliminary Virial Black Hole Mass and Eddington Ratio
The virial black hole mass can be determined from the
virial relation for the BLR, t=M f c GFWHM• vir BLR
2 =
( ) ´-
+
M1.134 100.072
0.089 9
, which was calculated assuming the
virial factor equal to unity, the average time-delay for Mg II
inferred earlier, and the best-fit FWHM of -
+
4380 15
14
km s−1
. In
general, however, the virial factor may deviate from unity,
which is indicated by the study of Mejía-Restrepo et al. (2018),
which implies the anticorrelation between the virial factor and
the line FWHM, which is in our case the main source of
uncertainty. According to Mejía-Restrepo et al. (2018), we
have
⎜ ⎟
⎛
⎝
⎞
⎠
( )
( )=
 -

f
FWHM Mg II
3200 800 km s
, 5vir,Mg II
obs
1
1.21 0.24
which for = -
+
FWHM 4380 15
14
km s−1
leads to the virial factor
less than unity, fvir,Mg II=0.42–0.92, and the virial black hole
mass in the range of M•=4.8×108
–1.0×109
Me, hence we
have a factor of 2 uncertainty in the virial black hole mass. The
Eddington luminosity can be estimated as
⎛
⎝
⎜
⎞
⎠
⎟ ( )

= ´ -L
M
M
1.256 10
10
erg s , 6Edd
47 •
9
1
while the bolometric luminosity may be calculated using
the bolometric correction with respect to λ=3000 Å,
Lbol=(5.62±1.14)L3000 (Richards et al. 2006), which leads
to the Eddington ratio of ηEdd=Lbol/LEdd≈2.18. Using the
power-law calibration of the bolometric correction by Netzer
(2019), we obtain Lbol;2.8L3000, which gives ηEdd≈1.27.
Hence, these values imply close to the Eddington or even the
super-Eddington accretion mode.
5.2. Position in the Radius–Luminosity Plane
By combining the rest-frame time-delay and the monochromatic
luminosity of HE 0413-4031, we can position the source
on the radius–luminosity plane alongside the other quasars to
check for the potential deviation of HE 0413-4031 due to its
high accretion rate, as was previously detected for superEddington
sources monitored in the broad Hβ line (Wang et al.
2014a, 2014b; Martínez-Aldama et al. 2019).
With the rest-frame time-delay of t = -
+
302.6 33.1
28.7
days and
the monochromatic luminosity of = -
+
Llog 46.7543000 0.132
0.028
,
the source HE 0413-4031 lies below the expected
radius–luminosity relation, R(Mg II)−L3000 (Vestergaard &
Osmer 2009). We demonstrate this in Figure 5, in which we
compiled all the sources whose time-delay was determined for
the Mg II line (10 sources, see Table 3 in Czerny et al. 2019),
including CTS C30.10 and the new source HE 0413-4031. The
list of all the sources with measured time-delays and
determined monochromatic luminosities is in Table 2. With a
large scatter (σ=0.246 dex), the sources approximately follow
the radius–luminosity relationship previously derived for the
Table 1
Summary List of the Time-delays Expressed in Light Days in the Observer’s Frame between the Continuum and Mg II Line-emission Lightcurves for the Flatspectrum
Radio Quasar HE 0413-4031
Method With Shifted BMT data Without BMT data
ICCF interpolated continuum—centroid [days] -
+
1004.6 246.2
196.8
-
+
1003.2 235.4
205.3
ICCF interpolated line—centroid [days] -
+
1008.4 276.9
142.2
-
+
1034.171 248.9
139.1
ICCF symmetric—centroid [days] -
+
1009.7 211.5
113.6
-
+
1021.7 207.8
114.5
DCF peak time-delay—bootstrap [days] -
+
720.4 147.9
115.1
-
+
726.0 145.7
114.4
zDCF maximum likelihood -
+
720.9 527.3
323.9
-
+
720.9 100.1
331.3
JAVELIN peak time-delay [days] -
+
1053.7 163.6
79.8
-
+
1058.5 150.7
77.1
Von Neumann peak—bootstrap [days] -
+
498.9 125.9
170.9
-
+
711.3 139.5
149.0
Bartels peak—bootstrap [days] -
+
710.9 173.0
172.3
-
+
714.6 164.6
176.1
c2 peak—bootstrap [days] -
+
720.4 102.2
145.6
-
+
727.7 85.2
160.0
Average of the most frequent peak—observer’s frame [days] -
+
718.2 145.8
102.8
-
+
720.1 58.3
89.8
Average of the most frequent peak—rest frame -
+
302.2 61.4
43.3
-
+
303.0 24.5
37.8
Average of the secondary peak—observer’s frame [days] -
+
1019.1 114.2
69.9
-
+
1029.4 107.0
71.0
Average of the secondary peak—rest frame [days] -
+
428.8 48.1
29.4
-
+
433.2 45.0
29.9
Note. We distinguish for all methods two cases—with and without magnitude-shifted BMT data.
8
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
103
Mg II line (Vestergaard & Osmer 2009),
⎡
⎣
⎢
⎤
⎦
⎥
⎛
⎝
⎜
⎞
⎠
⎟
( )
‐
( )
t
= + -
L
log
Mg II
1lt day
1.572 0.5 log
10 erg s
, 73000
44 1
as well as the radius–luminosity relationship derived for the Hβ
line for lower-redshift sources by Bentz et al. (2013),
⎡
⎣
⎢
⎤
⎦
⎥
⎛
⎝
⎜
⎞
⎠
⎟
( )
‐
( )
t b
= + H
L
log
1lt day
1.391 0.533 log
10 erg s
, 83000
44 1
in which we replaced L5100 monochromatic luminosity by L3100
using L5100;0.556 L3000, using the power-law relations for
the bolometric corrections derived by Netzer (2019). The
scatter of the sources around the relation by Bentz et al. (2013)
is σ=0.269 dex, which is comparable to the scatter with
respect to the relation by Vestergaard & Osmer (2009).
We also fitted the general radius–luminosity relationship
( ‐ )tlog 1 lt day = ( )a+ -K Llog 10 erg s3000
44 1 to all available
data. We obtained the best-fit parameters of
K=1.45±0.08 and α=0.42±0.05 with χ2
=76.6 and
c = 8.5red
2
. Subsequently, we removed 2 outliers—CTS252
and HE 0413-4031—that are significantly below RL relations
in Equation (7) and Equation (8). This helped to improve the
fit, with the best fit with χ2
=36.7 and c = 5.2red
2
, and the
Figure 5. Radius–luminosity relation for the reverberation-mapped sources in the broad Mg II line resembles the radius–luminosity relation for the Hβ line. Left panel:
radius–luminosity relation for the RM quasars monitored in the broad Mg II line. Clearly, the sources follow within uncertainties the scaling relationship previously
derived by Vestergaard & Osmer (2009) for the Mg II line (dashed blue line) as well as the Hβ radius–luminosity relationship of Bentz et al. (2013) (dashed green
line). The best-fit relationships are also displayed, both for the case when all the sources are included in the fitting procedure (solid orange line) and for the case when
two outliers that are below the radius–luminosity relations are removed (CTS252 and HE 0413-4031) toward the higher luminosities (solid red line). Individual
sources are color-coded to show the logarithm of the dimensionless accretion-rate parameter M (see Equation (11)), according to the color bar to the right. Right panel:
the strong anticorrelation (with the Pearson correlation coefficient of p=−0.940) of the parameter Δτ, which expresses the rate of departure from the radius–
luminosity relation (see also Equation (12)), with respect to the dimensionless accretion-rate parameter M expressed by Equation (11).
Table 2
Characteristics of Reverberation-mapped Sources Monitored Using the Broad Mg II Line
Source z τ (days) ( ( ))-Llog erg s3000
1 FWHM (Mg II) (km s−1
) M Δτ τcorr (days)
141214.20+532546.71,2
0.45810 -
+
36.7 4.8
10.4
44.63882±0.00043 2391±46 -
+
8.21 5.58
6.94
- -
+
0.28 0.07
0.13 +
80.710.6
22.9
141018.04+532937.51,2
0.46960 -
+
32.3 5.3
12.9
43.7288±0.0051 3101±76 -
+
0.30 0.21
0.31
-
+
0.20 0.08
0.18
-
+
27.1 4.4
10.8
141417.13+515722.61,2
0.60370 -
+
29.1 8.8
3.6
43.6874±0.0029 3874±86 -
+
0.23 0.20
0.15
-
+
0.18 0.14
0.06 +
22.46.8
2.8
142049.28+521053.31,2
0.75100 -
+
34.0 12.0
6.7
44.6909±0.0009 4108±39 -
+
4.87 4.57
3.57
- -
+
0.35 0.16
0.09
-
+
64.2 22.6
12.6
141650.93+535157.01,2
0.52660 -
+
25.1 2.6
2.0
43.778±0.002 4066±202 -
+
0.39 0.27
0.26
-
+
0.06 0.06
0.05
-
+
22.6 2.3
1.8
141644.17+532556.11,2
0.42530 -
+
17.2 2.7
2.7
43.9480±0.0011 2681±96 -
+
2.87 2.03
2.03
- -
+
0.20 0.07
0.07
-
+
27.8 4.4
4.4
CTS2523,4
1.89000 -
+
190.0 114.0
59.0
46.79±0.09 3800±380 -
+
251.55 367.22
261.03
- -
+
0.84 0.28
0.18
-
+
1136.2 682.0
353.1
NGC41515,6
0.00332 -
+
6.8 2.1
1.7
42.83±0.18 4823±1105 -
+
0.15 0.23
0.23
-
+
0.05 0.17
0.15
-
+
4.7 1.4
1.2
NGC41515,6
0.00332 -
+
5.3 1.8
1.9
42.83±0.18 6558±1850 -
+
0.16 0.27
0.28
- -0.06 0.18
0.19
-
+
3.7 1.2
1.3
CTS C30.107,7
0.90052 -
+
564 71
109
46.023±0.026 5009±325 -
+
1.29 0.98
1.05
+ -
+
0.09 0.09
0.11
-
+
721.4 90.8
139.4
HE 0413-40318,9
1.37648 -
+
302.6 33.1
28.7
46.754±0.080 4380±14 -
+
66.04 44.76
44.17
- -
+
0.61 0.11
0.11
-
+
1223.9 134.1
116.4
Note. From the left to the right column, the table lists the source name, redshift, measured time-delay in light days in the rest frame, the logarithm of the
monochromatic luminosity at 3000 Å, FWHM of Mg II in km s−1
, the dimensionless accretion rate as defined in Equation (11), departure parameter Δτ defined by
Equation (12), and the corrected time-delay expressed in light days in the rest frame (see also Equation (14)). The superscripts to source names indicate the sources,
from which we obtained the measured time-delay (first source) and the monochromatic luminosity at 3000 Å (second source): (1) Shen et al. (2016); (2) Shen et al.
(2019); (3) Lira et al. (2018); (4) NED, NUV, GALEX; (5) Metzroth et al. (2006); (6) Code & Welch (1982); (7) Czerny et al. (2019); (8) this work; and (9) a script of
Kozłowski et al. (2010).
9
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
104 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
final relation based on Mg II data can be expressed as
⎡
⎣
⎢
⎤
⎦
⎥
⎛
⎝
⎜
⎞
⎠
⎟
( )
‐
( ) ( )
( )
t
=  + 
´ -
L
log
Mg II
1lt day
1.46 0.06 0.58 0.07
log
10 erg s
. 93000
44 1
Both best-fit relations are depicted in Figure 5 with solid lines.
The time-delay offset can be explained by the higher
accretion rate implied by the super-Eddington luminosity. The
correlation of the time-delay offset with the accretion rate was
shown previously for reverberation-mapped sources in the Hβ
line (Du et al. 2018; Martínez-Aldama et al. 2019), and we will
demonstrate it in the following section for the broad Mg II line.
By moving the source HE 0413-4031 back onto the radius–
luminosity relation, we can estimate the corrected black hole
mass using (Vestergaard & Osmer 2009)
⎡
⎣⎢
⎤
⎦⎥
⎛
⎝
⎜
⎞
⎠
⎟
( )
( )( ) l
= l l
- -
M
L
10
FWHM Mg II
1000 km s 10 erg s
, 10zp
•
Mg II
1
2
44 1
0.5
which for FWHM(Mg II)= -
+
4380 15
14
km s−1
and zp(λ)=6.86
(λ=3000 Å) yields = ´M M3.31 10•
Mg II 9 using the
monochromatic luminosity of =Llog 46.7543000 .
Hence, the black hole mass obtained from the radius–
luminosity relation is larger by a factor of at least ∼3 than the
maximum mass inferred from the RM time-delay, taking into
account the uncertainty in the virial factor. The Eddington ratio
for the higher mass then drops to ηEdd=0.77 for the constant
bolometric correction factor of BC=5.62 (Richards et al.
2006). For the more precise luminosity-dependent bolometric
correction of BC=25×(L3000/1042
erg s−1
)−0.2
=2.80 for
L3000=1046.754
erg s−1
(Netzer 2019), we get an even smaller
Eddington ratio of ηEdd=0.38, which is also consistent with
the SED fitting presented in Section 6.3.
5.3. Correction of the Accretion-rate Effect along the Radius–
Luminosity Relation
In the optical range, it has been observed that the accretion
rate is responsible for the departure of the radius–luminosity
relation more than the intrinsic scatter. Du et al. (2018, and
references therein) showed that the sources with the highest
accretion rates have time-delays shorter than expected from the
optical radius–luminosity relation. However, the accretion-rate
effect can be corrected, recovering the standard results
(Martínez-Aldama et al. 2019). Following this idea, we
repeated the same exercise for all Mg II reverberation-mapped
data (see Table 2).
The black hole mass was estimated assuming a virial factor
anticorrelated with the FWHM of the emission line
(Equation (5)), which apparently corrects the orientation effect
to a certain extent. Because the Eddington ratio has shown a
large scatter in comparison with other expressions of the
accretion rate (Martínez-Aldama et al. 2019), we will use the
dimensionless accretion rate (Du et al. 2016),
⎜ ⎟
⎛
⎝
⎞
⎠
( )
q
= -
M
l
m20.1
cos
, 1144
3 2
7
2
where l44 is the luminosity at 3000 Å in units of 1044
erg s−1
,
θ=0.75 is the inclination angle of disk to the line of sight, and
m7 is the black hole mass in units of 107
Me. In Figure 5 (left
panel), we show the variation of the dimensionless accretion
rate along the radius–luminosity relation, which is similar to the
observed one in the optical range.
To estimate the departure from the radius–luminosity
relation, we use the parameter Δτ, which is simply the
difference between the observed time-delay and the expected
one from the radius–luminosity relation,
⎛
⎝
⎜
⎞
⎠
⎟ ( )t
t
t
D =
log
. 12obs
R L
We estimate τR−L from the radius–luminosity relation
described in Equation (9). Values are reported in Table 2.
The largest departure from the radius–luminosity relation is
associated with the highest accretion-rate sources, which is
clearly evidenced in Figure 5 (right panel). The Pearson
coefficient (p=−0.940) also indicates a strong anticorrelation
between Δτ and M. Performing a linear fit, we get the relation
( ) ( ) ( )
( )
 tD = -  + - M M0.297 0.033 log 0.049 0.026 ,
13
for which χ2
=6.75 and c = 0.75red
2
. This expression can be
used to recover the expected values from the radius–luminosity
relation using the relation
( ) · ( )( ) 
t t= t-DM 10 . 14M
corr obs
The corrected rest-frame time-delays are listed in Table 2.
Based on them, we construct a new version of the radius–
luminosity relation for the Mg II line corrected for the
accretion-rate effect (see Figure 6). It shows a smaller scatter
of σ=0.104 dex in comparison with the radius–luminosity
relation before the correction, which is σ=0.221 dex when all
the sources are included and σ=0.186 dex with two outliers
Figure 6. The radius–luminosity relation for the Mg II broad-emission line; the
rest-frame time-delays were corrected for the accretion-rate effect. The best-fit
linear relation in the log space is ( )tlog 1 lt. day =
( ) ( ) ( ) +  -L1.48 0.03 0.60 0.02 log 10 erg s3000
44 1 , with χ2
=11.40
and c = 1.27red
2
. For comparison, we also show the radius–luminosity relation
as inferred by Bahk et al. (2019), which has the same normalization factor as
our relation, but a smaller slope of 0.5. In addition, we depict the radius–
luminosity relation constructed by Trakhtenbrot & Netzer (2012), which, on the
other hand, has a comparable slope of α=0.615, but a smaller normalization
factor of K=1.33.
10
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
105
removed. The best-fit linear relation has smaller uncertainties
with χ2
=11.40 and c = 1.27red
2
and can be expressed as
⎡
⎣
⎢
⎤
⎦
⎥
⎛
⎝
⎜
⎞
⎠
⎟
( )
‐
( ) ( )
( )
t
=  + 
´ -
L
log
Mg II
1lt day
1.48 0.03 0.60 0.02
log
10 erg s
. 153000
44 1
The dispersion around the new relation is very small, equal
to 0.104 dex. This is smaller than the dispersion of 0.13 dex in
the original radius–luminosity relation of Bentz et al. (2013)
after an artificial removal of outliers, despite the fact that the
Mg II relation covers a broad range of the luminosities,
redshifts, and Eddington ratios. It is not clear at this point
whether the smaller dispersion is a property of the Mg II
emission or it just results from the fact that the Mg II data do
not come from so many different monitoring campaigns.
The normalization coefficient in Equation (15) is within
uncertainties consistent with the normalization factor inferred
from the Mg II–based black hole mass estimator by Bahk et al.
(2019),
⎡
⎣
⎢
⎤
⎦
⎥
⎛
⎝
⎜
⎞
⎠
⎟
( )
‐
( )
t
+ -
L
log
Mg II
1lt day
1.499 0.5 log
10 erg s
, 163000
44 1
where we adopted their fitting Scheme 4 and assumed the virial
factor fvir≡1 while transforming ( )µ DM L V• 3000
0.5 2
relation to
t µ L3000
0.5
relation. The relation 16 is also shown in Figure 6 for
comparison with our best-fit relation 15.
However, the best-fit slope is larger than the slope of 0.5 in
Equation (16), which is also expected from the simple
photoionization arguments. Currently, this may be just a
systematic effect due to a small number of reverberationmapped
sources using the Mg II line. The larger slope currently
yields a significantly small scatter, because for the relation
given by Equation (16) the scatter is σ=0.187 dex for the
corrected time-delays. For the uncorrected rest-frame timedelays,
the scatter is σ=0.247 dex and σ=0.189 for the
whole Mg II sample (sources in Table 2) and the Mg II sample
without the two outliers (CTS252 and HE 0413-4031),
respectively.
On the other hand, our best-fit slope is very similar to the
value of α=0.615 inferred by Trakhtenbrot & Netzer (2012),
who, on the other hand, have a smaller normalization factor
K=1.33. Our slope value is also located between the slopes
derived for the τ(Mg II)–L3000 relation by McLure & Jarvis
(2002) (α=0.47) and by McLure & Dunlop (2004)
(α=0.62). However, all of the above-mentioned Mg II–based
radius–luminosity relations were calibrated based on the UV
spectra of sources for which only Hβ line RM was performed.
Certainly, more reverberation-mapped sources using the Mg II
line are required to further constrain the τ(Mg II)–L3000 relation.
6. Discussion
Using the SALT data and the supplementary photometric
monitoring, we were able to derive the time-delay of the Mg II
line with respect to the continuum in z=1.37648 quasar HE
0413-4031. The source is very bright in the absolute term, but
the delay is formally established as t = -
+
302.6 33.1
28.7
days in the
comoving frame. Although the analysis of the Mg II complex
with the underlying power-law continuum and Fe II pseudocontinuum
emission is a complex task with a certain degree of
degeneracy, we showed that the peak value of the time-delay
distribution is not sensitive to different Fe II templates; only its
uncertainty may be affected due to a different number of
parameters used in each model (see also Appendix C for a
detailed discussion).
This delay is shorter than derived for CTS C30.10 (Czerny
et al. 2019), but similar to the delay measured for another bright
quasar by Lira et al. (2018). We show that the dispersion in the
measured time-delay of the Mg II line for a given range of the
monochromatic flux is related to the Eddington ratio in the source,
as in the Hβ time-delay (Martínez-Aldama et al. 2019), and with
the appropriate correction for this effect, the dispersion around the
radius–luminosity is actually very small, with σ=0.104 dex in
comparison with σ=0.221 dex before the correction (when all
the sources are included; σ=0.186 dex with two outliers
removed), which opens up a possibility for the future applications
of this relation for cosmology.
In this section, we discuss more generally the validity and
the accuracy of using Mg II lines in black hole mass
determination. Furthermore, we show that the intrinsic Baldwin
effect is present in our source, which is another way of showing
that the Mg II line responds to the thermal AGN continuum. To
verify if the reverberating Mg II line in our source is a reliable
probe of its black hole mass, we performed a fit of the accretion
disk model to the optical and UV continuum data of the
source SED.
6.1. Nature of Mg II Emission
Marziani et al. (2013) showed that the FWHM of the Mg II
line is systematically narrower by ∼20% than the Hβ line,
which holds for all of its components as well as the full profile.
The simple explanation is that Mg II is emitted at larger
distances than Hβ from the photoionizing continuum source.
The intrinsically symmetric profile of the Mg II line found in
this work characterized by a one-component Lorentzian is
consistent with the origin of the Mg II emission in the virialized
BLR clouds, as for the Hβ broad line (Marziani et al. 2013).
The Lorentzian profile may be physically explained by the
turbulent motion of the emitting medium and the line
broadening by its rotation (Kollatschny & Zetzl 2011; Goad
et al. 2012; Kollatschny & Zetzl 2013a, 2013b). This model of
the Lorentzian line profile is also consistent with the failed
radiatively accelerated outflow (FRADO) model as such
(Czerny & Hryniewicz 2011), in which the turbulence arises
due to the failed outflow and the subsequent inflow, and the
rotation is represented by the dominant Keplerian field (see also
Figure 8). For Population A sources where the Mg II profile is
symmetric, the Mg II gas may be considered virialized. For
Population B sources, a small degree of asymmetry and the
blueshift of the Mg II line may be related to outflows of the
Mg II–emitting gas (Marziani et al. 2013).
Our results, in particular the studied intrinsic Baldwin effect
in Section 6.2, are also consistent with the work of Yang et al.
(2020), who found for the sample of 33 extreme variability
quasars that the Mg II flux density responds to the variable
continuum, but with a smaller amplitude. However, they also
stress that the FWHM of the Mg II line does not respond to the
continuum as the Balmer lines do. Therefore, black hole mass
estimations based on single-epoch measurements can be
luminosity-biased.
11
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
106 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
Previous works also find an overall consistency between Hβbased
and Mg II–based black hole mass estimators. Trakhtenbrot
& Netzer (2012) found the scatter between these two
spectral regions of 0.32 dex in terms of the black hole mass
estimation, smaller than for the C IV line, for which the scatter
with respect to Hβ is 0.5 dex. In addition, the same authors
found that FWHM(Mg II);FWHM(Hβ) up to 6000 km s−1
,
beyond which the FWHM of Mg II seems to saturate. This is
again different for the C IV line, which does not show any
correlations with either the Hβ or the Mg II line. Also, the
FWHM(C IV)FWHM(Hβ) for nearly half of the studied
sources (see also Shen & Liu 2012, for a similar result), which
contradicts RM results. Ho et al. (2012) also showed that
Mg II–based black hole masses are comparable within
uncertainties to those based on Hα, while C IV–based mass
estimates differed by as much as a factor of 5. Hence, the usage
of the broad Mg II line for black hole mass estimating is
justified for sufficiently large samples, while C IV should not be
applied as a reliable virial black hole mass estimator. This is in
line with the overall picture, where low-ionization lines (Hα,
Hβ, Mg II) originate in the bound line-emitting, photoionized
clouds, and high-ionization lines (C IV) originate in the
unbound outflowing gas (Collin-Souffrin et al. 1988).
For the γ-ray blazar 3C 454.3, León-Tavares et al. (2013)
found a significant correlation between the increase in the Mg II
flux density and the γ-ray flaring emission (in 2010 fall), which
could be related to the superluminal radio component in this
source. This implies that Mg II–emitting gas responds to the
nonthermal continuum alongside the thermal continuum of the
accretion disk. This is also in agreement with the significant
correlation between the Mg II flux density and the γ-ray flux
increase in the blazar CTA102 (Chavushyan et al. 2020), in
which the superluminal radio component was also present. In
addition, the Mg II broad line was broader and blueshifted at
the maximum of the γ-ray activity in comparison to the
minimum. The BLR material in this source was inferred to be
located ∼25 pc from the central source. Chavushyan et al.
(2020) conclude that the black hole mass estimation using
Mg II is only reliable for the sources in which UV continuum is
dominated by the central accretion disk, which is also the case
for our source HE 0413, as we show in Section 6.3 based on the
SED fitting, which is based on the thermal disk emission.
In summary, based on our findings and previous findings of
other authors, a significant fraction of the Mg II–emitting gas is
virialized and reverberating to the variable thermal continuum,
as we also find in this work. For sources with a significant
nonthermal emission due to the jet in the UV and the optical
domain, outflowing gas at larger distances from the standard
BLR region can respond to the nonthermal continuum, and this
contributes to the broadening and a blueshifting of the Mg II
line. Hence, when using the Mg II line in the reverberation
studies, time-delay analysis should be complemented by SED
modeling whenever possible to verify if photoionizing
continuum is dominantly of thermal nature.
In terms of the quasar main sequence and the four-dimensional
Eigenvector 1 (4DE1, Sulentic et al. 2000; Marziani et al. 2018),
considering the equivalent width ( -
+
27.45 0.10
0.12
Å) and the FWHM
( +
-4380 km s15
14 1
) exhibited by the Mg II line, HE0413-4031
could be cataloged as a Population B1 in the 4DE1 scheme
(Table 2 of Bachev et al. 2004). However, HE0413-4031 shows a
clear single-component Lorentzian profile associated with Population
A sources (Section 2.3). According to the analysis presented
in Appendix C using a different model template for Fe II emission,
the Mg II emission could also be modeled with two kinematic
components, although their nature appears to be more problematic
to interpret. Moreover, the FWHM of the 2 Gaussian components
and their relative shift with respect to the Fe II emission depends
strongly on the source redshift in the studied interval of
z;1.37–1.39 (see our analysis in Appendix C, especially
Figure C1).
As a high luminosity source, HE 0413-4031 can be found in
the Population B spectral bins, being still a Population A source
(Marziani et al. 2018). Because of its large Eddington ratio of
∼0.4, it can be further classified as an extreme Population A
source (xA), with the Fe IIλ 4570 strength larger than unity
RFe II>1, with the FWHM(Hβ)>4000 km s−1
because the
Mg II line is generally narrower than Hβ line. The difficult
spectral-type classification of HE0413-4031 stems from the
fact that Population A sources are typically highly accreting
sources with smaller black hole masses, and Population B
sources have larger black hole masses and low Eddington ratios
(Marconi et al. 2009; Fraix-Burnet et al. 2017). In this sense,
HE0413-4031 has mixed properties: a large black holes mass
of a few 109
Me and a high Eddington ration of ∼0.4.
However, these general distinctions are based on the analyses
of lower-luminosity low-redshift sources, while our source is at
the intermediate redshift of z∼1.4 and of a high luminosity of
1047
erg s−1
. Hence the apparent discrepancy may be solved by
the cosmological argumentation that the current massive black
holes with low accretion rates were highly accreting sources at
higher redshifts. With a black hole mass of a few billion solar
masses, HE 0413 falls into the expected mass range for type 1
AGN between redshifts of 1 and 2 (see Figure 15 of
Trakhtenbrot & Netzer 2012, where HE 0413 is located at
the age of the universe of 4.66 Gyr for z=1.37). On the other
hand, HE 0413 is still an outlier in terms of the accretion rate
close to the Eddington limit for a black hole mass of a few
billion solar masses. Trakhtenbrot & Netzer (2012) suggest that
a majority of such massive AGNs do not accrete close to their
Eddington limits even at z;2.
Because HE 0413-4031 can be classified as a radio-loud AGN
given its luminosity at 1.4 GHz, L1.4≈2.5×1026
W Hz−1
>
1024
W Hz−1
(Tadhunter 2016), its radio-optical properties can be
studied in the broader context. Ganci et al. (2019) studied the
radio properties of type-1 AGNs across all main spectral types
along the quasar main sequence, in particular for three classes of
Kellermann’s radio-loudness criterion, which is defined as the
ratio of the radio and optical flux densities, RK=Sradio/Soptical.
We follow Ganci et al. (2019), who use 1.4 GHz flux density for
Sradio and g-band flux density for Soptical and divide sources into
three radio classes: radio detected (RD, RK<10), radio
intermediate (RI, 10„RK<70), and radio-loud (RL,
RK…70). We derive the corresponding 1.4 GHz and g-band
flux densities for HE 0413-4031 by linear interpolation of the
averaged SED points in the log space (see Figure 9),
S1.4=21.04 mJy and Sg=0.434 mJy, which yields RK=48.5.
Hence, HE 0413-4031 can be classified as an RI source with an
inverted and flat radio spectrum toward higher frequencies
according to Vizier SED,13
because the spectral index α, using
the notation Sν ∝ ν+ α
, is α1–5 ; 0.7, α5–8 ; 1.7, α8–20 ; −0.02
between 0.843 GHz, 5 GHz, 8 GHz, and 20 GHz, respectively.
Sources with inverted to flat radio spectral indices are
13
http://vizier.u-strasbg.fr/vizier/sed
12
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
107
characterized by a compact, optically thick radio core or a corejet
system (Zajaček et al. 2019a, 2019c).
Ganci et al. (2019) found that the occurrence of RD, RI, and
RL sources differs along the main sequence. The classification of
our source as RI with inverted-flat spectrum is consistent with its
location in the extreme A population according to Ganci et al.
(2019), because core-dominated sources in A3 and A4 bins are
mostly RI. The source of radio emission in extreme A population
can be partially due to a high star formation rate, but also the corejet
activity. In our case, the radio spectral index implies the
presence of a compact core-jet system, hence the high star
formation rate is not necessarily required. On the other hand, the
presence of gas material is necessary to account for the high
Eddington ratio of ∼0.4–0.5. The optically thick radio core could
be a sign of a restarted AGN activity (Czerny et al. 2009;
Padovani et al. 2017), which will eventually heat up the cold gas
content and/or blow it away and slow down the star formation.
6.2. Response of Mg II Emission to Continuum Changes—
Intrinsic Baldwin Effect
The expected properties of the Mg II line were recently
modeled by Guo et al. (2020), where the authors using the
CLOUDY code and the locally optimally emitting cloud (LOC)
scenario showed that at the high Eddington ratio of ∼0.4, the
Mg II line flux saturates and does not further increase with the
rise of the continuum.
We confront this theoretical prediction with our observations of
the quasar HE 0413-4031. We used the logarithm of both the
continuum and Mg II line-emission flux densities, i.e., magnitudes.
Subsequently, we applied the determined time-delay shift to the line
emission, i.e., we shifted the Mg II lightcurve by 719.9 days in the
observer’s frame. For the continuum lightcurve, we tried both the
cases with and without BMT data, by given the fact that the BMT
data are present for the epochs longer than 8000 days, they do not
have a significant effect on the following analysis. As the next step,
we interpolate the photometry data to the time-shifted line-emission
data to have corresponding line-continuum pairs. As before, given
that the photometry data come from different instruments with
various uncertainties, we make use of the weighted least-squares
linear B-spline interpolation with the inverse of uncertainties as
weights. We show the continuum and the time-shifted line
lightcurves in Figure 7 (left panel) alongside the interpolate values,
which can also serve as a cross-check that the determined timedelay
of ∼720 days in the observer’s frame represents the realistic
similarity between the shapes of both lightcurves.
Finally, we plot the Mg II line magnitude with respect to the
continuum magnitude in Figure 7 (right panel). This relation
has a significant correlation with the correlation coefficient of
r=0.73. The best-fit linear relation is ml=(0.43±
0.10)mc+(9.60±1.73), which is displayed in Figure 7 with
the corresponding uncertainties. Our linear fit implies directly
the power-law relation between the Mg II and continuum
luminosities, µ 
L LMg II 3000
0.43 0.10
. In combination with the
measured time-delay of 303 days in the rest frame, we can
conclude that the Mg II line responds to the continuum
variability even for the source, which is highly accreting with
the Eddington ratio of ∼0.4 (see also Section 6.3 for a detailed
SED modeling). Hence, our source does not exhibit a
nonresponsive Mg II line with a rather constant dependency
on the continuum luminosity, as was analyzed and shown by
Guo et al. (2020) (see also their Figure 4). Moreover, from
Figure 7 (right panel) it is apparent that the line and the
continuum magnitudes consist of an uncorrelated part for
continuum magnitudes of more than 16.7 mag (with the
correlation coefficient of r=0.10, R2
=0.01). The part of
the dependency with continuum magnitudes less than 16.7 mag
is strongly correlated with the correlation coefficient of
r=0.79 (R2
=0.63), and the best-fit linear fit is
ml=(0.82±0.26)mc+(3.04±4.25), hence the line luminosity
responds even stronger to the continuum luminosity in
this part with the relation µ 
L LMg II 3000
0.82 0.26
, which is
marginally consistent with the linear dependency within the
uncertainty.
Guo et al. (2020) analyze the LOC model and Mg II response
for the smaller black hole mass and the 3000 Å luminosity
(M•=108
Me and L3000=1044–45
erg s−1
). However, their
upper limit for the Eddington ratio, ηEdd=0.4, is comparable
to our estimated Eddington ratio and hence their flattening of
Figure 7. Determination of the continuum–line magnitude (luminosity) relation. Left panel: superposition of the continuum and the time-shifted line-emission
lightcurves. Interpolated photometry points are also shown. Right panel: Mg II line-emission magnitude vs. continuum magnitude has a clear linear correlation in the
logarithmic scale with the correlation coefficient of r=0.73 (R2
=0.53), with the best-fit relation of ml=(0.43±0.10)mc+(9.60±1.73). The blue line represents
the linear fit to the data, with the continuum magnitude less than 16.7. In this case, the correlation coefficient is higher (r=0.79, R2
=0.63) and the best-fit relation
has a larger slope: ml=(0.82±0.26)mc+(3.04±4.25).
13
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
108 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
Mg II luminosity close to L3000=1045
erg s−1
is not confirmed
for HE 0413-4031. On the other hand, we observe a similar
dependency of the Mg II line luminosity on the continuum
luminosity, as Guo et al. (2020) inferred for hydrogen
recombination broad lines (Hα, Hβ) at lower Eddington ratios.
For the luminosity range [ ( )]-Llog erg s3000
1
=42–44, the
slope for Hβ is α∼0.45 and α∼0.42 for Hα. In addition,
Guo et al. (2020) show a slower rise of Mg II luminosity with
respect to the continuum with the slope of ∼0.38, which is
smaller than our value. This implies that at least for our source,
the LOC model with the initial assumption of (Rout, Γ)=
(1017.5
, −2)14
does not apply.
The models with the larger radial extent of the BLR with
Rout=1018
cm as shown in Figure 9 of Guo et al. (2020) seem
to be more consistent with our slope of 0.43, as they show a
continuous rise of Mg II luminosity even for larger continuum
luminosities around the Eddington ratio of ∼0.4. This is also in
agreement with our inferred travel distance of t= =R cMg II
~+
0.254 pc 10 cm0.016
0.020 17.9
. In comparison, the location of the
dusty torus is still further. Its inner radius is given by the
sublimation radius, Rsub∼0.4 pc L
T45
0.5
1500
2.6
=5.04 pc∼
1019.2
cm (Elitzur & Shlosman 2006; Nenkova et al. 2008),
for our estimate of the bolometric luminosity Lbol=1.589×
1047
erg s−1
and the dust sublimation temperature of 1500 K.
The outer radius of the dusty torus is expected to be at
Rtorus∼YRsub, where Y∼5–10 (Elitzur & Shlosman 2006).
The light-travel distance, which can serve as a proxy for the
BLR location in HE 0413-4031, is also in agreement with the
model of the failed radiatively accelerated dusty outflow
(FRADO, Czerny & Hryniewicz 2011). The failed dusty wind
requires the existence of dust in the accretion disk, which is
possible at and below ∼1000 K. This sets the inner radius of
the BLR to ( ) h=r R M m0.031000 sub 8
1 6 1 6
0.1
1 2
, where M8 is
the black hole mass scaled to 108
Me,   =m M MEdd is the
dimensionless accretion rate, and η is the accretion efficiency
(Lbol= hMc2). Using the best-fit SED model, see Section 6.3,
we adopt M=2.5×109
Me,  =m 0.51, and h = 0.1,
which leads to r1000/Rsub=0.0574 or r1000=0.289 pc=
1017.95
cm, which is within uncertainties consistent with the
light-travel distance RMg II. We illustrate these basic lengthscales
of the quasar HE 0413-4031 in Figure 8.
For the continuum magnitudes smaller than 16.7 mag, the
slope of the line-continuum dependency (0.82±0.26) is even
larger than for the case when the whole range is considered.
Interestingly, this slope is comparable to the exponent of the
line-continuum relation as studied for the sample of flatspectrum
radio quasars (Patiño Álvarez et al. 2016), which is
related to the global Baldwin effect between the equivalent
width of originally broad UV lines (C IV, Lyα) and the
corresponding continuum luminosities (at 1350 Å); see the
original works by Baldwin (1977), Baldwin et al. (1978), and
Wampler et al. (1984). In general, the equivalent width
decreases with the increasing luminosity, which can be
described as a power-law relation, µ g
LEWline cont. This can
be rewritten as a relation between the line and the corresponding
continuum luminosities using EW;Lline/Lcont, which
yields µ g+
L Lline cont
1
. The original Baldwin effect is also called
global or ensemble (Baldwin 1977; Carswell & Smith 1978),
which is derived based on single-epoch observations of an
ensemble of AGNs, while the analogical relation studied for
individual AGNs is related to as an intrinsic Baldwin effect
(Pogge & Peterson 1992).
Patiño Álvarez et al. (2016) analyze the line-continuum
luminosity relation Lline−Lcont, including the Mg II line and
3000 Å continuum, for a sample of 96 FSRQ sources (core-jet
blazars). For FSRQ, they found the slope of 0.796±0.153,
which is smaller than the slope of 0.909±0.002 for the control
sample of RQ AGN. Within uncertainties, their slope derived for
the whole sample is comparable to our slope µ 
L LMg II 3000
0.82 0.26
.
Hence, our detected intrinsic Baldwin effect is in agreement with
the global one derived for the population of FSRQ. Previously,
Rakić et al. (2017) studied the intrinsic Baldwin effect for 6 type-I
AGN, and they detected it for the broad recombination lines, Hα
and Hβ. They found that the intrinsic Baldwin effect is not related
to the global one. Patiño Álvarez et al. (2016) found the difference
of the global Baldwin effect between the radio-loud (blazar) and
radio-quiet AGN, which could imply the importance of the
nonthermal component, i.e., boosted jet emission, to the ionizing
continuum for radio-loud sources. Apparently, more data for our
quasar as well as more radio-loud and radio-quiet sources are
needed to study in detail both the intrinsic and global Baldwin
effect and their potential relation, especially taking into account
the potential nonthermal contribution for radio-loud sources.
In summary, we detect a significant correlation between
Mg II and the 3000 Å continuum after the removal of the lighttravel
time effect. The relation Lline−Lcont is not linear, but has
a slope of 0.43±0.10 when all the corresponding lineluminosity
points are combined. The slope is larger,
γ+1=0.82±0.26, when only a higher correlated part of
the points is selected. These results are consistent with the
Mg II broad-line emission being at least partially driven by the
underlying continuum.
6.3. SED Fitting
Our determination of the black hole mass in Section 5.1 is
not unique, because it requires additional assumptions about
Figure 8. Illustration of the basic length-scales of the quasar HE 0413-4031.
The BLR clouds are depicted with the dominantly Keplerian velocity field with
a smaller outflow-inflow turbulent component according to the failed
radiatively accelerated outflow model (FRADO, Czerny & Hryniewicz 2011).
The axis along the bottom of the figure is expressed in the corresponding
logarithms of basic radii in centimeters. From the left to the right side of the
image, we include the Schwarzschild radius of 2.5×109
Me black hole,
=Rlog 14.9Schw , the light-travel distance of Mg II emission,
=Rlog 17.9Mg II , and the inner radius of the dusty torus, =Rlog 19.2sub .
14
Locally optimally emitting cloud (LOC) models assume the power-law
radial distribution of clouds, f (r)∝rΓ
.
14
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
109
the virial factor. As a test of the mass range we obtained, we
attempted to obtain the constraints for the black hole mass
directly, from the accretion disk fitting to the continuum.
We used the data points available from Vizier SED photometric
viewer.15
After removal of the multiple entries and converting
the measurements to the rest frame (assuming z = 1.37648
as determined in Section 3.1), and adopting H0 = 69.5,
Ωm = 0.286, ΩL = 0.714 (Bennett et al. 2014), we obtain the
IR to UV SED (see Figure 9). We corrected the data for the
Galactic extinction, although the effect is not strong in the
direction of HE 0413-4031. The data points come from various
epochs. Therefore, we added an additional error of 0.08 (in log
space) to the measurements to account for the variability. For
disk fitting, we used only points at the frequencies above 14.5
in the log scale, rest frame, because the rest frame near-IR
emission in quasars comes from the hot dust component. We
did not assume any presence of the blazar component because
the data point did not seem to suggest its need.
We used the fully relativistic Novikov–Thorne model
(Novikov & Thorne 1973), with all propagation effects as
described in Czerny et al. (2011). The model is characterized
by the black hole mass, accretion rate (in Eddington units,
assuming the fixed efficiency of 1/12 in the definition, i.e., in
units of 1.678×1018
(M/Me) g s−1
), spin, and viewing angle.
We performed the fitting without constraints for any of those
parameters. First, we performed the fitting for all the data
points available, and we obtained the best-fit model with the
parameters: M=3.0×109
Me, m=0.35, a=0.31, and
ι=34 deg. We present this fit in Figure 9. Second, we also
performed the fitting for the error-weighted averages of the
data, and for the uncertainties we used error-weighted standard
deviations. In this case, the best-fit solution was formally with
the parameters: M=2.5×109
Me,  =m 0.51, a=0.025, and
ι=33.8 deg. However, fits are highly degenerate, so the χ2
allows for a broad mass range from 1×109
Me to masses even
above 5×109
Me (see Table 3). Large masses, however, do
not provide an acceptable solution because they also require a
very high viewing angle. A high viewing angle is not expected
because the unification scheme of AGN excludes it due to the
presence of the dusty/molecular torus (see, e.g., Padovani et al.
2017 for a recent review), and the clear excess in the near-IR
shows that the torus is present in HE 0413-4031.
If we constrain the allowed parameters to ι<45 deg, the
upper limit for the black hole mass is M=3.5×109
Me. In
our fits, the black hole spin is never large. For very small black
hole masses, the accretion rate is super-Eddington and the spin
is retrograde; the highest value of the spin we get is 0.52.
However, this determination highly relies on one data point—
the far-UV Galaxy Evolution Explorer measurement, which is
in the spectral range where relativistic effects are important. If
there is some internal reddening in the quasar, the allowed spin
probably could be higher, but the SED data quality is not good
enough to attempt more complex modeling.
The obtained black hole mass range 1.5× 109
Me–3.5×
109
Me is consistent with those presented in Section 5.1.
By integrating the best-fit SED, we can derive the bolometric
correction BC for the monochromatic luminosity at 3000 Å. We
obtain Lbol=2.8L3000, which is smaller than the mean value of
5.62±1.14 provided by Richards et al. (2006) for the same
wavelength. However, it is consistent with the luminositydependent
relation for the bolometric correction derived by Netzer
(2019), which gives BC=25×(L3000/1042
erg s−1
)−0.2
=2.80
for L3000=1046.754
erg s−1
. The consistency with the power-law
relation of Netzer (2019) stems from the fact that they used
essentially the same model of an optically thick, geometrically
thin accretion disk that is used in this work to fit the SED.
In summary, the SED fitting showed that the canonical thin,
optically thick accretion disk can still account for the dominant
part of the continuum in our highly accreting quasar. At higher
accretion rates, the inner parts of the accretion flow are
expected to become geometrically and optically thick, as in
slim accretion disks, which can account for the reduction of the
ionizing flux and shortening of time-delays (Wang et al.
2014b). This is indeed supported by the existence of stable
geometrically thick and optically thick “puffy” accretion disks
in global 3D GRMHD simulations for sub-Eddington accretion
rates comparable to our values of m=0.3–0.6 (Lančová et al.
2019). However, the current computational facilities still do not
allow a self-consistent treatment of the accretion disk-BLR
dynamics on the scales of as much as 1000 gravitational radii,
while the analytical and semi-analytical models explain the
main observational features (Czerny et al. 2011; Czerny &
Hryniewicz 2011).
Figure 9. The SED data and the accretion disk model for HE 0413-4031 shown
as the dependency of the luminosity νLν (in erg s−1
) on the frequency ν (in Hz)
in the log space. The data are taken from the Vizier SED data (seehttp://
vizier.u-strasbg.fr/vizier/sed). For the fitting, we use error-weighted averages
of the data. The best-fit SED model is represented by a solid red line and is
based on the parameters M• = 3.0 × 109
Me,  =m 0.35 (here measured in units
of 1.678 × 1018
(M/Me g s−1
)), a = 0.31, and ι = 34 deg.
Table 3
Best-fitted Parameters for the Black Mass in the Range of 1–5×109
Me
M (109
Me) Spin m ι (deg) χ2
1 −0.99 1.81 0.0 31.57
1.5 −0.94 1.08 0.0 19.38
2 −0.13 0.60 0.0 19.54
2.5 0.025 0.51 33.8 19.17
3 0.46 0.31 25.8 19.31
3.5 0.52 0.26 33.6 19.23
4 0.44 0.29 49.8 20.20
4.5 0.0062 0.54 68.2 20.31
5 0.044 0.50 69.5 20.30
Note. The parameters include the spin, the accretion rate m (here measured in
units of 1.678×1018
(M/Me g s−1
)), and the viewing angle ι. The smallest χ2
of 19.17 is for the case with the parameters M=2.5×109
Me, m=0.51,
a=0.025, and ι=33.8 deg.
15
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110 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
7. Conclusions
We summarize the main findings of the paper as follows:
1. Using seven different methods, we found a rest-frame timedelay
between the continuum and Mg II line emission for the
bright quasar HE 0413-4031, t = -
+
302.6 33.1
28.7
days, which
was the most frequent peak in time-delay distributions.
2. In combination with the data for 10 other sources monitored
in the Mg II line, we construct a radius–luminosity relation,
which is consistent with the theoretically expected dependency,
R∝L1/2
. The new quasar HE 0413-4031 with the
monochromatic luminosity of = -
+
Llog 46.7543000 0.132
0.028
lies
below the expected relation, which can be explained by its
higher accretion rate. In general, for all Mg II sources, the
departure from the radius–luminosity relation, i.e., the
shortening of their time-delays, is larger for higher-accreting
sources. The same effect was previously observed for the
sources monitored in Hβ.
3. We determined the response of the Mg II line luminosity to
the photoionizing continuum luminosity, µ 
L Lline cont
0.43 0.10
,
which is comparable to the response of recombination
emission lines Hα and Hβ, according to theoretical
photoionization models. This is consistent with the outer
radius of the BLR at Rout=1018
cm, which is in turn in
agreement with the light-travel distance inferred from the
rest-frame time-delay.
4. The virial black hole mass determined based on the measured
rest-frame time-delay, ( )  = ´M f M1 1.1 10RM
uncorr 9 , is
smaller by a factor of 4 than the value expected from the
radius–luminosity relation, ( )  = ´M f M1 4.6 10RM
corr 9 .
The black hole mass inferred from fitting a thin accretion disk
model to the source SED, MSED=1.5×109
Me–3.5×
109
Me, is in agreement with these values within the
uncertainty. Other best-fitted parameters for the source are
the Eddington ratio of  m0.26 1.08, the black hole spin
of −0.94„a„0.52, and the viewing angle of 0„ι„34
degrees.
We thank the referee for constructive comments that helped
to improve the clarity of the manuscript. The authors
acknowledge the financial support by the National Science
Centre, Poland, grant No.2017/26/A/ST9/00756 (Maestro
9), and by the Ministry of Science and Higher Education
(MNiSW) grant DIR/WK/2018/12. G.P. acknowledges the
grant MNiSW DIR/WK/2018/09. K.H. acknowledges support
by the Polish National Science Centre grant 2015/18/E/
ST9/00580. The OGLE project has received funding from the
National Science Centre, Poland, grant MAESTRO 2014/14/
A/ST9/00121. The Polish participation in SALT is funded by
grant No. MNiSW DIR/WK/2016/07.
Software:IRAF (Tody 1986, 1993), JAVELIN (Zu et al.
2011, 2013, 2016), PyCCF (Sun et al. 2018), vnrm.py (Chelouche
et al. 2017), zdcf_v2.f90 (Alexander 1997), plike_v4.f90
(Alexander 1997), delay_chi2.f (Czerny et al. 2013).
Appendix A
Photometric and Spectroscopic Data
In this section, we summarize the characteristics of Fe II and
Mg II lines in Table A1, where we specifically list the Fe II and
Table A1
Table of Fe II and Mg II Equivalent Widths in Å, Velocity Shift in km s−1
, Line Width in Å, and the Mg II Flux Density in erg s−1
cm−2
Å−1
Obs. JD EW(Fe II) EW(Mg II) Shift Width Flux density
No. −2 450 000 Å Å km s−1
Å erg s−1
cm−2
Å−1
1 6314.4087 -
+
13.71 0.93
0.91
-
+
34.18 0.49
0.51
-
+
1666.98 16.65
17.04
-
+
2149.29 40.08
28.50
(3.836±0.074)×10−14
2 6320.3859 -
+
9.75 1.32
1.34
-
+
35.89 0.74
0.79
-
+
1723.70 22.96
23.73
-
+
2196.68 52.86
54.72
(4.000±0.114)×10−14
3 6523.5954 -
+
10.73 2.22
2.28
-
+
34.67 1.20
1.25
-
+
1529.11 39.12
39.28
-
+
2165.96 81.07
88.44
(3.966±0.178)×10−14
4 6651.4751 -
+
10.38 1.72
1.77
-
+
36.59 1.02
1.04
-
+
1598.83 31.09
31.86
-
+
2289.73 64.80
81.43
(4.051±0.152)×10−14
5 6697.3600 -
+
14.13 1.34
1.32
-
+
37.93 0.75
0.78
-
+
1617.81 22.60
22.58
-
+
2316.05 61.37
46.37
(4.219±0.114)×10−14
6 6892.5678 -
+
17.07 1.03
1.11
-
+
36.06 0.58
0.56
-
+
1554.76 18.05
18.02
-
+
2218.54 38.86
41.03
( ) ´ -3.911 0.094 10 14
7 7003.5182 -
+
13.25 0.64
0.58
-
+
35.64 0.34
0.36
-
+
1608.01 11.35
11.37
-
+
2307.95 23.98
24.90
( ) ´ -3.908 0.067 10 14
8 7082.2985 -
+
13.29 0.82
0.83
-
+
31.20 0.44
0.48
-
+
1615.91 17.14
17.11
-
+
2300.84 35.14
46.54
(3.702±0.080)×10−14
9 7243.6124 -
+
13.93 0.72
0.69
-
+
30.65 0.36
0.41
-
+
1597.95 14.64
14.64
-
+
2250.33 28.81
34.74
(3.856±0.069)×10−14
10 7289.4741 -
+
13.57 0.86
0.89
-
+
31.14 0.46
0.47
-
+
1613.10 17.45
17.51
-
+
2213.75 31.14
45.45
(3.953±0.082)×10−14
11 7341.3298 -
+
12.46 0.87
0.82
-
+
32.33 0.49
0.45
-
+
1597.92 17.10
16.98
-
+
2296.71 39.59
40.25
(4.127±0.082)×10−14
12 7374.4950 -
+
13.43 0.83
0.83
-
+
28.87 0.45
0.43
-
+
1594.19 17.77
19.07
-
+
2200.05 35.27
36.00
(3.681±0.075)×10−14
13 7423.3702 -
+
10.12 0.72
0.74
-
+
29.97 0.44
0.41
-
+
1669.13 16.53
16.79
-
+
2331.95 39.93
34.35
(3.860±0.073)×10−14
14 7656.2474 -
+
10.64 0.61
0.63
-
+
28.06 0.33
0.36
-
+
1664.97 13.65
14.98
-
+
2290.71 30.11
35.96
(4.204±0.075)×10−14
15 7687.3943 -
+
10.65 0.62
0.65
-
+
28.08 0.35
0.36
-
+
1664.77 14.89
15.31
-
+
2288.94 30.63
37.67
(3.979±0.067)×10−14
16 7722.5591 -
+
11.99 0.66
0.66
-
+
26.62 0.34
0.38
-
+
1672.60 15.95
16.16
-
+
2254.84 40.84
29.84
(3.781±0.066)×10−14
17 7752.4673 -
+
10.26 0.58
0.58
-
+
27.94 0.32
0.34
-
+
1682.02 14.03
14.26
-
+
2298.09 33.91
29.95
(4.125±0.065)×10−14
18 7953.6598 -
+
12.10 0.64
0.64
-
+
25.37 0.34
0.33
-
+
1648.26 15.69
15.85
-
+
2208.36 31.79
32.31
(3.683±0.054)×10−14
19 7979.5920 -
+
11.83 0.62
0.59
-
+
28.05 0.34
0.35
-
+
1640.45 14.73
14.78
-
+
2363.17 35.90
33.85
(4.072±0.067)×10−14
20 8114.4800 -
+
10.35 0.65
0.56
-
+
27.40 0.32
0.36
-
+
1681.22 14.81
14.14
-
+
2337.25 37.38
33.20
(4.250±0.067)×10−14
21 8167.3265 -
+
9.26 0.58
0.53
-
+
26.59 0.27
0.34
-
+
1649.54 14.32
14.75
-
+
2358.10 34.15
33.34
(4.025±0.063)×10−14
22 8376.5021 -
+
13.63 0.62
0.65
-
+
29.30 0.35
0.36
-
+
1631.38 14.41
14.73
-
+
2326.37 29.91
30.10
(4.380±0.069)×10−14
23 8498.4167 -
+
10.98 0.65
0.61
-
+
29.25 0.37
0.37
-
+
1800.13 14.75
15.32
-
+
2343.83 41.66
30.65
(4.323±0.070)±10−14
24 8543.3100 -
+
8.85 0.62
0.61
-
+
29.55 0.36
0.38
-
+
1751.82 14.00
15.48
-
+
2368.61 42.12
33.36
(4.361±0.071)×10−14
25 8719.5708 -
+
15.47 0.91
0.94
-
+
32.19 0.52
0.54
-
+
1667.05 19.16
19.55
-
+
2359.25 40.14
52.31
(4.722±0.092)×10−14
Note. The flux density was calculated for the case without the BMT data; see the text for the description.
16
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
111
Mg II equivalent widths in Å, velocity shift in km s−1
, line
width in Å, and the Mg II flux density in erg s−1
cm−2
Å−1
. The
continuum magnitudes (V band) from the three instruments—
OGLE, SALTICAM, and BMT—are included in Tables A2
and A3.
Appendix B
Overview of Time-delay Determination Methods
B.1. Interpolated Cross-correlation Function (ICCF)
The ICCF is a standard method for determining the timedelay
between the continuum and line-emission lightcurves. In
general, both lightcurves are unevenly sampled, while the ICCF
by its definition requires regular sampling with a certain timestep,
which is achieved by the interpolation of the continuum
lightcurve with respect to the line-emission lightcurve or
vice versa (asymmetric ICCF). The definition of the ICCF
Table A2
Table of Continuum Magnitudes with Uncertainties
JD Magnitude (V band) Error Instrument
−2450,000 mag mag No.
6199.79634 16.763 0.005 1
6210.81464 16.755 0.003 1
6226.67656 16.771 0.004 1
6246.69516 16.761 0.004 1
6257.74660 16.763 0.005 1
6268.68051 16.767 0.004 1
6277.68239 16.738 0.003 1
6286.66584 16.782 0.004 1
6297.61482 16.770 0.004 1
6307.57245 16.769 0.004 1
6317.63928 16.799 0.004 1
6330.65489 16.789 0.003 1
6351.54598 16.788 0.004 1
6363.57130 16.782 0.003 1
6379.48424 16.762 0.004 1
6379.49181 16.755 0.004 1
6387.50984 16.780 0.003 1
6637.66923 16.767 0.003 1
6651.62009 16.806 0.003 1
6665.60325 16.812 0.004 1
6678.59717 16.796 0.003 1
6689.67132 16.792 0.003 1
6700.63473 16.809 0.004 1
6715.57393 16.791 0.003 1
6740.48864 16.789 0.004 1
6892.59242 16.830 0.011 2
7003.54330 16.819 0.012 2
7036.65108 16.747 0.004 1
7048.65280 16.731 0.003 1
7060.60356 16.700 0.004 1
7082.30016 16.749 0.012 2
7084.53369 16.732 0.005 1
7118.50567 16.731 0.005 1
7243.61293 16.664 0.011 2
7253.88913 16.668 0.003 1
7261.88037 16.684 0.004 1
7267.91217 16.650 0.004 1
7273.84457 16.683 0.004 1
7283.84655 16.659 0.004 1
7289.47056 16.698 0.012 2
7295.84011 16.661 0.004 1
7306.77839 16.677 0.004 1
Note. The epoch is given in Julian dates (−2450,000). The last column denotes
three different instruments used to obtain the photometry data: 1. OGLE, 2.
SALTICAM, 3. BMT. The BMT photometry points were shifted by 0.171 mag
to larger magnitudes to match the last OGLE point with the closest BMT point
in the lightcurve.
Table A3
Table of Continuum Magnitudes with Uncertainties
JD Magnitude (V band) Error Instrument
−2450,000 mag mag No.
7317.73770 16.678 0.004 1
7327.77204 16.686 0.004 1
7340.70393 16.655 0.003 1
7341.32488 16.671 0.011 2
7355.69184 16.656 0.004 1
7363.66368 16.627 0.003 1
7374.49091 16.654 0.011 2
7374.70619 16.657 0.003 1
Table A3
(Continued)
JD Magnitude (V band) Error Instrument
−2450,000 mag mag No.
7385.55446 16.624 0.003 1
7398.61439 16.641 0.003 1
7415.58224 16.634 0.003 1
7423.36782 16.633 0.011 2
7426.56315 16.653 0.003 1
7436.52206 16.626 0.004 1
7447.52422 16.623 0.003 1
7457.51899 16.641 0.003 1
7656.47709 16.545 0.011 2
7687.38749 16.543 0.011 2
7717.70291 16.541 0.003 1
7722.55378 16.513 0.011 2
7752.46369 16.496 0.011 2
7973.91046 16.518 0.006 1
7979.59391 16.502 0.011 2
8038.85902 16.509 0.004 1
8084.30756 16.429 0.011 2
8090.70000 16.338 0.008 3
8114.47660 16.193 0.011 2
8138.70000 16.305 0.008 3
8139.60000 16.311 0.004 3
8146.60000 16.284 0.003 3
8165.60000 16.296 0.005 3
8167.32241 16.464 0.011 2
8173.60000 16.277 0.007 3
8180.50000 16.261 0.006 3
8196.50000 16.291 0.008 3
8205.50000 16.274 0.006 3
8365.90000 16.285 0.006 3
8377.50208 16.486 0.011 2
8386.90000 16.302 0.008 3
8414.80000 16.319 0.005 3
8498.41249 16.509 0.011 2
8543.30431 16.484 0.011 2
8566.50000 16.319 0.008 3
8719.57089 16.498 0.011 2
Note. The epoch is given in Julian dates (−2450 000). The last column denotes
three different instruments used to obtain the photometry data: 1. OGLE, 2.
SALTICAM, 3. BMT. The BMT photometry points were shifted by 0.171 mag
to larger magnitudes to match the last OGLE point with the closest BMT point
in the lightcurve.
17
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
112 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
between the two lightcurves, xi and yi, with the step-size of
Δt=ti+1−ti, is
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
( )
( )
) ( )(
( ) ( ) ( ) ( )
( )
t
=
å - å
- å -
=
-
+
CCF
N x x y y
N x x N y y
1
1 1
, B1
k
i
N k
i i k
i
N
i i
N
i
1
2 1 2 2 1 2
where τk is the time-shift τk=kΔt, where the index
k=1,...,N−1, of the second lightcurve with respect to the
first one, and where x and y are the means of the two
lightcurves xi and yi. The final, symmetric ICCF is obtained by
averaging the ICCFs from both interpolations.
We apply the Python implementation of ICCF, the script
PYCCF (Sun et al. 2018) based on an earlier ICCF analysis of
Peterson et al. (1998), which calculates the ICCF including the
continuum, line-emission, and symmetric interpolation. Using
1,000 Monte Carlo realizations of random subset selection
(RSS) and flux randomization (FR), we obtained ICCF peak
and centroid distributions, including their corresponding
uncertainties.
First, we cross-correlated the full continuum lightcurve,
which included SALTICAM, OGLE, and flux-shifted BMT
data, in total 86 points, with the Mg II lightcurve (25 points). In
addition, given the systematic offset of the BMT flux densities
from SALTICAM points, we decided to perform the ICCF
analysis also without them, which reduced the photometric
lightcurve to 73 points. The ICCF values with respect to the
time-delay, for which we separately calculated the continuuminterpolated,
line-interpolated, and symmetric ICCF, with the
corresponding peak and centroid distributions (for symmetric
CCF) are displayed in Figure B1 with and without BMT points
in the top and bottom panels, respectively. We summarize the
peak and centroid values of the ICCF for the interpolated
continuum, interpolated line-emission, and symmetric case in
Table B1, where the cases with and without BMT data points
are separated as well. When comparing these two cases in
Table B1, the peak and centroid values for the case without the
BMT data are generally comparable within the uncertainties,
which is also visible in centroid and peak distributions in
Figure B1.
The maximum values of the ICCF are about 0.8 (for the
interpolation of the photometry), which for such a relatively
short emission-line lightcurve is a high value, supporting the
view that the delay determination should be in general reliable
because the line and continuum are well correlated. For
comparison, the maximum value of the ICCF for the quasar
CTS C30.10, with similar formal data quality, was only 0.65
(Czerny et al. 2019; Zajaček et al. 2019b).
Figure B1. Interpolated cross-correlation coefficient as a function of time-delay in the observer’s frame. Top panel: the interpolated cross-correlation function (ICCF)
as a function of time-delay, including shifted BMT points. The middle panel displays the distribution of cross-correlation centroids, while the right panel shows the
distribution of cross-correlation peaks. Bottom panel: the same as in the top panel but without BMT data.
18
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
113
We also tested if the linear trend present in the continuum
should be eventually subtracted before the time-delay is
measured. However, we noticed that such a trend subtraction
decreases the maximum value of the correlation in ICCF. For
example, for the interpolated continuum, without BMT data
points, rmax decreases from 0.85 down to 0.61. Thus we
conclude that the trend subtraction is not beneficial for the
time-delay analysis. The presence of the trend is natural if the
lightcurve of the red noise character, as here, covers the period
shorter than the maximum timescale present in the system. The
time-delay measurement is not strongly affected anyway; we
obtain for the same case the peak time-delay of 1037.0 days
instead of 1061.0 days. Thus, in further analysis, we do not
consider the trend subtraction.
B.2. Discrete Correlation Function (DCF)
Edelson & Krolik (1988) suggested using the DCF because
the ICCF by definition introduces additional interpolated data
points and can thus distort the time-delay determination,
especially for the unevenly and sparsely sampled pairs of
lightcurves. The basic algorithm is to search for data pairs (xi,
yj) between the two lightcurves that fall into the time-delay bin
τ−δτ/2„Δtij<τ+δτ/2, where τ is the time-delay, δτ is
the chosen time-delay bin, and Δtij=tj−ti. Given M such
pairs, we can calculate the unbinned discrete correlation
coefficient for each of them,
( )( )
( ) ( )
( )
s s
=
- -
-
x x y y
s s
UDCF , B2
i j
x x y y
ij
2 2
where x and y are the lightcurve means in the given time-delay
bin; sx, sy are the variances; and σx, σy are the mean
measurement errors for a given bin. The discrete correlation
function for a given time-delay is calculated by averaging over
M data point pairs,
( ) ( )åt =
M
DCF
1
UDCF . B3
ij
ij
The error of the DCF can be formally inferred from the relation
( ) [ ( )] ( )ås t t=
-
-
M
DCF
1
1
UDCF . B4DCF ij
2
For our DCF analysis, we make use of the Python code
pyDCF by Robertson et al. (2015) with the possibility of
applying the Gaussian weighting scheme to matching pairs of
both lightcurves. We also tested different time-delay bins as
well as the searched time-delay intervals. In addition, we
extended the DCF analysis by including the bootstrap
technique to construct time-delay distributions and to infer
the actual peaks and their uncertainties.
We explore the correlation of the two lightcurves on two
timescales:
1. Between 0 and 1500 days, with a time-step of 120 days,
2. Between 200 and 1100 days, with a smaller time-step of
20 days.
As before for the ICCF analysis, we perform the DCF
analysis with and without flux-shifted BMT data. The timedelays
for the peak values of the DCF are shown in Table B2.
The figures of the DCF versus the time-delay are in Figure B2
for the case with and without BMT data points in the left and
right panels, respectively. In the top panels of Figure B2, we
show the whole explored time-range between 0 and 1500 days
(with a time-step of 120 days); in the bottom panels, we display
the DCF analysis in the time-range (200, 1100) days with a
smaller time-step of 20 days.
To determine the uncertainty of the DCF peaks as well as the
mean values for the time-delay, we perform 500 bootstrap
simulations by randomly selecting subsamples of the
Table B1
Results of the Interpolated Cross-correlation Function Applied to HE 0413-84031 Lightcurves
With Shifted BMT Data Without BMT Data
Interpolated continuum—centroid [days] -
+
1004.6 246.2
196.8
-
+
1003.2 235.4
205.3
Interpolated continuum—peak [days] -
+
1060.0 342.6
228.0
-
+
1061.0 270.8
228.2
Interpolated line—centroid [days] -
+
1008.4 276.9
142.2
-
+
1034.171 248.9
139.1
Interpolated line—peak [days] -
+
984.0 349.0
227.6
-
+
1001.0 282.0
252.3
Symmetric—centroid [days] -
+
1009.7 211.5
113.6
-
+
1021.7 207.8
114.5
Symmetric—peak [days] -
+
1056.0 332.1
197.0
-
+
1057.0 343.8
196.0
Note. We include centroids and peaks with uncertainties for interpolated continuum lightcurve, interpolated emission lightcurve, and symmetric ICCF. Cases with and
without BMT data are separated. The time-delays are expressed in light days in the observer’s frame.
Table B2
Time-delay in Light Days Corresponding to the Peak Values of DCF in the Observer’s Frame
With Shifted BMT Data Without BMT Data
Time-delay at the DCF peak (0,1500; 120) 812.7 (DCF = 0.82) 812.7 (DCF = 0.80)1
Time-delay at the DCF peak (200,1100; 20) 730.0 (DCF = 0.93) 730.0 (DCF = 0.92)
Peak time-delay—bootstrap [days] -
+
720.4 147.9
115.1
-
+
726.0 145.7
114.4
Mean time-delay—bootstrap [days] -
+
658.7 139.2
116.2
-
+
665.4 142.8
115.0
Note. Two time intervals are analyzed: between 0 and 1500 days, and the narrower interval between 200 and 1100 days. The bottom two lines show the peak and the
mean time-delay as inferred from 500 bootstrap realizations. (1) This is the value for the maximum DCF for time-delays less than 1300 days; the time-delay at
1315 days has the larger DCF of 0.82, but this value can be excluded as it approaches the end of the observational run.
19
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
114 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
lightcurves for both the cases with the flux-shifted BMT data
and without them. The values of the peak and mean time-delays
are in Table B2. The peak time-delay (for the largest DCF
value) is clearly in the interval around 720–730 days, as is also
visible in the histograms in Figure B3 for both the cases with
and without BMT data in the left and right panels, respectively.
B.3. z-transformed Discrete Correlation Function (zDCF)
Alexander (1997) proposed the zDCF to correct several
biases of the classical DCF (Edelson & Krolik 1988); namely,
it replaces equal time-lag binning with equal population
binning and uses Fisher’s z-transform. The minimum required
number of observed points is 11; therefore, the z-transformed
DCF is specially suited for undersampled, sparse and
heterogeneous pairs of lightcurves, which is the case for our
continuum and line-emission lightcurves, as they are combined
from different instruments. In addition, zDCF does not assume
any lightcurve properties, such as smoothness, or any AGN
variability process. Moreover, from Monte Carlo generated
pairs of lightcurves with randomized errors, it is possible to
infer the uncertainty from the averaged zDCF values.
For our zDCF analysis, we first used 86 continuum
measurements (including data from OGLE, SALTICAM, and
flux-corrected BMT) and 25 Mg II line-emission points (from
SALT spectral observations). The zDCF values as a function of
the time-delay are displayed in Figure B4, including both errors
for the time-delay and the zDCF value. Two peaks are
apparent, τ1=720.9 days with zDCF=0.92, and
τ2=1059 days with zDCF=0.91. To evaluate the uncertainties
of these peaks, we ran the maximum-likelihood (ML)
analysis for the surroundings of each peak, between 500 and
1000 days for the peak at 721 days and 1000 and 1500 days for
the peak at 1059 days. In the next step, we performed global
ML analysis of the time-delay peaks between 0 and 2000 days,
with the most likely peak at -
+
721 527
324
days. The results are
shown in Table B3 (left column).
In the continuum lightcurve, the BMT points needed to be
systematically shifted toward smaller flux densities to match
OGLE and SALTICAM values. Therefore we also performed
zDCF analysis without BMT points, with the total of 73
continuum points and 25 Mg II line-emission points. The
overall results concerning the time-delay peaks were not
affected; see Table B3 (right column) and Figure B4 (right
panel). The global peak remained at -
+
720.9 100.1
331.3
days with a
smaller lower uncertainty interval than for the case including
BMT data points, but with a comparable likelihood value.
B.4. The JAVELIN Code Package
Another way of estimating the time-delay is to model the
AGN continuum variability as a stochastic process via the
Figure B2. The discrete correlation function (DCF) as a function of the time-delay in the observer’s frame. Top panels: the DCF determined between 0 and 1500 days,
with a time-step of 120 days. To the left we include the shifted BMT flux densities for the continuum; to the right, they are omitted. The vertical dashed line denotes
the time-delay for the maximum DCF. Bottom panels: similar to the panel above, the DCF analysis was performed for the time-interval of 200–1100 days with a
smaller time-step of 20 days. The vertical dashed line denotes the time-delay for the maximum DCF.
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The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
115
damped random walk process (DRW; Kelly et al. 2009;
Kozłowski et al. 2010; MacLeod et al. 2010; Kozłowski 2016).
The emission-line lightcurve is then modeled as a time-delayed,
scaled, and smoothed response to the continuum stochastic
variability. Based on this model assumption, JAVELIN (Just
Another Vehicle for Estimating Lags In Nuclei) code was
developed (Zu et al. 2011, 2013, 2016).16
The JAVELIN
package employs Markov Chain Monte Carlo (MCMC) to
obtain posterior probabilities of the continuum variability
timescale and amplitude. With these two parameters, distributions
of three parameters—time-delay, smoothing width of the
top-hat function, and scaling factor (ratio of the continuum and
line-emission amplitudes Aline/Acont)—that describe the lineemission
lightcurve are searched for.
In Figure B5, we show the distributions of the time-delay
and scaling factor in the top panels with and without
(magnitude-shifted) BMT data in the left and the right panels,
respectively. Both the peak and the mean of the distributions
are consistent within the uncertainties, with the peak close to
1050 days.
To estimate the uncertainties for these time-delays, we ran
200 bootstrap realizations, generating randomly subsets of both
Figure B3. Histograms of the time-delays constructed from 500 bootstrap realizations of the DCF analysis. Left panel: with flux-shifted BMT data included. Right
figure: without BMT data. In both panels, the red vertical line marks the histogram peak value, and the two green horizontal lines stand for 1σ uncertainties of
the peak.
Figure B4. The zDCF values as a function of the time-delay, including the uncertainties for the time-delay and the zDCF values. Left panel: zDCF values as a function
of the time-delay in the observer’s frame based on the continuum lightcurve (including OGLE, SALTICAM, and flux-corrected BMT data) and Mg II line-emission
lightcurve (SALT telescope). The red dashed vertical line denotes the most prominent peak at 721 days. Right panel: zDCF values vs. the time-delay in the observer’s
frame as in the left panel, but without BMT data points.
Table B3
Maximum-likelihood (ML) Analysis for the zDCF Time-delay Values with and
Without Flux-shifted BMT Points Included
Time-delay Interval With Shifted BMT Data Without BMT Data
500–1000 days -
+
720.9 24.1
78.8
, = 0.51 -
+
720.9 84.5
80.6
, = 0.48
1000–1500 days -
+
1059.0 22.09
219.5
, = 0.53 -
+
1059.0 19.6
224.9
, = 0.54
0–2000 days -
+
720.9 527.3
323.9
, = 0.1434 -
+
720.9 100.1
331.3
, = 0.12
Note. The time-delays are expressed in light days in the observer’s frame. The
table contains results for the localized ML analysis, taking into account the
surroundings of the two most prominent peaks at 721 and 1059 days. The
lower part contains the peak of the global ML analysis in the searched interval
between 0 and 2000 days. The actual maximum likelihood is denoted as  and
its value is listed for the time-delay in each interval.
16
Please visithttps://bitbucket.org/nye17/javelin/src/develop/ for more
information on the code usage and application.
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116 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
lightcurves. The distributions of the means of time-delays are
shown in the bottom panels of Figure B5 both with shifted
BMT data (left panel) and without them (right panel). The peak
and mean time-delays with corresponding uncertainties are
listed in Table B4.
B.5. Measures of Regularity/Randomness—Von Neumann
Estimator
A novel technique to investigate time-delays is to measure
regularity or randomness of data (Chelouche et al. 2017), which
has previously been extensively applied in cryptography or
electronic data compression. This method does not require
interpolation of lightcurves as the ICCF, nor does it require
binning in the correlation space as for DCF and zDCF. Moreover,
the analysis is not based on any assumptions concerning the AGN
variability in a way as the JAVELIN assumes for the continuum
lightcurve. One of the most robust measures of the data regularity
is an optimized Von Neumann scheme, which uses the combined
lightcurve ( ) {( )}t = =F t t f, ,i i i
N
1 = È t
F F1 2 , where F1 is the
continuum lightcurve and t
F2 is the time-delayed lineemission
lightcurve. Based on the combined lightcurve, the
Von Neumann estimator is defined as the mean successive
difference of F(t, τ),
( ) [ ( ) ( )] ( )åt º
-
-
=
-
+E
N
F t F t
1
1
. B5
i
N
i i
1
1
1
2
The minimum of the estimator E is reached for a certain timedelay
t t= ¢, which is expected to be close to the actual timedelay,
t t¢ = 0.
We applied the estimator to the data of HE 0413-4031 to
estimate the time-delay between the continuum and Mg II line
lightcurves. We made use of the Python implementation of the
estimator in Equation (B5), which was demonstrated in
Chelouche et al. (2017).17
In Figure B6, we show the estimator
value as a function of the time-delay with and without
magnitude-shifted BMT data in the left and the right panels,
respectively. For the case with shifted BMT data, we obtain the
minimum of E(τ) at 499.3 days, while without BMT data, the
minimum is for the time-delay of 715.18 days.
To construct distributions of the estimator minima, we
perform 10,000 boostrap realizations for both cases with and
without shifted BMT data. For both of these cases, the peak and
the mean of the distributions are listed in Table B5. The
Figure B5. Color-coded plots of JAVELIN code results in the time-delay/scaling factor plane. Top row: time-delay distribution including magnitude-shifted BMT
data (left panel) and without them (right panel). Bottom row: distribution of the time-delay mean values from 200 bootstrap realizations—including shifted BMT data
(left panel) and without them (right panel).
17
For the script, visitwww.pozonunez.de/astro_codes/python/vnrm.py.
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The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
117
minima and the peaks differ by about 200 days for the cases
with and without BMT data. However, the minimum around
710 days is present for both cases, being a local minimum for
the case with BMT data. This makes the peak at 710 days more
robust, while we do not obtain any significant result for the
peak at 1060–1070 days, which we obtained using JAVELIN
and ICCF methods.
In addition, we perform the same analysis using the Bartels
estimator, which is a modification of the Von Neumann
estimator using the ranked unified lightcurve FR(t, τ)
(Bartels 1982). In comparison with the pure Von Neumann
scheme, the Bartels modification of the estimator has a
consistent global minimum at 713.43 and 715.18 days for both
cases with and without BMT photometry data, respectively; see
Figure B7 (left and right panels, respectively). The peak values
of the time-delay distribution in the observer’s frame are also
comparable; see Table B5. The mean value of the time-delay
distribution is smaller for the case with the BMT data included,
but within uncertainties the mean values of the time-delay are
still comparable.
B.6. χ2
Method
As for the quasar CTS C30.10 (Czerny et al. 2019), we also
apply the χ2
method to the lightcurves. It was found that the χ2
method, which is frequently used in quasar lensing studies,
works better than the ICCF for the AGN variability modeled as
a red noise process (Czerny et al. 2013). The lightcurves were
prepared as for the standard ICCF, that is, mean values were
subtracted from them and they were normalized by their
corresponding variances. Subsequently, the spectroscopic
lightcurve was time-shifted with respect to the photometry
lightcurve. The data points were linearly interpolated, but
because the photometry lightcurve is denser than the spectroscopic
lightcurve, we interpolated the photometry to the
spectroscopy, i.e., we performed an asymmetric interpolation.
Finally, we estimated the degree of similarity between shifted
lightcurves by calculating the χ2
, whose minimum may be
considered as the most likely time-delay between the
continuum and the line emission.
Table B4
The Peak and Mean Values of the Time-delay Distribution (in the Observer’s
Frame) from 200 Bootstrap Realizations of JAVELIN
With Shifted BMT Data Without BMT Data
Peak time-delay [days] -
+
1053.7 163.6
79.8
-
+
1058.5 150.7
77.1
Mean time-delay [days] -
+
1002.1 161.8
77.0
-
+
1016.0 148.2
70.5
Note. Time-delays are expressed in light days.
Figure B6. The Von Neumann estimator as a function of the time-delay. Left figure: the case with magnitude-shifted BMT data; the minimum at 499.33 days is
depicted by a red vertical line. Right panel: the case without BMT data; the minimum at 715.18 days is represented by a red vertical line.
Figure B7. Bartels estimator as a function of the time-delay. Left figure: the case with magnitude-shifted BMT data; the minimum at 713.43 days is depicted by a red
vertical line. Right panel: the case without BMT data; the minimum at 715.18 days is represented by a red vertical line.
23
The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
118 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
In Figure B8, we show the χ2
values as a function of the
time-delay in the observer’s frame of reference for the case
with the magnitude-shifted BMT data included (left panel) and
without them (right panel). In both cases, the global minimum
of χ2
is close to τ=727 days. To determine the uncertainty of
this minimum, we construct the distributions of the time-delay
by performing 10,000 bootstrap realizations, i.e., by creating
randomly selected subsets of both lightcurves and using the χ2
method for each new pair. The distributions are displayed in
Figure B9. Both cases with and without the BMT data have one
main peak and secondary peaks toward longer time-delays. The
peak and mean values of the distributions are listed in
Table B6. The peak and mean values are within uncertainties
consistent, with the mean values shifted toward larger values
with respect to the peak values because of the presence of
secondary peaks at larger time-delays.
Figure B8. The values of the χ2
statistic as a function of the time-delay expressed in days with respect to the observer’s frame of reference. Left panel: the χ2
values
calculated for the case with the shifted BMT photometry data. Right panel: the χ2
values calculated for the case without the BMT photometry data.
Figure B9. Distributions of the time-delays expressed in days in the observer’s frame of reference for 10,000 bootstrap realizations. Left panel: the time-delay
distribution based on the χ2
analysis calculated for the case with the shifted BMT photometry data. Right panel: the time-delay distribution based on the χ2
analysis
calculated for the case without the BMT photometry data.
Table B5
The Upper Part of the Table Shows the Minima of the Von Neumann Estimator, the Peak and the Mean of Minimum Distributions for the Case With and Without
Magnitude-shifted BMT Data in the Left and the Right Columns Respectively
Estimator With Shifted BMT Data Without BMT Data
Von Neumann: Minimum of E(τ) [days] 499.33 715.18
Von Neumann: Bootstrap (10,000 )–peak [days] -
+
498.9 125.9
170.9
-
+
711.3 139.5
149.0
Von Neumann: Bootstrap (10,000 )–mean [days] -
+
588.5 108.0
157.3
-
+
708.1 137.9
147.0
Bartels: Minimum of E(τ) [days] 713.43 715.18
Bartels: Bootstrap (10,000 )–peak [days] -
+
710.9 173.0
172.3
-
+
714.6 164.6
176.1
Bartels: Bootstrap (10,000 )–mean [days] -
+
634.6 159.9
161.9
-
+
725.5 150.3
172.8
Note. The lower part displays the same information as above, but for the Bartels estimator, which is the modification of the Von Neumann scheme using the ranked
combined lightcurve. Time-delays are expressed in light days in the observer’s frame.
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The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
119
Appendix C
Tests of Complementary UV Fe II Templates
We used the theoretical Fe II templates from Bruhweiler &
Verner (2008) (hereafter d12 template) in our basic modeling,
because one of these templates, d12-m20-20-5.dat, allowed us
to get very nice and simple fits to all data sets. However, other
Fe II templates are also used. Therefore, for our mean spectrum,
we additionally tested two other templates. The first one was a
semiempirical template of Tsuzuki et al. (2006) (hereafter T06)
based on a combination of 14 low-redshift quasars and
CLOUDY modeling of the Fe II emission to disentangle the
Fe II and Mg II contribution. This template combined the
advantage of the previously used purely observational template
of Vestergaard & Wilkes (2001) and a theoretical modeling.
The results are given in Table C1. The fits obtained with this
template had the same number of free parameters as the fits
with d12-m20-20-5.dat, if a single Lorentzian is used for Mg II,
but the fit quality is always lower. The fits do not depend
strongly on the doublet ratio, because the Mg II line is
unresolved, and the change of the doublet ratio is easily
compensated with the change of the redshift and the shift of the
Mg II line with respect to the Fe II emission. Even if we add the
second kinematic component, fits do not improve considerably,
and final χ2
is higher than for our canonical fits.
Next we incorporate the semiempirical UV Fe II template18
(hereafter referred to as the KDP15 template, KovačevićDojčinović
& Popović 2015; Popović et al. 2019) to fit the Fe II
pseudo-continuum i spectral window 2700–2900 Å. This
model includes overall 7 free parameters, which includes 5
multiplets, namely, 60 (a4
D–z6
Fo
), 61 (a4
D–z6
Po
), 62
(a4
D–z4
Fo
), 63 (a4
D–z4
Do
), and 78 (a4
P–z4
Po
). Additionally,
there is an empirically added component, “I Zw 1 lines,” that is
represented with two Gaussians (at λλ2720,2840 Å). This
additional empirical set of lines was included in the model
because they were not identified in the emission within
∼2825–2860 Åand 2690–2725 Å. The remaining parameter
is the line width (see Appendix A1 in Popović et al. 2019, for
more details).
The fits with this template, also given in Table C1. In the
case of a single kinematic component, the provided fits are
again not better in comparison with our standard fits. However,
if we allow for two kinematic components for Mg II, indeed the
resulting χ2
is lower, particularly if we optimize the redshift to
the new template. Although during the fitting we allowed for all
the six template components to vary, we noticed in the final fits
that the multiplets 61, 63, and 78 converge to values close to
zero, and only the multiplets 60 and 62 and the “I Zw 1 lines”
return nonzero values. This is consistent with the Figure A1 in
the paper of Popović et al. (2019). In their figure, the multiplets
60 and 78 are outside our spectral window, and the multiplet 63
has a very weak contribution (by a factor ∼3–3.5 times with
respect to multiplet 62).
This new best fit implies a different shape of the Mg II line
and different kinematics of the Fe II– and Mg II–emitting
region. With d12-m20-20-5.dat, the Mg II line was represented
by a single Lorentzian, and FWHM of the Mg II line was
somewhat broader than the requested FWHM of the Fe II
(4380 km s−1
, and 2800 km s−1
, respectively), implying that
Fe II emission comes on average from a little more distant part
of the BLR. In the case of the new best fit, the requested
FWHM of Fe II is larger, 4000 km s−1
, and the two components
of Mg II, if treated as separate components, have the
corresponding values of FWHM of 3100 km s−1
and 9050 km
s−1
, respectively, thus considerable part of the Mg II emission
should originate at a larger distance than Fe II. If the two Mg II
components are treated as a single asymmetric line, then the
FWHM of Mg II is 4250 km s−1
just above that for Fe II
emission in this model, but effectively similar to the FWHM of
Mg II from the basic model. However, the overall line shape is
widely different, and we present the new fit in Figure C1. The
very broad Mg II component is then located at the same
position as the Fe II emission, but the narrower Mg II
component is again shifted considerably by 1545 km s−1
with
respect to Fe II, which is comparable to the shift of 1620 km s−1
in our basic fits using a single Lorentzian component discussed
in Section 3.1.
In addition, we verify statistically whether the fit using the
KDP15 template provides an overall improvement. We
compare the KDP15 template with the original fit using
the d12 Fe II template, which has p1=8 parameters (2 for
Fe II, 3 for the Mg II single Lorentzian component, 2 for the
power-law continuum, and 1 for the redshift). The KDP15
template uses 7 parameters for the Fe II pseudo-continuum, 5
parameters for the Mg II line with 2 Gaussian components, 2
for the power-law continuum, and 1 for the redshift, overall
p2=15 parameters. Given the c = 2088.421
2
for the d12
fitting, c = 1711.342
2
for the KDP15 template, and the total
number of data points of n=579, we can calculate the F
statistic with the null hypothesis that the apparently better fit
using the KDP15 template does not lead to an improvement.
The F statistic can be calculated as follows
( ) ( )
( )
( )
c c
c
=
- -
-
F
p p
n p
, C11
2
2
2
2 1
2
2
2
which for the values above gives F=17.75. When the three
parameters in the KDP15 template that converge to zero are
removed from the calculation, we get ¢ =F 31.23. Because
these values are larger than the test statistic critical value,
which is between 1 and 2 for our F distribution with (7564)
degrees of freedom,19
the null hypothesis is rejected and
formally, the fit using the KDP15 template with 2 Gaussian
components for the Mg II line is better.
The new fit still implies a considerable shift between Fe II
and Mg II components, which is not expected according to
Table B6
Results of the χ2
Analysis of the Time-delay for Two Cases: With and Without
Shifted BMT Data
Statistic
With Shifted
BMT Data Without BMT Data
χ2
minimum [days] 726.86 727.41
Bootstrap (10,000)–
peak [days]
-
+
720.4 102.2
145.6
-
+
727.7 85.2
160.0
Bootstrap (10,000)–
mean [days]
-
+
818.6 85.2
133.0
-
+
900.0 91.3
110.8
Note. We list the χ2
minima, the peaks, and the means of the time-delay
distributions expressed for the observer’s frame of reference. Time-delays are
expressed in light days.
18
http://servo.aob.rs/FeII_AGN/link7.html
19
https://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm
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120 CHAPTER 3. PAPER 2: REVERBERATION-MAPPING OF HE 0413-4031
Kovačević-Dojčinović & Popović (2015) and Marziani et al.
(2013). However, with the KDP15 Fe II template, the fitting
results highly depend on the adopted redshift. When we
performed the analysis assuming that the redshift value given
by NED is the right one, the decomposition of the spectrum
changed significantly. Now the two Gaussians are rather
similar; the dominating Gaussian coincides with the position of
Fe II emission, and the second one is shifted only by 404 km
s−1
toward shorter wavelengths. This happened because now
the Fe II contribution peaks at shorter wavelengths than before,
and the ratio of the multiplet 63 to multiplet 62 is 0.49, while in
the previous fits the contribution from the multiplet 63 was
negligible. On the other hand, formally this fit is worse, with χ2
of 1991.62 versus 1711.34 for the redshift 1.37617. This
stresses the importance of an independent and precise
measurement of the redshift in this source.
Because the χ2
for the new fit of the mean spectrum is better
than our basic fit, we also refitted all individual 25 spectra using
this model. Because three of the six parameters were
unimportant for the mean spectrum fit, we optimize our model
fitting and reduce the parameter space to account only for the
contribution from these three nonzero Fe II components. The
result is shown in Figure C2. The overall trend of the higher
values followed with the decrease in the second part of the data
is still seen, but the errors are much larger. This is directly
related to the larger number of parameters, and the Mg II error
is determined allowing for all the other parameters to vary
Table C1
An Overview of the Parameters Used for Fitting Different Fe II Templates to the Mean Spectrum as Well as the Inferred Best-fit Parameters
Fe II Mg II Shape Redshift Doublet Ratio Fe II Smear Velocity EW(Mg II) χ2
Template Shape [km s−1
]
d12 1 Lorentz 1.37648 1.6 2800 27.44 2088.42
T06 1 Lorentz 1.38205 1.0 4500 29.64 2476.92
T06 1 Lorentz 1.38323 1.7 4700 29.77 2482.84
T06 2 Lorentz 1.38323 1.7 4700 29.74 2299.37
KDP15 1 Lorentz 1.37648*
1.6 5000 25.45 2921.12
KDP15 2 Gauss 1.37648*
1.6 4000 22.13 1749.18
KDP15 2 Gauss 1.37617 1.6 4000 22.46 1711.34
KDP15 2 Gauss 1.389 (NED) 1.6 5600 19.02 1991.62
Note. From left to right, the parameters are the template name (d12 according to Bruhweiler & Verner 2008, T06 according to Tsuzuki et al. 2006, and the KDP15
template based on Kovačević-Dojčinović & Popović, 2015; Popović et al. 2019), the Mg II shape (number of either Lorentzian or Gaussian profiles), the redshift (the
star *
for the KDP15 template means that the redshift was fixed in this case based on the best-fit d12 value), the Mg II doublet ratio (between one and two), Fe II smear
velocity, the equivalent width of the Mg II line, and χ2
in the last column.
Figure C1. Left panel:the best fit to the mean spectrum with the Fe II template (Kovačević-Dojčinović & Popović, 2015; Popović et al. 2019) and 2 Gaussian
components, for the best-fit redshift of 1.37617. Visually, the residuals are similar, but the implied shape of the Mg II line (dashed magenta) is very different from our
standard fit shown in Figure 1. Right panel:fit of the same model but for the redshift from NED, z=1.389.
Figure C2. The equivalent width of the Mg II line in each of 25 observations
measured from the standard d12 model (black points, Bruhweiler & Verner 2008)
and from the new model based on the Fe II template (Kovačević-Dojčinović &
Popović, 2015; Popović et al. 2019) and 2 Gaussian components. The equivalent
width based on the KDP15 template has noticeably larger errors.
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The Astrophysical Journal, 896:146 (28pp), 2020 June 20 Zajaček et al.
121
(apart from the redshift, the doublet ratio, and the Fe II width,
kept at values optimized for the mean spectrum). In particular,
the parameters of the second, very broad component of the
Mg II line are considerably degenerate with respect to the
underlying power law and Fe II parameters.
The new Mg II lightcurve was used again to measure the
time-delay using different methods. The values are comparable,
but as expected the uncertainties are generally larger and the
correlation coefficient between the two lightcurves is lower.
For the ICCF, we include the centroid and the peak values for
the interpolated continuum, the interpolated line emission, and
the symmetric case in Table C2. In Figure C3, we show the
correlation coefficient as a function of the time-delay in the
observer’s frame with the centroid as well as the peak
distributions in the central and the right panels, respectively.
The peak value of the correlation coefficient is 0.65 for the
time-delay of 751 days, whereas for the d12 template, we
previously got the peak value of 0.86 for the time-delay of
1058 days for the case without BMT points. For the zDCF
method, we obtain the peak at t =- -
+
382.30 1000 59.1
401.1
days
according to the ML analysis in the interval of 0–1000 days.
When the interval is narrowed down to 500–1000 days, the ML
peak is at t =- -
+
765.3500 1000 79.8
70.2
days, which is comparable
within uncertainties to t =- -
+
720.9500 1000 84.5
80.6
days using
the d12 template without the BMT data in the same interval.
The χ2
-based method gives t = -
+
721d12 45
57
days for the
original d12 template, while for the Mg II lightcurve inferred
from the KDP15 template fitting, we obtained
t = -
+
751KDP15 150
104
days. In summary, the basic result of our
analysis—the time-delay of the response of the Mg II line—is
comparable to the previous analysis based on d12 template,
only the uncertainty is larger for the KDP15 template.
ORCID iDs
Michal Zajaček https://orcid.org/0000-0001-6450-1187
Bożena Czerny https://orcid.org/0000-0001-5848-4333
Mary Loli Martinez–Aldama https://orcid.org/0000-0002-
7843-7689
Mateusz Rałowski https://orcid.org/0000-0002-0297-3346
Aleksandra Olejak https://orcid.org/0000-0002-6105-6492
Swayamtrupta Panda https://orcid.org/0000-0002-
5854-7426
Krzysztof Hryniewicz https://orcid.org/0000-0002-
2005-9136
Marzena Śniegowska https://orcid.org/0000-0003-
2656-6726
Mohammad-Hassan Naddaf https://orcid.org/0000-0002-
7604-9594
Grzegorz Pietrzyński https://orcid.org/0000-0002-
9443-4138
C. Sobrino Figaredo https://orcid.org/0000-0001-
9704-690X
Martin Haas https://orcid.org/0000-0002-7284-0477
Andrzej Udalski https://orcid.org/0000-0001-5207-5619
Marek Gorski https://orcid.org/0000-0002-3125-9088
Marek Sarna https://orcid.org/0000-0003-4745-3923
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123
Chapter
4
Paper 3: Red-Giant Depletion in the
Galactic Center
While performing near-infrared observations, it was found that the carbon-monoxide (CO)
bandhead absorption is decreasing inside ∼ 0.5 pc (Sellgren et al. 1990). Since the CO
bandhead feature is a proxy of the surface-brightness of late-type stars, it was recognized that
this signifies the drop in the number of late-type stars (red giants and supergiants, asymptotic
giant-branch stars). It has triggered several discussions and the formation of models how this
could have arisen close to the compact radio source Sgr A*, which is associated with the
supermassive black hole. The proposed red-giant depletion models include their collisions
with other stars, red giant-accretion disc interactions, and the tidal disruption of red-giant
envelopes. In this paper, we propose novel mechanism – the interaction of red giants with
the nuclear jet – which is capable of ablating the upper layers of red-giant envelopes. The
ablation by the jet has been motivated by the recent indications that the Galactic center was
much more active several million years ago (Bland-Hawthorn et al. 2019). This increased
Seyfert-like activity may be linked to the formation of the large-scale γ-ray Fermi bubbles as
well as X-ray eROSITA bubbles above and below the Galactic plane.
Depending on the duration of the active jet phase, the number of stellar passages through
the jet can vary, but typically it reaches ∼ 103
− 104
interactions with the jet when it is
active at least for 0.5 million years. For the moderate jet luminosity of Lj ∼ 1042
erg s−1
, the
stagnation radius can in principle be only ∼ 30 Solar radii at ∼ 0.04 pc from Sgr A* and the
detached mass per one passage is in the range 10−10
− 10−2
M⊙. Since the detached mass after
one passage depends steeply on the stellar radius and the distance, ∆M1 ∝ R4
⋆z−2
, large red
giants that orbit Sgr A* within the S cluster are affected the most, which is consistent with
the flattened surface-density profiles of bright late-type stars. We also constructed surfacedensity
profiles of a mock nuclear star cluster composed of late-type stars. Initially, the stars
have a cusp-like distribution resulting from the two-body relaxation. Once the jet activity
starts, late-type stars brighter than 14 mag develop a core-like distribution. For the largest
possible jet luminosities of Lj = 1044
erg s−1
close to the Eddington luminosity of Sgr A*, red
giants brighter than 12 mag develop a core-like distribution up to ∼ 0.4 pc, while fainter red
giants keep their initial cusp-like profiles. This is qualitatively consistent with the findings
of Schödel et al. (2020), who found similar surface-density distributions: core-like for the
brightest late-type stars and cusp-like for the fainter ones.
Credit: Zajaˇcek et al. (2020), ApJ 903, 140. Reproduced with permission ©AAS.
125
Depletion of Bright Red Giants in the Galactic Center during Its Active Phases
Michal Zajaček1
, Anabella Araudo2,3
, Vladimír Karas3
, Bożena Czerny1
, and Andreas Eckart4,5
1
Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland; zajacek@cft.edu.pl
2
ELI Beamlines, Institute of Physics, Czech Academy of Sciences, CZ-25241 Dolní Břežany, Czech Republic
3
Astronomical Institute of the Czech Academy of Sciences, Boční II 1401, CZ-14100 Prague, Czech Republic
4
I. Physikalisches Institut der Universität zu Köln, Zülpicher Strasse 77, D-50937 Köln, Germany
5
Max-Planck-Institut für Radioastronomie (MPIfR), Auf dem Hügel 69, D-53121 Bonn, Germany
Received 2020 February 25; revised 2020 September 10; accepted 2020 September 29; published 2020 November 12
Abstract
Observations in the near-infrared domain showed the presence of the flat core of bright late-type stars inside
∼0.5 pc from the Galactic center supermassive black hole (Sgr A*
), while young massive OB/Wolf–Rayet stars
form a cusp. Several dynamical processes were proposed to explain this apparent paradox of the distribution of the
Galactic center stellar populations. Given the mounting evidence on the significantly increased activity of Sgr A*
during the past million years, we propose a scenario based on the interaction between the late-type giants and a
nuclear jet, whose past existence and energetics can be inferred from the presence of γ-ray Fermi bubbles and
bipolar radio bubbles. Extended, loose envelopes of red giant stars can be ablated by the jet with kinetic luminosity
in the range of Lj≈1041
– -10 erg s44 1
within the inner ∼0.04 pc of SgrA*
(S-cluster region), which would lead to
their infrared luminosity decrease after several thousand jet–star interactions. The ablation of the atmospheres of
red giants is complemented by the process of tidal stripping that operates at distances of 1 mpc, and by the direct
mechanical interaction of stars with a clumpy disk at 0.04 pc, which can explain the flat density profile of bright
late-type stars inside the inner half parsec from SgrA*
.
Unified Astronomy Thesaurus concepts: Galactic center (565); Red giant stars (1372); Red supergiant stars (1375);
Relativistic jets (1390); Stellar dynamics (1596)
1. Introduction
The Galactic center supermassive black hole (hereafter SMBH)
with the mass of 4.1×106
Me is located at the distance of
8.1 kpc (Boehle et al. 2016; Gillessen et al. 2017; Parsa et al.
2017; Gravity Collaboration et al. 2018) and provides a unique
laboratory for studying detailed dynamical processes and the
mutual interaction between a nuclear star cluster (NSC) and a
central massive black hole (Alexander 2005; Genzel et al. 2010;
Eckart et al. 2017; Ali et al. 2020) as well as with the multiphase
gaseous-dusty circumnuclear medium (Morris & Serabyn 1996;
Różańska et al. 2017). The compact radio source Sgr A*
associated with the SMBH is embedded in the Milky Way NSC,
which is one of the densest stellar systems in the Galaxy
(Alexander 2017; Schödel et al. 2014), and in addition, it is
surrounded by an ionized, neutral, and molecular gas and dust
(see, e.g., Moser et al. 2017 and references therein).
The NSC consists of both late-type (red giants, supergiants
and asymptotic giant branch stars) and early-type stars of O and
B spectral classes (Krabbe et al. 1991; Buchholz et al. 2009; Do
et al. 2009; Gallego-Cano et al. 2018), which imply star
formation during the whole Galactic history, albeit most likely
episodic (Pfuhl et al. 2011; Schödel et al. 2020) with the star
formation peak at 10 Gyr, the minimum at 1–2 Gyr, and a
recent increase in the last few hundred million years.
In the innermost parsec of the Galactic center, there is a
surprising abundance of young massive OB/Wolf–Rayet stars
that have formed in situ in the last 10 million years (Ghez et al.
2003). These young stars form an unrelaxed cusp-like distribution.
On the other hand, previous studies of the distribution of late-type
stars showed that they exhibit a core-like distribution inside the
inner ∼0.5 pc, which has a projected flat or even decreasing
profile toward the center (Buchholz et al. 2009; Do et al. 2009;
Sellgren et al. 1990). More recent studies provided a precise
analysis of the distribution of late-type stars because of increasing
their sensitivity toward larger magnitudes, i.e., fainter giants
(Gallego-Cano et al. 2018; Habibi et al. 2019). Using photometric
number counts and diffuse light analysis, Gallego-Cano et al.
(2018) found that fainter late-type stars with magnitudes of
K≈18 exhibit a cusp-like distribution within the sphere of
influence of SgrA*
with a 3D power-law exponent of γ;1.43.
In comparison, there is an apparent lack of bright red giants with
K=12.5–16 at the projected radii of 0.3 pc from SgrA*
.
Gallego-Cano et al. (2018) estimate the number of missing giants
to 100 for this distance range. The study of Habibi et al. (2019)
also finds a cusp-like distribution for late-type stars with K<17
within 0.02–0.4 pc. In agreement with Gallego-Cano et al. (2018),
they found a core-like distribution for the brightest giants with
K<15.5, although the number of missing giants appears to be
lower than 100 according to their analysis. Although the surfacebrightness
distribution of late-type stars brighter than 15.5 mag
appears to be rather flat, already in Figure 11 of Buchholz et al.
(2009) the inner point at 0 5 (where 1″∼0.04 pc at the Galactic
center) of the distribution of late-type stars as well as of the
distribution of all stars indicates the presence of a cusp.
In summary, there appears to be an internal mechanism
within the NSC that preferentially depleted bright, large red
giants on one hand, which has led to their apparent core-like
distribution, and at the same time has been less efficient for
early-type as well as fainter late-type stars, on the other hand.
Such a mechanism has altered either the spatial, luminosity, or
the temperature distribution of the bright red giant stars so that
they effectively fall beyond the detection limit or they instead
mimic younger, “bluer” stars. So far, it is mainly the following
four mechanisms that have been discussed to explain the
apparent lack of bright red giants:
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 https://doi.org/10.3847/1538-4357/abbd94
© 2020. The American Astronomical Society. All rights reserved.
1
126 CHAPTER 4. PAPER 3: RED-GIANT DEPLETION IN THE GALACTIC CENTER
1. complete or partial tidal disruption of red giants by the
SMBH (Hills 1975; Bogdanović et al. 2014; King 2020;
envelope removal),
2. envelope stripping by the collisions of red giants with the
dense clumps within a self-gravitating accretion disk
(Armitage et al. 1996; Amaro-Seoane & Chen 2014;
Kieffer & Bogdanović 2016; Amaro-Seoane et al. 2020;
envelope removal),
3. collisions of red giants with field stars and compact
remnants (Phinney 1989; Morris 1993; Genzel et al.
1996; Bailey & Davies 1999; Alexander 2005; Davies &
King 2005; Dale et al. 2009; envelope removal),
4. mass segregation effects: the dynamical effect of a
secondary massive black hole (Baumgardt et al. 2006;
Merritt & Szell 2006; Portegies Zwart et al. 2006;
Matsubayashi et al. 2007; Löckmann & Baumgardt 2008;
Gualandris & Merritt 2012) or of an infalling massive
cluster (Kim & Morris 2003; Ernst et al. 2009; Antonini
et al. 2012) or of stellar black holes (Morris 1993; altered
spatial distribution),
where in parentheses we include the mechanism responsible for
altering the population of late-type stars. The importance of
star–star and star–disk interactions was also analyzed generally
for active galactic nuclei (AGNs) in terms of the effects on the
accretion disk and broad-line region structure as well as the
NSC orbital distribution (Zurek et al. 1994; Armitage et al.
1996; Karas & Šubr 2001; Vilkoviskij & Czerny 2002; Kieffer
& Bogdanović, 2016; MacLeod & Lin 2020).
We propose here another mechanism based on the jet–star
interactions (Barkov et al. 2012a; Araudo et al. 2013; Araudo
& Karas 2017), which most likely coexisted with the
mechanisms proposed above. In particular, the star–accretion
disk collisions are expected to be accompanied by star–jet
crossings during previous active phases of SgrA*
. Because red
giant stars have typically large, loosely bound tenuous
envelopes, dense compact cores, and slow winds with the
terminal velocity -100 km s 1, they are in particular susceptible
to mass removal in encounters with higher-pressure
material (MacLeod et al. 2012; Amaro-Seoane & Chen 2014;
Kieffer & Bogdanović 2016).6
Therefore, during the red giant–
jet interactions, the jet ram pressure will remove the outer
layers of the stellar envelope during the passage. We illustrate
this idea in Figure 1.
After several star–jet crossings, the atmosphere is removed
similarly as for repetitive star–disk crossings (Amaro-Seoane
et al. 2020), and the giant is modified in a way that it follows an
evolutionary track in the Hertzsprung–Russell (HR) diagram
approximately along the constant absolute magnitude toward
higher effective temperatures. We show that this mechanism
quite likely operated in the vicinity of SgrA*
during its active
Seyfert-like phase in the past few million years (BlandHawthorn
et al. 2019) when the jet kinetic luminosity could
have reached ~ -10 erg s44 1
. In principle, even in the quiescent
state, a tidal disruption event (TDE) every ∼104
yr, which can
be estimated for the Galactic center (Syer & Ulmer 1999;
Alexander 2005), can temporarily reactivate the jet of SgrA*
,
and some of the bright red giants could be depleted during its
existence. This makes the red giant–jet interaction in the
Galactic center relevant and highly plausible in its recent
history, and the dynamical consequences can be inferred based
on the so-far detected traces of the past active phase of SgrA*
as well as the currently observed stellar density distribution.
Previous jet–star interaction studies were focused on the
emergent nonthermal radiation, in particular in the gamma-ray
domain, and mass-loading and chemical enrichment of jets by
stellar winds (see e.g., Komissarov 1994; Barkov et al. 2012a;
Bosch-Ramon et al. 2012; Araudo et al. 2013; Bednarek &
Banasiński 2015; de la Cita et al. 2016). Here we focus on the
effect of the jet on the stellar population. In most jetted AGNs,
this is perhaps a secondary problem because stellar populations
in the host bulge cannot be resolved out, i.e., one can only
analyze the integrated starlight. In contrast, within the Galactic
center NSC, one can not only disentangle late- and early-type
stars, but it is also possible to study their distribution as well as
the kinematics of individual stars. Although in the current lowluminosity
state there is no firm evidence for the presence of a
relativistic jet, there are nowadays several multiwavelength
signatures of the past active Seyfert-like state of SgrA*
that
occurred a few million years ago (Bland-Hawthorn et al. 2019;
Heywood et al. 2019; Ponti et al. 2019). However, even in the
current quiescent state of SgrA*
, studies by Yusef-Zadeh et al.
(2012) and Li et al. (2013) indicate the existence of a lowsurface-brightness
parsec-scale jet. In addition, the presence of
the cometary-shaped infrared-excess bow-shock sources X3,
X7 (Mužić et al. 2010), and recently X8 (Peißker et al. 2019)
indicates that the star–outflow interaction is ongoing even in a
very low state of the SgrA*
activity. The morphology of these
sources can be explained by the interaction with a strong
Figure 1. Illustration of the jet–red giant interaction in the vicinity of SgrA*
during its active phase. The large, loosely bound envelope of the red giant
(colored as red and orange), which has an initial luminosity, radius, and
temperature (L R T, ,0 0 0), is ablated by the jet ram pressure during several
encounters as the lifetime of the jet tjet∼0.5 Myr is much longer than the
orbital timescale in the inner ∼0.5 pc, ( )~P a1500 0.1 pc yrorb
3 2 . After a few
hundred encounters, star has modified parameters (L R T, ,1 1 1), which change the
overall outlook of the giant in the near-infrared domain. Inspired by Barkov
et al. (2012a) and Bosch-Ramon et al. (2012).
6
The estimate of the terminal wind velocity is given by the escape
velocity
⎛
⎝
⎜
⎞
⎠
⎟ ( )

=
-

v
M
M
62
1
km s
R
Resc
1 2
100
1 2
1.
2
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
127
accretion wind originating from SgrA*
or with the collective
wind of the cluster of young stars.
This paper proposes a new mechanism that could have
affected the current population of bright late-type stars, namely
their appearance as well as number counts in specific
magnitude bins, in the Galactic center. We apply analytical
and semianalytical calculations to assess whether the potential
past jet–star interactions could have had an effect on the stellar
population in the sphere of influence of SgrA*
. Although the
analytical calculations introduce several simplifications, we
show that the mechanism could have operated and the
estimated number of affected red giants is in accordance with
the most sensitive, up-to-date studies (Gallego-Cano et al.
2018; Habibi et al. 2019). A more detailed computational
treatment including magnetohydrodynamic numerical simulations
as well as a stellar evolution will be presented in our
future studies.
The paper is structured as follows. In Section 2, we derive
the stagnation radius, basic timescales, and the envelope mass
removed for red giant stars interacting with the jet of SgrA*
during its past active phase. In Section 3, we discuss the
observational signatures in the near-infrared domain. Subsequently,
in Section 4, we estimate the number of red giants that
could be affected by the jet interaction and visually depleted
from the immediate vicinity of SgrA*
. In Section 6, we discuss
additional processes related to the red giant–jet interaction in
the Galactic center. Finally, we summarize the main results and
conclude with Section 7.
2. Derivation of the Jet–Star Stagnation Radius and the
Jet-induced Stellar Mass Loss
The evidence for the active phase of SgrA*
that is estimated to
have occurred 4±1 Myr ago is based on the X-ray/γ-ray
bubbles with a total energy content of 1056
–1057
erg (BlandHawthorn
et al. 2019). The first evidence for the nuclear outburst
was the kiloparsec-scale 1.5 keV ROSAT X-ray emission that
originated in the Galactic center (Bland-Hawthorn & Cohen 2003).
The X-ray structure coincides well with the more recently
discovered Fermi γ-ray bubbles extending 50◦
north and south of
the Galactic plane at 1–100 GeV (Su et al. 2010). The X-ray/
γ-ray bubbles are energetically consistent with the nuclear AGNlike
activity associated with the jet and/or disk-wind outflows
with jet power = ´+
-L 2.3 10 erg sj 0.9
5.1 42 1
and age -
+
4.3 Myr1.4
0.8
(Miller & Bregman 2016). In comparison, the starburst origin of
the Fermi bubbles is inconsistent with the bubble energetics by a
factor of ∼100 (Bland-Hawthorn & Cohen 2003). On intermediate
scales of hundreds of parsecs, the base of the Fermi
bubbles coincides with the bipolar radio bubbles (Heywood et al.
2019) as well as with the X-ray chimneys (Ponti et al. 2019).
Using hydrodynamic simulations, Guo & Mathews (2012)
reproduce the basic radiative characteristics of the Fermi bubbles
with the AGN jet duration of ∼0.1–0.5 Myr, which corresponds
to the jet luminosity ( )» - =-L 10 erg 0.1 0.5 Myrj
56 57
´ - ´ -6.3 10 3.2 10 erg s42 44 1. The jet is dominated by the
kinetic luminosity h=L Lj j acc, where hj is the conversion
efficiency from the accretion luminosity Lacc to the jet kinetic
luminosity. The accretion luminosity is L Lacc Edd, where the
Eddington luminosity is
⎛
⎝
⎜
⎞
⎠
⎟ ( )

= ´
´
-L
M
M
5.03 10
4 10
erg s , 1Edd
44 •
6
1
and ηj<0.7 for most radio sources (Ito et al. 2008). This yields
the maximum jet kinetic luminosity for SgrA*
of » ´L 3.5j
-10 erg s44 1
. We will consider » - -L 10 10 erg sj
41 44 1
, where
the lower limit is given by the putative jet present in the current
quiescent state (Yusef-Zadeh et al. 2012), with the inferred kinetic
luminosity of ~ ´ -L 1.2 10 erg smin
41 1, and the upper limit is
given by the Eddington luminosity.
We assume a conical jet with a half-opening angle θ and width
q=R z tanj , where z is the distance to SgrA*
. The jet footpoint
for SgrA*
can be estimated to be located at ~ ´z 20
( )´ =- M M R10 4 10 pc 525
•
6
Schw (Junor et al. 1999), where
( )= = ´ ´-R GM c M M2 3.8 10 4 10 pcSchw •
2 7
•
6 is the
Schwarzschild radius. Any red giant or supergiant with radius7
Rå and mass må is not expected to plunge below z0 as the tidal
disruption radius ( )=  r R M m2t •
1 3 (Hills 1975; Rees 1988)
is at least a factor of 2 larger,
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )
  
=
´

r
R
R
R
M
M
m
M
1 20
10 4 10
. 2t
Schw
•
6
1
3
1
3
=R R10 and må=1 Me are typical intermediate values for
the evolved late-type giants with extended envelopes (Merritt
2013). For numerical estimates, we consider the range of radii
for red giants and supergiants, – ~R R4 1000 , as indicated
by the HR diagram. These late-type stars have a large range of
bolometric luminosities, Lå∼10–72,000Le, and the temperature
range of Tå∼5000–3000 K, which corresponds to the
spectral classes K and M, respectively. The K-band magnitude
range is K∼15.2 mag for Rå=4 Re, Tå=5000 K, and
K∼4.4 mag for Rå=1000 Rå, Tå=3000 K. More specifically,
we focus on late-type stars of K=16 mag and brighter,
which appear to form a core-like density distribution in the
central 0.5 pc. Using the isochrones obtained with the Parsec
code (Bressan et al. 2012), these stars have Rå∼4 Re and
larger for an age of 5 Gyr. The late-type stars that are
completely absent in the S cluster (inner ∼0.04 pc) were
inferred to have Rå=30 Re and larger (Habibi et al. 2019).
Therefore, numerical estimates are typically scaled to
Rå=30 Re unless otherwise indicated.
We will further focus on the region between the tidal radius
of red giants and the outer edge of the S cluster, which
approximately corresponds to the Bondi radius of the hot
bremsstrahlung plasma (Baganoff et al. 2003; Wang et al.
2013),
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )

= =
´
-
R
GM
c
M
M
T
0.12
4 10 10 K
pc, 3B
•
s
2
•
6
p
7
1
which is two to three orders of magnitude larger than the tidal
radius of red giants, ~ ´R R3.1 10B
5
Schw. More generally
speaking, the population of predominantly B-type stars lies
within the innermost arcsecond (∼0.04 pc, S cluster), while the
population of young massive OB/Wolf–Rayet stars stretches
from ∼0.04 pc up to ∼0.5 pc, a fraction of which forms a
warped stellar disk (Genzel et al. 2010).
The stellar-wind ram pressure at a distance r from the center
of the star can be estimated as ( )r p~ =P v m v r4sw w w
2
w w
2 ,
7
The stellar radius is the sum of the core radius and the envelope
radius, = +R R Rc env.
3
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
128 CHAPTER 4. PAPER 3: RED-GIANT DEPLETION IN THE GALACTIC CENTER
where mw is the mass-loss rate and vw is the terminal wind
velocity. Using typical values for red giants with
 » - -m M10 yrw
8 1 and » -v 10 km sw
1 (e.g., Reimers 1987;
de la Cita et al. 2016),8
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟ ( )



=
´
- - -
-
-
P
m
M
v
r
R
0.012
10 yr 10 km s
30
erg cm . 4
sw
w
8 1
w
1
2
3
The ram pressure of a relativistic jet with bulk motion
Lorentz factor Γ is r= GP vj j j
2
, where the jet density is
[( ) ]r s= G -L c v1j j
2
j j and s p= Rj j
2
is the jet cross-sectional
area. By assuming vj∼c and Γ∼10, the jet kinetic pressure
for SgrA*
can be written as
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )
s p q
» =
= -
-
-
P
L
c
L
cz
L z
tan
0.014
10 erg s 0.04 pc
erg cm , 5
j
j
j
j
2 2
j
42 1
2
3
where we have assumed θ;12°.5, which corresponds to the
jet sheath half-opening angle estimated for the current
candidate jet of SgrA*
(Li et al. 2013). Note that the innermost
arcsecond (z∼0.04 pc) is also the outer radius of fast-moving
stars in the S cluster (Genzel et al. 2010; Eckart et al. 2017).
By equating Psw=Pj, we obtain the stagnation distance
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟ ( )

 
=
´
- -
-
-
R
R
z m
M
v L
27
0.04 pc 10 yr
10 km s 10 erg s
, 6
stag w
8 1
1
2
w
1
1
2 j
42 1
1
2
which characterizes by how much the red giant envelope can be
ablated by the jet in one encounter. Note that < R Rstag for
late-type giants and supergiants with Rå∼100–1000 Re (see
Figure 2). The very tenuous wind of red giants cannot balance
the jet ram pressure, and therefore, the jet plasma impacts on
the stellar surface. As a consequence, a fraction of the stellar
envelope is removed as estimated by Equation (6).
Interestingly, giant stars with  R R30 appear to be
missing in the S cluster. Only late-type stars with Rå between 4
and 30 Re (with absolute bolometric magnitudes between
−1.05 and 3.32, respectively, for the effective temperature
of 4000 K) were detected by Habibi et al. (2019; see their
Figure 2). Stars with 4„Rå/Re„30 within 0.02pc have
Rstag/Rå∼1 when ´ ´- L2 10 erg s 1.1 1041
j
1 43
, as
indicated in Figure 2. This is in agreement with the estimated
jet power ~ ´ -L 2.3 10 erg sj
42 1 from X- and γ-ray bubbles
(Miller & Bregman 2016). Therefore, an apparent lack of
late-type giant stars with envelopes  R R30 in the inner
∼0.04 pc of Galactic center could result from the jet-induced
ablation of the stellar envelope during the last active phase of
SgrA*
, a few million years ago.
2.1. Basic Timescales of the Jet–Star Interaction
The red giant will enter the jet and not mix with its sheath
layers on the surface if vorb  vsc, where ( )~v GM zorb •
1 2 is
the Keplerian orbital velocity of the star around SgrA*
and
( )r r~ G v csc j is the sound speed inside the shocked obstacle.
This condition can be written as
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟ ( )

r
r
´
G
´
-


z M
M
5.2 10
0.01 pc 10 4 10
, 7
j
5 •
6
1
which means that stellar atmosphere layers of comparable
density or greater than indicated by Equation (7) will enter the
jet, and the less dense upper layers will mix with the jet surface
layers.
Once inside, the bow shock is formed inside the jet on the
very short timescale of ( )~ ~ t R c R R232 100 sbs . A
shock also propagates through the red-giant atmosphere on the
shock-crossing or dynamical timescale, td∼Rå/vsc, whose
lower limit is imposed by the condition of penetration,
vorb  vsc, which leads to ( )= ~ t R v R z GMd orb •
( )( ) ( ) ´ R
R z M M53063 100 0.01 pc 4 10 s1 2
•
6 1 2 . The
dynamical, shock-crossing time is at least ∼10 times longer
than the bow-shock formation time close to the footpoint of the
jet, but the ratio becomes larger with the distance from SgrA*
as ( ) ( )´ -t t z M229 0.01 pc 4 10d bs
1 2
•
6 1 2.
The star-crossing time through the jet can be estimated as
~t R v2 j orb. Using q=R z tanj and the condition v vsc orb,
we obtain
( )
q
~


t
t
z
R
2 tan
1966, 8
d
which implies that the shock propagates throughout the
detached envelope, which is dragged by the jet and mixed
with its material. Eventually, after several td, the envelope
material will reach the velocity of vj∼c. Note that tå/td∼1
when z∼10−5
pc; hence, the removed envelope material
should be dragged by the jet throughout the whole NSC.
The ablated red giant after the first crossing through the
jet would first expand adiabatically to the original size on the
Figure 2. Stagnation radius Rstag/Re. The two horizontal white solid lines indicate
the radial extent of the S cluster between the S2 pericenter distance and the outer
radius at ∼0.04 pc. The two white dashed lines stand for the atmosphere radius
limits of late-type stars in the S cluster, 4Re and 30Re (Habibi et al. 2019). The
dotted–dashed green lines indicate the jet luminosity limits that would yield the
stellar atmosphere ablation at 30 and 4Re at z=0.02 pc.
8
For red giants, – » - - -m M10 10 yrw
6 9 1 according to Reimers (1987).
4
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
129
thermal expansion timescale ( )m~ = = t R c R m k Texp s H B atm
( )( )
R
R T0.2 100 10 K yratm
4 1 2 because of the pressure of
the warmer, underlying layers as the star adjusts its size to reach a
hydrodynamic equilibrium. This expansion timescale is shorter
than the orbital timescale
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )

p=
=
´
-
P
z
GM
z M
M
2
47
0.01 pc 4 10
yr. 9
orb
3
•
1 2
3 2
•
6
1 2
Kieffer & Bogdanović (2016) infer a similar timescale for the
envelope expansion using the hydrodynamic simulations of red
giant–accretion-clump collisions. According to their Figure 7,
the envelope expands to a larger size than the original stellar
radius in texp∼1.5tdyn after the star emerges from the accretion
clump, where tdyn is a dynamical timescale of the star,
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )
 
~


t
R
R
m
M
0.32
100 1
yr, 10dyn
3 2 1 2
which leads to ~ ´ »t 1.5 0.32 yr 0.5 yrexp .
The timescale of the thermal evolution of a star after the jet–
star interaction is expressed by the Kelvin–Helmholtz (KH) or
thermal timescale,
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )
  
»
=
- -

 
  
t
Gm
R L
m
M
R
R
L
L
210
1 100 1500
yr, 11
KH
2
2 1 1
where we estimated the stellar luminosity using =L
p s R T4 2 4
for Tå=3500–3700 K typical of red giants. For
the whole range of stellar radii Rå∼4–1000 Re and stellar
luminosities Lå∼10–7.2×103
Le, tKH differs considerably
—from ∼106
yr for the smallest giants to ∼0.43 yr for the
largest ones.
Based on the comparison between the time between jet–star
collisions tc=Porb/2 and the KH timescale, one can
distinguish cool colliders when tc  tKH, i.e., the star had
enough time to radiate away the accumulated collisional heat,
and it cools down and shrinks before the next collision. For the
case when tc<tKH, there is not enough time to radiate away
the excess collisional heat, and the star is warmer and larger at
the time of the subsequent collision—these are the so-called
warm colliders. In the nuclear star cluster when the jet was
active, there were both types of colliders with the approximate
division given by tc≈tKH, which leads to
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )
 
 
p
»
=
´
´
- -

 

 
z
Gm M
R L
m
M
M
M
R
R
L
L
0.04
1 4 10
100 1500
pc. 12
c
4 3
•
1 3
2 3 2 3 2 3
4 3
•
6
1 3
2 3 2 3
The length scale zc implies that red giants located inside the
inner S cluster were collisionally heated up and bloated, which
increased their mass removal during repetitive encounters with the
jet. Stars orbiting at larger distances managed to cool down and
shrink in size before the next collision, which has subsequently
diminished their overall mass loss. However, note that
Equation (12) is a function of the stellar parameters må, Rå, and
Lå, hence zc differs depending on the red giant stage and its mass.
For the smallest late-type stars with Rå∼4 Re and Le∼8.9 Le,
zc∼10.5 pc; therefore, they can be classified as warm colliders
throughout the nuclear star cluster. On the other hand, the latetype
supergiants with Rå∼103
Re and Le∼7.2×104
Le have
zc∼0.7 mpc, hence they can be classified as cool colliders
beyond milliparsec distances.
2.2. Jet-induced Envelope Removal
The stellar evolution after a jet–star encounter is generally
complicated given that the envelopes of red giants become
bloated after the first passage through the jet. This is because of
the pressure of lower, hotter layers and their subsequent nearly
adiabatic expansion, which can make the red giant even larger
and brighter (Kieffer & Bogdanović 2016). Note that the
number of encounters ncross=2tjet/Porb, where tjet∼0.5 Myr
is the jet lifetime, is typically ?1. In particular,
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
( )

~ ´
´
-
n
t M
M
z
2 10
0.5 Myr 4 10 0.01 pc
.
13
cross
4 jet •
6
1
2
3
2
The number of encounters is also at least two orders of magnitude
larger than the one expected from the star–accretion-clump
interaction investigated by Kieffer & Bogdanović (2016) and
Amaro-Seoane et al. (2020). After the first passage, the bloated
red giant has an even larger cross section than before the
encounter, which increases the mass removed during subsequent
encounters (Armitage et al. 1996; Kieffer & Bogdanović
2016). The jet–star interaction phase proceeds during the red
giant lifetime, which is trg∼108
yr (MacLeod et al. 2012).
During the red giant phase, there are = ~ ´n t P 2.1orb rg orb
( )-z10 0.01 pc6 3 2 orbits around SgrA*
, out of which ncross
= ~n t t2 1%orb jet rg involve the interaction with the jet,
assuming there was only one period of increased activity of
SgrA*
in the last 100 million years. This ensures that the
repetitive jet–red giant interaction leads to substantial mass loss,
and the upper layer of the envelope is eventually removed.
The mass removal in a single passage due to atmosphere
ablation ΔM1 can be estimated through the balance of the jet
ram force and the gravitational force acting on the envelope,
i.e., p D  P R G M m Rj
2
1
2
, giving (Barkov et al. 2012a)
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟ ( )
 

q
D
» ´
´
-
-
- -


M
M
L R
R
z m
M
4 10
10 erg s 100
0.04 pc 0.22
. 14
1
max
10 j
42 1
4
2 2 1
In Figure 3, we plot ΔM1. Note that ΔM1=må and, therefore,
the orbital dynamics is not significantly affected by a single
passage through the jet. However, given that D µ M
R z1
4 2
, the
mass loss can be about one-thousandth to one-hundredth of the
mass of a star for the largest giants on the asymptotic giant branch
with ~R R103 and distances an order of magnitude smaller
than z;0.04 pc (see the yellowish region in Figure 3). In fact, the
5
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
130 CHAPTER 4. PAPER 3: RED-GIANT DEPLETION IN THE GALACTIC CENTER
value of D = ´ = ´ -M M6 10 g 3 101
28 5 discussed by
Barkov et al. (2012a) for powerful blazars in connection to their
very high-energy γ-ray emission can be reached in the Galactic
center for red giants with radii Rå>200 Re at z<0.01 pc. Such a
large mass-loss with a certain momentum with respect to the star
can already have an effect on the orbital dynamics, taking into
account repetitive encounters of the red giant with the jet. In other
words, the mass removal takes place at the expanse of the kinetic
energy of the star, which has implications for the dynamics of the
NSC; see also Kieffer & Bogdanović (2016) for discussion. In
addition, already for jets with a lower power corresponding to the
active phase of the Galactic center, jet–red giant interactions can
affect the short-term TeV emission in these sources. These effects
are beyond the scope of the current paper and will be investigated
in our future studies.
The mass removal during a single jet encounter given
by Equation (14) can be considered as an upper limit as we
assume that the cross section of the star is given by its radius
during the entire passage of the star through the jet, hence
( )pD »  M P R Gm1
max
j
4
. However, this is only an approximation
as realistically, during a few shock-crossing or dynamical
timescales td, the ram pressure of the jet will shape the red giant
and its detached envelope into a comet-like structure (see Figure 1)
for which the interaction cross section is given by Rstag rather than
by Rå, which gives us a lower limit on the mass removal,
( )pD » D M P R Gm M1
min
j stag
4
1
max
. Using Equation (6),
DM1
min
can be expressed in terms of the basic parameters of the
star and the jet, and it can numerically be expressed by the same
units as in Equations (14) and (6),
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟ ( )
( )




qD
»
= ´
´
-
-
-
- - -


15
M
M
c m v z
Gm L
L m
M
m
M
v z
tan
16
2.1 10
10 erg s
10 yr 10 km s 0.04 pc
,
1
min
w w
2
j
12 j
42 1
1 1
w
8 1
2
w
1
2 2
where we adopted θ∼12°.5 as before. In comparison with
DM1
max
in Equation (14), which is proportional to z−2
, DM1
min
in
Equation (15) increases as z2
. This implies that D DM M1
min
1
max
holds for z„zstag, where at zstag, Rå=Rstag. In other words, only
at z<zstag is the mass removal due to the jet activity from the red
giant atmosphere possible, while at distances larger than zstag, the
jet ablation is limited to the stellar-wind material, as is the case for
the observed comet-shaped sources X3, X7, and X8 (Mužić et al.
2010; Peißker et al. 2019). From Equation (6), the relation for zstag
follows as
⎜ ⎟
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
( )



q
»
´
-
-
-
-
-
-

z
R
R
L
m
M
v
0.15
100 0.22 10 erg s
10 yr 10 km s
pc. 16
stag
1
j
42 1
w
8 1
w
1
1
2
1
2
1
2
The dependence of zstag on the stellar radius and the massloss
rate is shown in Figure 4 (left panel). It is apparent that the
volume around the reactivated SgrA*
, where the jet ablation
can occur for a particular red giant, depends considerably on
mw, which spans over three orders of magnitude depending on
the evolutionary stage,  » -- - -m M10 10 yrw
9 6 1 (Reimers
1987). In particular, for red giants with Rå=10 Re, zstag
shrinks from 0.047 pc to 0.0015 pc as the mass-loss rate
increases from  = - -m M10 yrw
9 1 to 
- -M10 yr6 1.
In Figure 4 (right panel), we show an exemplary case for the
mass removal range from the red giant atmosphere (red giant
with the parameters of Rå=100 Re,  = - -m M10 yrw
8 1, and
= -v 10 km sw
1) due to the single crossing through the jet with
the luminosity of = -L 10 erg sj
42 1
and the opening angle of
25◦
. Toward zstag, the mass removal due to a single encounter
approaches the mean value of ( )D = D = =M M z z1 1
max
stag
( )D =M z z1
min
stag ,
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )




 
D
=
= ´
´
-
- -
-


 
M
M
m v R
Gm
m
M
v
R
R
m
M
4
2.9 10
10 yr 10 km s
100 1
. 17
1 w w
2
11 w
8 1
w
1
2 1
Because of the estimated several thousands of red giant–jet
encounters according to Equation (13), the cumulative mass loss
from the red giant can be derived as D ~ DM n Mcross 1, giving
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
( )
 
 
q
D
»
´
´
-
-
-
-


M
M
L R
R
z
m
M
t M
M
10
10 erg s 100 0.01 pc
0.22 0.5 Myr 4 10
.
18
4 j
42 1
4
2 1
jet •
6
1
2
7
2
In Figure 5, we plot ΔM for Lj=1042
and -10 erg s44 1
, and
Rå=50 and 100 Re. Additionally, we plot ΔM for the longer
jet lifetime of tjet=1 Myr and = -L 10 erg sj
44 1
and
Rå=100 Re, which can be considered as an upper limit of
ΔM for a red giant orbiting SgrA*
. We find that ΔM within
the S cluster is comparable to the mass removal inferred from
Figure 3. Mass removed from the red giant envelope for a single jet–star
interaction, ΔM in Equation (14), for the case with = -L 10 erg sj
42 1,
må=1 Me, and θ=12°.5. The two horizontal lines indicate the radial extent of
the S cluster between the S2 pericenter distance and the outer radius at z∼
0.04 pc. Dashed lines indicate D = -M M 10 10, 10−6
, and 10−2
. The dotted–
dashed green line corresponds to ΔM=3×10−5
Me, which is equivalent to
ΔM=6×1028
g in Equation (6) of Barkov et al. (2012a).
6
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
131
the red giant–clump collision simulations by Kieffer &
Bogdanović (2016). In Figure 5, we plot the upper and lower
limits of ΔM obtained by Kieffer & Bogdanović (2016).
Beyond z=0.03 pc, ΔM for the star–jet interaction is
progressively smaller than 3.5×10−4
Me, which implies that
the jet impact on the stellar evolution is the most profound for
S-cluster red giants. In this region, there also lies the division
between the warm and the cool colliders as discussed in
Section 2.1, with warm colliders present inside zc∼0.04 pc,
which is also marked in Figure 5 with a vertical dotted–dashed
line. Because warm colliders are warmer and bigger, this
further enhances the mass removal inside the S cluster. In
addition, the mass removal due to the jet interaction is of a
comparable order of magnitude to the mass loss expected from
cool winds during the time interval of the active jet D »Mw
– ~ ´ -m t M0.5 5 10w jet
4
when – » - - -m M10 10 yrw
6 9 1
(Reimers 1987), as indicated by the shaded rectangle in
Figure 5. This implies that the jet–star interaction perturbs the
stellar evolution of passing red giants, in particular in the
innermost parts of the NSC.
Note that, on one hand, ΔM is supposed to be a lower limit as
after the first passage through the jet, the giant is expected to
expand to an even larger radius before the next encounter, which
increases the mass removal efficiency (Kieffer & Bogdanović
2016). On the other hand, the resonant relaxation of stellar orbits
as well as a jet precession may change the frequency of the jet–
star interactions (see Sections 4 and 6.1), and therefore, ncross
should be considered as an upper limit of the number of
encounters. Overall, ΔM in Equation (18) can be applied as an
approximation for the total mass removal due to the red giant–jet
interactions. Hence, the truncation of stellar envelopes of late-type
stars by the jet during active phases of SgrA*
appears to be
efficient and complementary to other previously proposed
processes, mainly tidal disruptions of giants and stellar collisions
with other stars and/or the accretion disk.
3. Missing Red Giants in the Near-infrared Domain
Red giants are post-main-sequence evolutionary stages of
stars with initial mass   M m M0.5 10 . These stars
exhausted hydrogen supplies in their cores, and the hydrogen
fusion into helium continues in the shell. As a result, the mass
of the helium core gradually increases, and this is linked
to the increase in the atmosphere radius as well as luminosity.
Stellar evolutionary models of red giants show that their
atmosphere radius and bolometric luminosity depend primarily
on the mass of the helium core mc as (Refsdal & Weigert 1971;
Figure 4. Mass removal during a single encounter of the red giant with the jet. Left panel: the color-coded distance in parsecs from SgrA*
, where Rå=Rstag as a function of
mw and Rå. The dashed white lines mark zstag equal to 0.004 pc, 0.04 pc, and 0.5 pc from the left to the right, respectively. Right panel: an exemplary mass removal range
DM1
min
–DM1
max
(green-shaded region) for Rå=100 Re,  = - -m M10 yrw
8 1, = -v 10 km sw
1
, = -L 10 erg sj
42 1, and θ=12°.5. The dotted–dashed vertical orange line
marks zstag (see Equation (16)), where Rå=Rstag. The red dashed line marks the mean mass removal DM1 (see Equation (17)), ( )D = D = =M M z z1 1
max
stag
( )D =M z z1
min
stag .
Figure 5. Cumulative mass removal ΔM due to the repetitive red giant–jet
encounters as a function of the distance from SgrA*
. We fixed Lj=1042
and
-10 erg s44 1 and Rå=50 and 100 Re. In addition, we plot ΔM for
= -L 10 erg sj
44 1, Rå=100 Re, and a longer duration of the jet activity,
tjet=1 Myr. For comparison, we also show the mass removal limits as inferred
by Kieffer & Bogdanović (2016) for the red giant–clump collisions and the
mass range as expected from the cumulative red giant (RG) mass loss due to
stellar winds analyzed by Reimers (1987). The red dotted–dashed line marks
the division between warm and cool colliders according to Equation (12).
7
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
132 CHAPTER 4. PAPER 3: RED-GIANT DEPLETION IN THE GALACTIC CENTER
Joss et al. 1987)
( )


m
m m
m
m m
»
+ +
»
´
+ +


L
L
R
R
10
1 10 10
,
3.7 10
1 1.75
, 19
5.3
c
6
0.4
c
4 0.5
c
5
3
c
4
c
3
c
4
where μc≡mc/Me. This also holds for red supergiants with
carbon–oxygen cores and burning hydrogen and helium in their
shells (Paczyński 1970). In the red giant stage, the dominant
energy source is the p–p process, and hence, the luminosity is
mainly determined by the growth rate of the helium core mc,
⎛
⎝
⎜
⎞
⎠
⎟ ( )

 
- -
L
L
m
M
1.02
10 yr
. 20c
11 1
Equations (19) and (20) imply that the bolometric luminosity
is not significantly affected by the jet–red giant interaction, as
only the tenuous shell is ablated by the jet, and the dense core is
left untouched. Then, the effective temperature T1 of the
ablated giant is
⎛
⎝
⎜
⎞
⎠
⎟ ( )=
T
T
R
R
, 211
0
0
1
1
2
where T0 is the original effective temperature, and R0 and R1
are the atmosphere radii before and after the truncation,
respectively. Here we implicitly assume that the red giant
underwent ncoll interactions with the jet during the active phase
given by Equation (13), which eventually leads to the
decreased radius of R1≈Rstag according to Equation (6). The
luminosity in the infrared domain between frequencies ν1 and
ν2 can be expressed using the Rayleigh–Jeans approximation9
as ( ) ( )p n n- µ   L c R k T R T8 3IR
2 2
B 2
3
1
3 2
(see Alexander
2005 for a similar analysis), which using Equation (21)
leads to
⎛
⎝
⎜
⎞
⎠
⎟ ( )~
L
L
R
R
. 221
0
1
0
3
2
For instance, the ablation of a red giant atmosphere from 120
to 30Re would result in the increase of effective temperature
by a factor of 2 and a decrease by a factor of 8 in the IR
luminosity or ∼2.26 mag. The ablation of the envelope
from 120 to 4Re would result in the decrease by as much as
∼5.5 mag. The difference of 2–5 mag can already affect the
count rate of late-type stars in the near-infrared domain in the
central arcsecond of the Galactic center.
As an exemplary case, we set up a simplified temporal
evolution of a red giant using Equations (19) and (20). We
perform this calculation to estimate the potential difference in
near-infrared magnitudes, and the color change for late-type
stars before and after the active jet phase—it does not represent
realistic stellar evolution tracks, but can provide insight into the
basic trends in the near-infrared magnitude evolution and the
effective temperature. We evolve the stellar luminosity and the
radius for an increasing core mass m m m= + dtc c 0 c , where
m = 0.104c 0 and the time step is =dt 10 yr4
. The overall
evolution from mc 0 to μc=0.55 takes ∼8.41×109
yr, when
neither the effect of stellar winds nor that of rotation is taken
into account. The initial and the final core masses were chosen
according to the limiting values for lighter stars, må<2 Me, in
which case m ~ 0.1c
min
and m ~ 0.5c
max
. These are stars with
degenerate helium cores and hydrogen-burning shells (Refsdal
& Weigert 1971). The lower core-mass value of 0.1 also
approximately corresponds to the Schönberg–Chandrasekhar
limit. The total duration is comparable to the time that stars of
1 Me spend on the giant and asymptotic giant branches, which
is of the order of 109
yr according to MacLeod et al. (2012).
To assess the observational effects of the star–jet collision in the
near-infrared domain, we calculate the effective temperature at
each step using ( ) ( )  = 
 T T L L R R1 4 1 2. Subsequently,
we calculate the monochromatic flux density in K band (2.2 μm)
and L′ band (3.8 μm) using ( ) ( )p=n n F R d B TGC
2 , where
Bν(Tå) is the spectral brightness given by the Planck function at
the given effective temperature. The corresponding magnitudes
are calculated using ( )= -m F2.5 log 653 JyK K and =¢mL
( )- F2.5 log 253 JyK , from which the color index follows
as = - ¢CI m mK L .
For the analysis in this section as well as in Section 5, we
calculate intrinsic stellar magnitudes mK and ¢mL . The
calculated magnitudes and colors can then be compared to
extinction-corrected magnitudes and the derived surfacebrightness
profiles of the nuclear star cluster, i.e., those
corrected for the foreground extinction. To compare our results
to observed magnitudes and derived surface profiles that are
just corrected for the differential extinction but not for the
foreground extinction (Buchholz et al. 2009; Habibi et al. 2019;
Schödel et al. 2020), it is necessary to increase the magnitudes
using the corresponding mean extinction coefficients (see, e.g.,
Schödel et al. 2010), in particular AK=2.54±0.12 mag and
= ¢A 1.27 0.18L mag.
The imprint of the ablation of the stellar atmosphere by a jet,
whose kinetic luminosity is fixed to = ´ -L 2.3 10 erg sj
42 1
, is
modeled by assuming that the radius of an interacting red giant
keeps evolving according to Equation (19) when <R Rstag at
a given distance z from SgrA*
. After the stellar radius reaches
the scale of the stagnation radius at a given distance z, we set
Rå=Rstag for the rest of the evolution, which can by justified
by the fact that the red giant propagates through the jet ncoll
times and the envelope is removed after repetitive encounters.
The expected number of encounters is 6×105
, 2×104
, and
632 for z=0.001 pc, 0.01 pc, and 0.1 pc, respectively; see
Equation (13). In Figure 6, we show three magnitude–effective
temperature curves of the ablated red giants that underwent
repetitive encounters with the jet at their orbital distances of
0.001, 0.01, and 0.1 pc from SgrA*
, which led to their
truncation to a smaller radius close to the corresponding
stagnation radius at a given distance. In addition, we compare
the magnitude–temperature curves of ablated giants with an
unaffected evolution. We list the stellar parameters at the time
of the atmosphere truncation when Rå=Rstag at the corresponding
distance as well as the parameters for the final state of
ablated giants in Table 1. This is compared to an unaffected
final state with the core mass of 0.55 Me; see the bottom row of
Table 1. The basic signature of the jet–star interaction is that
the star gets progressively warmer (with a bluer, more negative
color index) and fainter in the near-infrared Ks band in
comparison with the normal evolution without any atmosphere
ablation. This trend is more apparent for red giants that are
9
Strictly speaking, for Tå=5000 K, the condition kBTå>hν applies for
wavelengths longer than 2.9 μm.
8
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
133
closer to SgrA*
because of the smaller jet–star stagnation
radius and hence a larger fraction of the stellar atmosphere that
is removed.
Although we do not calculate stellar evolutionary tracks,
only basic trends in terms of near-infrared magnitude and
effective temperature, our results are consistent with those of
Amaro-Seoane et al. (2020) who calculated evolutionary tracks
specifically for late-type stars ablated due to the red giant–
accretion-clump collisions. They show in their Figure 2 that the
collision affects the stellar evolution of a red giant in a way that
after repetitive encounters it follows a track along a nearly
constant absolute bolometric magnitude toward higher effective
temperatures. The constant absolute bolometric magnitude or
bolometric luminosity in combination with an increasing
effective temperature results in the drop in the near-infrared
luminosity, because µ L
L TIR bol
3
. We used their evolutionary
tracks calculated using the CESAM code (Morel &
Lebreton 2008) for estimating Ks-band near-infrared magnitudes.
These tracks are depicted in Figure 6 for the case of a
normal evolution of a star with Må=1.4 Me and Rå=60 Re
(black solid line) and different collision cases for clumps with
surface densities in the range –S = ´ -2 10 10 g cm4 6 2
(see
the legend). Qualitatively, the perturbed stellar evolutionary
tracks follow the temperature trends that we can also observe
for giant–jet collisions: ablated giants move toward higher
effective temperature. Also, they become fainter in the nearinfrared
domain in comparison with an unperturbed evolution.
The main difference in comparison with the analysis of AmaroSeoane
et al. (2020) is their trend toward larger magnitudes
(stars become fainter), while we see a small gradual increase in
brightness. This difference is due to our simplifying assumption
of a constant radius after the series of collisions with the
jet, while in reality the radius should evolve, especially after the
jet ceases to be active. Because µ  L R TIR
2
, the near-infrared
luminosity grows linearly with increasing temperature for the
fixed stellar radius. This motivates further exploration of the
effect of star–jet collisions using a modified stellar evolutionary
code.
For asymptotic giant branch stars, an extreme transition from a
red, cool luminous giant to a hot and faint white dwarf is possible
when it is completely stripped of its envelope. This was studied by
King (2020) for tidal stripping close to the SMBH but cannot be
excluded also for asymptotic giant branch stars and jet collisions
for a case when the giant star is at milliparsec separation from
SgrA*
and less, in which case the stagnation radius is typically a
fraction of the solar radius. In fact, an active jet can enlarge the
volume around the SMBH where asymptotic giant branch stars
are turned into white dwarfs. Considering Equation (6), we can
derive that in order for Rstag to be of the order of a white-dwarf
radius ~R R0.01wd , the giant needs to orbit the SMBH at
z≈0.15 mpc so that the jet with = -L 10 erg sj
44 1 can truncate it
down to the white-dwarf size. The stellar interior that is not
affected by tidal forces is characterized by the Hill radius
⎜ ⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )
 

» =
´
´
-


r z
m
M
z
m
M
M
M
R
3
29
0.15 mpc
1 4 10
, 23
Hill
•
•
6
1
3
1
3
1
3
from which we see that tidal forces alone will not truncate the
giant down to its white-dwarf core because rHill>Rstag at z.
In summary, the jet–star interaction could have affected the
appearance of late-type giants in the central arcsecond by
making them warmer or bluer in terms of color and hence
fainter in the near-infrared domain.
Figure 6. Near-infrared magnitude (K band, 2.2 μm, dereddened) and
temperature (or color index that is color-coded) of a red giant after crossing
the jet ncoll times. We compare three temperature–Ks-band magnitude curves
affected by a series of collisions with the jet at z=0.001, 0.01, and 0.1pc
(marked by black arrows) with a normal, unaffected evolution (marked by a
gray arrow). The evolution is driven by an increase in the helium core mass
from μc=0.104 to 0.55 Me with a time step of 104
yr. At each time step, we
calculate Rå and Lå using Equations (19). The overall evolution takes
∼8×109
yr. For comparison, we also show the evolutionary tracks for the
normal evolution (black solid line) and the evolution affected by the star–clump
collisions (lines according to the legend for different clump surface densities
listed in parentheses) as calculated by Amaro-Seoane et al. (2020, abbreviated
as AS+20) using the CESAM code (Morel & Lebreton 2008).
Table 1
Parameters at the Time of the Jet Ablation and Those of the Final State of a Red Giant, which is Evolved from the Core Mass of μc=0.104 to 0.55
Ablation Distance (pc) Ablation Time (yr) Rabl
(Re) Tabl
(K) Tfin
(K) mK
abl
(mag) mK
fin
(mag) CIfin
0.001 3.0×108
0.45 6205 68 759 19.6 16.4 −0.14
0.01 8.0×109
4.45 4662 21 744 15.2 12.8 −0.09
0.1 8.4×109
44.51 3526 6 876 10.7 9.4 −0.09
Normal Evolution L 255.21 (final radius) L 2 871 L 7.47 0.51
Note. The upper three lines contain parameters of the ablated red giants orbiting at distances 0.001, 0.01, and 0.1 pc (first column). The second column lists the time, at
which the ablation occurred with respect to the initial state of μc=0.104. The third column lists the truncation radius, when Rå=Rstag. The fourth column lists the
effective temperature at the time of truncation. The fifth column lists the final effective temperature at the final stage of their evolution (when μc=0.55). The sixth and
seventh columns contain dereddened magnitudes at the ablation and final times, respectively. The last column contains dereddened color indices, CI=mK − mL, at
the final state. The bottom line corresponds to the final state of a normal, unaffected evolution.
9
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
134 CHAPTER 4. PAPER 3: RED-GIANT DEPLETION IN THE GALACTIC CENTER
4. Fraction of Red Giants Interacting with the Jet
We estimate the number of late-type stars, i.e., stars that
form a cusp, that could have passed and interacted with the jet
during its estimated lifetime of ∼0.1–0.5 Myr (Guo &
Mathews 2012). For the density distribution of late-type stars
in the inner 0.5 pc, we adopt a cusp-like power-law distribution
( )» g-n n z zRG 0 0 , with  -n 52 pc0
3
, z 4.9 pc0 , and
γ;1.43 (Gallego-Cano et al. 2018). The expected number
of late-type stars within a certain distance zout is
( ) ( ) ( )ò p p
g
< = ¢ ¢ =
g
gN
z n z z dz n
z z
4 4
3
24
z
out
0
RG
2
0
0 out
3out
giving Nå≈610 and 25.8 inside 0.3 and 0.04pc, respectively.
The number of stars inside the jet at any time is given by the jet
covering factor fj in a spherical volume ( )p=V z4 3 out
3
. By
considering a conical jet and a counter-jet with the total volume
p=V R z2 3j j
2
out, the covering factor is ( )= ~f V V R zj j j out
2
and the number of red giants inside the jet is ( )< =N zj out
( ) ( ) ( )q< ~ < f N z N z tan 2j out out
2 . Then, the average number
of red giants that are simultaneously inside the jet is Nj≈14.8
and 0.62 inside 0.3pc and 0.04pc, respectively.
To estimate the number of stars crossing the jet per orbital
timescale, we first calculate the jet-crossing rate per unit of
time. Because we focus on the region z  0.5 pc, which is well
inside the radius of influence of SgrA*
, rh∼2 pc (Merritt
2013), we approximate the stellar velocity dispersion by the
local Keplerian velocity, s ~ = v GM z ;orb • see, e.g., Šubr
& Haas (2014). With the jet cross section q» ~S zR z tanjet j
2
,
the number of late-type stars entering both the jet and counterjet
per unit of time is
( ) s q» g gN
n S n z GM z2 2 tan . 25RG RG jet 0 0 •
3
2
The number of red giants crossing the jet per orbital timescale
is
( ) p q= = g g-N N P n z z4 tan , 26RG RG orb 0 0
3
where the orbital period in the sphere of influence of the SMBH
follows from the third Keplerian law, p=P z GM2orb
3 2
• . In
Figure 7, we plot NRG. The average number of crossing giants
per orbital period in the region with an outer radius zout is
( )
p
g
q=
g
gN
n z z
4
4
tan . 27RG 0 0 out
3
In particular, N 3.5RG and N 82RG when =zout
0.04 pc (S cluster) and =z 0.3 pcout , respectively (see
Figure 7).
In this case, NRG represents all late-type stars that cross the
jet sheath per orbital period on average. The fraction of giants
whose envelopes could have been stripped off by the jet can be
estimated by comparing the radii of stars with the corresponding
stagnation radius at a certain distance from SgrA*
. The
basic condition for the ablation is that Rå  Rstag at a given z
from SgrA*
. In particular, for z=0.04 pc and the jet
luminosity of = -L 10 erg sj
42 1
, the minimum stellar parameters
for ablation are Rå=27 Re, μc=0.3, Lå=129 Le,
Tå=3743 K, and mabl=11.7 mag, where mabl denotes the
upper magnitude limit, below which stars are expected to be
affected by the jet. Using the K-band luminosity function
approximated by the power law, b=d N dmlog K with
β;0.3 for late-type stars (Buchholz et al. 2009; Pfuhl et al.
2011) between 12 and 18 mag, we can estimate the fraction of
ablated stars as ( )h = ´ = b - +N N 100 10 %m m
abl tot
2abl max ,
where mmax is the limiting magnitude, which we set to 18
mag according to Pfuhl et al. (2011). Then, for z=0.04 pc and
= -L 10 erg sj
42 1
, we get η=1.27%. For the larger distance
z=0.5 pc and = -L 10 erg sj
42 1, we obtain the minimum
parameters of ablated stars as follows, Rå=338 Re, μc=
0.6, Lå=6081 Le, Tå=2775 K, mabl=6.95 mag with η=
0.05%. The limiting values and the percentage of ablated giants
are quite sensitive to the jet luminosity. Increasing Lj to
-10 erg s44 1
, we get Rå=2.7 Re, μc=0.16, Lå=3.97 Le,
Tå=4960 K, mabl=16.1 mag with η=26.5% for z=0.04
pc and Rå=33.8 Re, μc=0.31, Lå=181 Le, Tå=3645 K,
mabl=11.3 mag with η=0.95% for z=0.5 pc. We
summarize the relevant values in Table 2. Although the
fraction of affected late-type stars is small, it significantly
affects brighter stars with smaller magnitudes—stars brighter
than 14 mag constitute ∼6.3% of the total observed sample and
stars brighter than 12 mag constitute only 1.6%. We explicitly
show the change in the projected brightness distribution for
brighter stars in Section 5.
The jet ablation could partially have contributed to the
inferred four to five missing late-type giants in the region with
zout=0.04 pc (Habibi et al. 2019) as well as to the ∼100
missing late-type giants in the larger region with zout=0.3 pc
(Gallego-Cano et al. 2018), especially for higher luminosities
of the jet.
The number of stars that can interact with the jet is increased
via dynamical processes in the dense nuclear star cluster. In
particular, the vector resonant relaxation (VRR) changes the
direction of the orbital angular momentum (Alexander 2005;
Merritt 2013), and therefore, stars that were not passing
through the jet can do so on the resonant relaxation timescale.
More precisely, in the sphere of influence of the SMBH, stars
move on Keplerian ellipses, and the gravitational interactions
between stars are correlated. Given the finite number of stars,
there is a nonzero torque on a test star. During the time interval
Figure 7. Number of red giants crossing the jet per orbital period (black solid
line; see Equation (26)). The average number of red giant/jet interactions at
z„0.04 pc and 0.3pc are plotted in green dotted–dashed and blue-dashed
lines, respectively.
10
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
135
Dt, for which  DP t Torb coh and the coherence timescale
( )
p
g
p
= =
-
g
g
  
T
P
N
M
m Gn z
M
m
z
2
3
4
28coh
orb •
0 0
•
1
2
2
is inversely proportional to the square root of the number of
enclosed stars, the angular momentum of a test star changes
linearly with time.
The inclination of stellar orbits would change by ∼π only when
( ) –~T z t 0.1 0.5 Myrcoh j and hence essentially all late-type
stars could interact with the jet during its lifetime. The estimated
number of enclosed stars in the S cluster (zout∼0.04 pc) is
26<Nå<10,000, where the lower limit considers only late-type
stars according to the analysis by Habibi et al. (2019) and the upper
limit stands for all the stars including compact remnants. The upper
limit is supposed to be closer to the actual number of stellar objects
because the number of old neutron stars and stellar black holes in
the central arcsecond could be of that order of magnitude (Morris
1993; Deegan & Nayakshin 2007; Zhu et al. 2018). The total
number of massive objects naturally affects the coherence
timescale by more than an order of magnitude. In Figure 8, we plot
Tcoh. We see that when Nå∼1000 and more, Tcoh is comparable
to the lifetime of the jet in the inner parts of the S cluster. In
summary, the coherent resonant relaxation makes the number of
affected giants bigger and the estimates per orbital timescale NRG
can be considered as a lower limit. Another more hypothetical
effect that can enlarge the number of affected giants is the jet
precession (see Section 6.1).
The VRR can affect the number of encounters, ncross; see
Equation (13). In case Tcoh>tjet, i.e., for a smaller number of
enclosed objects (Nå  100), ncross is still mainly determined by
tjet; see Equation (13). However, then the mean number of
interacting giants NRG is also not significantly enlarged. On the
other hand, if Tcoh  tjet, then ncross is reduced approximately
by a factor of 2θ/π, which assumes that the angular momentum
vector shifts linearly with time during Tcoh. In that sense, the
interaction timescale with the jet is ( )q p~t T 2int coh . Considering
Tcoh∼tjet, the number of crossings is
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟ ( )

~
´
-
n
T M
M
z
2800
0.5 Myr 4 10 0.01 pc
, 29cross
RR coh •
6
1
2
3
2
which is smaller by an order of magnitude in comparison with
ncross.
5. Effect of Jet Ablation on the Surface-brightness Profile of
a Nuclear Star Cluster
To assess the observational signatures of the jet ablation of
late-type stars, we generate a mock spherical cluster of stars.
Their initial spatial distribution follows ( )= g-n n z zRG 0 0 with
= -n 52 pc0
3
, z0=4.9 pc, and γ∼1.43 (Gallego-Cano et al.
2018). This spatial profile suggests that there are in total ∼4000
late-type stars inside the inner 1 pc, which we generate using
the Monte Carlo approach to form a mock NSC; see Figure 9
(left panel) for illustration.
Each star is assigned its mass in the range from 0.08 Me to
100 Me following the initial mass function (IMF) according to
Kroupa (2001), i.e.,
⎧
⎨
⎪
⎩
⎪
( )
( )

 

z
a
a
a
=
= <
= < <
= >
a




m m
m M
M m M
m M
, where
0.03, 0.08 ,
1.3, 0.08 0.5 ,
2.3, 0.5 .
30
The Chabrier/Kroupa IMF is a good approximation for the
observed mass distribution of the late-type NSC population
(Pfuhl et al. 2011).
In the next step, we assigned the core mass to each star of the
mock cluster. Here, we fix the ratio between the core mass and
the stellar mass to μc/må=0.4, which is in between the value
inferred from the Schönberg–Chandrasekhar limit10
and the
final phases of the stellar evolution, where the white-dwarf core
constitutes most of the mass for solar-type stars. For more
precise simulations, core masses from the stellar evolution of
the NSC should be adopted; however, here we are interested in
the first-order effects of the jet activity on the surfacebrightness
distributions.
To construct the surface-brightness profiles of the late-type
population after the active jet phase in different magnitude bins,
we followed these steps:
Table 2
Limiting Minimal Stellar Radii, Maximum Apparent K-band Magnitudes (dereddened), and the Fraction of Ablated Giants for Two Distances from SgrA*
(0.04 and
0.5 pc) and Two Luminosities of Its Jet ( -10 erg s42 1 and -10 erg s44 1)
Distance = -L 10 erg sj
42 1 = -L 10 erg sj
44 1
0.04 pc Rå=27 Re, mabl=11.7, η=1.27% Rå=2.7 Re, mabl=16.1, η=26.5%
0.5 pc Rå=338 Re, mabl=6.95, η=0.05% Rå=33.8 Re, mabl=11.3, η=0.95%
Figure 8. The coherence timescale Tcoh for different numbers of stars in the S
cluster according to the legend. The shaded area stands for the expected
lifetime of the jet during the previous Seyfert-like activity of SgrA*
.
10
The Schönberg–Chandrasekhar limit expresses the ratio between the isothermal
core mass and the stellar mass, ( ) m m ~m m 0.37 0.1ic env ic
2 , where μenv
and μic are the mean molecular weights for the envelope and the isothermal core,
respectively.
11
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
136 CHAPTER 4. PAPER 3: RED-GIANT DEPLETION IN THE GALACTIC CENTER
1. We calculated Lå(μc) and ( )mR c using Equation (19).
2. If the jet was set active with a certain luminosity Lj, we
compared Rå and Rstag for a given distance z of the star. If
Rå…Rstag, then we set Rå=Rstag. In this case, we also
implicitly assumed that at a given distance, all of the
stars, for which Rå…Rstag, are eventually ablated by the
jet; hence, the resonant relaxation was assumed to be
efficient and hence Tcoh<tjet.
3. We estimated the effective temperature of a star
using ( ) ( )  = 
 T T L L R R1 4 1 2.
4. From the Planck function ( )n B T , we calculated the
monochromatic flux in the Ks band (2.2 μm)
( ) ( ) ( )p=n n   F R T R d B T, GC
2 and the corresponding
apparent magnitude mK (dereddened).
The initial relation between the Ks-band magnitude and the
stellar radius is shown in Figure 9 in the right panel. We calculate
the projected stellar density using concentric annuli with mean
radius R and width of ΔR, ( )s p= D N R R2 , where Nå is the
number of stars in an annulus. We estimate the uncertainty of the
stellar number counts as s » NN . Subsequently, we construct
the surface stellar profiles in two-magnitude bins starting at
mK=18 mag up to mK=10 mag, i.e., in total, four bins; see
Figure 10. In the top-left panel of Figure 10, we plot the nominal
projected distribution without considering the effect of the jet. The
brightness profile for all four magnitude bins can be approximated
by simple power-law functions, ( ) ( )= -GN R N R R0 0 , whose
slopes are listed in Table 3. Hence, the initial cluster distribution is
cusp like. In the top-right panel, we show the case with an active
jet with the luminosity of = -L 10 erg sj
42 1
. We see that the
profile for the brightest stars in the 10–12 mag bin becomes flat in
the inner arcsecond and can be described as a broken power-law
function, ( ) ( ) [ ( ) ]( )= +-G D G-G DN R N R R R R10 br br
0 , where
Rbr is a break radius, Γ is a slope of the inner part, Γ0 marks the
slope of an outer part, and Δ denotes the sharpness of the
transition. The larger surface-brightness values for this magnitude
bin may be interpreted as an extra input of ablated giants with
initial magnitudes mK<10 mag that after the ablation fall into
bins with a larger magnitude. Finally, we increase the jet
luminosity to = -L 10 erg sj
44 1
, which makes the flattening of
the brightest giants even more profound. The stars in the 12–14
mag bin also exhibit a flatter profile inside the inner arcsecond for
this case, which shows the significance of the jet luminosity in
affecting the observed surface profile of the NSC. We list the
power-law slopes for both a simple and a broken power-law
function and the break radii, where available, for all the magnitude
bins and the three jet-activity cases in Table 3.
Figure 10 demonstrates a potential signature of the jet
activity on the surface profile of the NSC. It is important to
study differential profiles, i.e., the distribution in different
magnitude bins, because the lower-luminosity jet starts
affecting the profile of bright stars (smaller magnitudes), while
with an increasing jet luminosity, the fainter stars become
affected as well, starting at smaller projected radii (<1″). Our
Monte Carlo simulation suggests that the active jet phase with
-L 10 erg sj
44 1
likely affected late-type stars with mK„14
mag that exhibit the flat profile inside the inner arcsecond. The
fainter stars of mK>14 mag can still keep a cusp-like profile
after the jet ceased its enhanced activity.
For better quantitative comparisons with observations, it is
necessary to include the stars of different ages and hence
different core masses. This is rather complex as there were
recurrent star formation episodes in the NSC, with 80% of the
stellar mass being formed 5 Gyr ago, the minimum in the star
formation rate close to 1 Gyr, and the renewed star formation in
the last 100–200 million years, although with the 10× lower
star formation rate than at earlier episodes (Pfuhl et al. 2011).
These findings were confirmed by Schödel et al. (2020), who
estimate that 80% of stars formed 10 Gyr ago or earlier, then
about 15% formed 3 Gyr ago, and the remaining fraction in the
last 100 Myr. Furthermore, the dynamical effects such as the
mass segregation and the relaxation processes could also have
played a role in shaping the final observed profile of the NSC,
and in addition, we might expect other bright-giant depletion
Figure 9. Initial properties of the Monte-Carlo-generated mock NSC. Left panel: the projected surface density distribution of 4000 stars with the illustrated active jet
with the half-opening angle of θ=12°.5. The gray streamers illustrate the mini-spiral arms according to the Keplerian model of Zhao et al. (2009). Right panel: the
K-band magnitude (dereddened)–stellar radius relation for our generated NSC.
12
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
137
processes (Alexander 2005). Despite these difficulties in
comparing theoretical and observed profiles, the basic trend
shown in Figure 10, in particular for = -L 10 erg sj
44 1
(bottom
panel), is consistent with the observational findings of Schödel
et al. (2020), who found cusp-like profiles for all magnitude
bins apart from the mK=14.5–14 mag bin (including
foreground field extinction), which shows a flat/decreasing
profile in their analysis. In our panels in Figure 10, this
corresponds to the dereddened 10–12 and 12–14 mag bins,
whose profiles become affected for = -L 10 erg sj
42 1
starting
from the projected radii below 1″. However, Schödel et al.
(2020) also note that precise surface profiles for late-type stars
are difficult to construct due to the contamination at all
magnitude bins by an unrelaxed population of young stars.
Figure 10. Potential effect of the jet activity on the surface distribution of the initially cuspy late-type NSC. The calculations assume that the coherent resonant
relaxation timescale is comparable to or shorter than the jet lifetime (∼0.5 Myr) within the S-cluster region. In all panels, the magnitude bins are dereddened. Top-left
panel: the projected profile of an initial cusp of late-type stars with the surface slope of Γ∼0.6–0.9 across all magnitude bins (2 mag bins). Top-right panel: a
modified projected profile for the jet luminosity of -10 erg s42 1. The 10–12 mag surface profile flattens inside the inner arcsecond, while the fainter stars (12–18 mag)
keep a cusp-like profile. Bottom panel: a modified surface profile for the jet luminosity of = -L 10 erg sj
44 1. The profile of the brightest stars (10–12 mag) flattens
even more and decreases inside the inner arcsecond. The stars with 12–14 mag exhibit a flat profile as well in the inner arcsecond. The stars in the 14–16 mag and
16–18 mag bins keep the cuspy profile. For all three panels, the solid lines represent the single and the broken power-law function fits to the surface stellar distribution
in four magnitude bins. The slopes and the break radii are listed in Table 3.
Table 3
Summary of the Power-law Slopes (for Both Single and Broken if Relevant) for the Four Magnitude Bins (2 mag Intervals Starting at 18 mag up 10 mag in the Nearinfrared
Ks Band; Magnitudes are Dereddened) and Three Jet-activity Cases (No Jet, = -L 10 erg sj
42 1, = -L 10 erg sj
44 1)
Magnitude Bin No Jet Jet = -L 10 erg sj
42 1 Jet = -L 10 erg sj
44 1
18–16 mag single: Γ=0.9 single: Γ=0.8 single: Γ=1.0
16–14 mag single: Γ=0.6 single: Γ=0.6 single: Γ=0.7
14–12 mag single: Γ=0.6 single: Γ=0.6 broken: Γ=0.2, Γ0=0.9, Rbr=1″
12–10 mag single: Γ=0.7 broken: Γ=−0.08, Γ0=1.4, Rbr=0 3 broken: Γ=0.04, Γ0=2.2, Rbr=6 6
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The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
138 CHAPTER 4. PAPER 3: RED-GIANT DEPLETION IN THE GALACTIC CENTER
Habibi et al. (2019) report a cusp-like profile for late-type stars
of mK<17 mag (including foreground extinction), which
approximately corresponds to our bin of 14–16 mag (yellow
points) that maintains a cusp-like profile even for the largest jet
luminosity (bottom panel). In conclusion, the expected trend of
preferential depletion of bright late-type stars by the jet is
confirmed.
6. Discussion
We investigated the effects of a jet during an active phase of
SgrA*
in the last million years on the appearance of late-type
giant stars with atmosphere radii more than 30Re. We found
that especially in the innermost arcsecond of the Galactic center
(the S cluster), the upper layers of the stellar envelope could be
removed by the jet ram pressure. Hence, the jet–red giant
interactions during the active phase of SgrA*
could have
contributed to the depletion of bright late-type stars. In other
words, the atmosphere ablation by the jet would alter the red
giant appearance in a way that would make them look bluer and
fainter in the near-infrared bands (mainly K′ and L bands), in
which stars in the Galactic center region are generally
monitored. In the following, we outline several additional
effects that could be associated with the jet/red giant
interaction.
6.1. Enlarging the Number of Affected Stars by the Jet
Precession
Jet precession is a phenomenon that accompanies the launching
of jets during the evolution of galaxies and stellar binaries. It is
caused by perturbations due to the misalignment of the accretion
flow and the black hole spin, the so-called Lense–Thirring
precession, or by a secondary black hole. The jet precession was
proposed to explain a long-term flux variability in radio galaxies,
e.g., OJ 287 (Britzen et al. 2018), 3C 84 (Britzen et al. 2019b), 3C
279 (Abraham & Carrara 1998), the neutrino emission from TXS
0506+056 (Britzen et al. 2019a), as well as in X-ray binaries
(Monceau-Baroux et al. 2015; Miller-Jones et al. 2019).
For the Galactic center, the Lense–Thirring precession of the
hot thick accretion flow was analyzed by Dexter & Fragile
(2013) in relation to the near-infrared and millimeter variability
of SgrA*
. This effect would also translate to the precession of
the jet under the assumption that it is coupled to the disk via the
launching mechanism (Blandford–Payne mechanism; see
Blandford & Payne 1982). The jet precession is also suggested
by wide UV ionization cones with the opening angle of 60◦
(Bland-Hawthorn et al. 2019), which is larger by a factor of a
few expected for the jet opening angle of ∼25° (Li et al. 2013).
We estimate the factor by which the volume of the affected red
giants is enlarged. We adopt the jet precession half-opening angle
of Ωp≈30° based on the scale of UV ionization cones (BlandHawthorn
et al. 2019). During the precession motion, the jet
circumscribes a cone with the radius = WR z sinp p. The factor by
which the volume at given distance z enlarges is given by
( )
p
p
q
= =
W
~f
R
R
2
2
sin
tan
7.1, 31prec
p
j
p
when θ=12°.5 and Ωp=30°. The number of affected latetype
stars would then increase by the same factor to Nj≈105
and 4.4 within 0.3 and 0.04 pc, respectively, which is
comparable to the number of missing bright red giants at these
scales—100 at z<0.3 pc (Gallego-Cano et al. 2018) and 4 at
z<0.04 pc (Habibi et al. 2019). The factor derived in
Equation (31) should be treated as an upper limit on the volume
enlargement as it assumes that the precession period is
comparable to or less than the jet lifetime, but it could also
be longer. On the other hand, a larger volume means that the
stars are affected correspondingly less (over a shorter period of
time) by the jet action, which is spread in different directions
with the precession duty cycle.
6.2. High-energy Particle Acceleration and Jet Mass Loading
due to Jet/Star Interactions
The detection of the Fermi bubbles in the GeV domain
indicates the presence of relativistic particles emitting gamma
rays. Guo & Mathews (2012) considered that particles can be
accelerated in the jet-launching region or in the jet termination
shocks. Note, however, that the coexistence of the jet with the
dense NSC in the Galactic center makes jet/star interactions
very likely. The NSC is composed of both early- and late-type
stars. In the former case, the powerful wind of OB and Wolf–
Rayet stars makes the stagnation distance  R Rstag , and
therefore, a double bow-shock structure is formed (Araudo
et al. 2013). In the latter case, the slow winds of low-mass stars
cannot create a big bow shock around the stars, but a shock in
the jet will be formed anyway. In both cases, particles can be
accelerated through the Fermi I acceleration mechanism in the
bow shocks (Bell 1978). Even when the interaction with
massive stars is a better scenario to accelerate particles up to
highest energies (given that the size of the acceleration region
is ∼Rstag), acceleration of particles up to GeV energies is not
difficult to achieve.
Barkov et al. (2010, 2012b) consider the interaction of AGN
jets with red giant stars to explain the TeV emission in radio
galaxies and blazars. The mass stripped from the red giant
forms clouds moving in the jet direction; see also our Figure 1.
Particles are accelerated in the bow shock around the cloud
formed by the pressure exerted by the jet from below. Another
shock propagates into the cloud, and as a consequence, it will
heat up and expand. After a certain time, there will be a
population of relativistic particles in the jet as well as chemical
enrichment by stellar envelopes (Perucho et al. 2017). These
effects were previously not taken into account in the jet models
of the Fermi bubbles.
6.3. Chemically Peculiar Stars as Remnant Cores of Ablated
Red Giants
The past ablation of red giants by the jet would contribute to
the apparent lack of late-type stars in the central region of the
Galactic center. Another potential imprint of the past jet–red
giant interaction would be the presence of chemically peculiar,
high-metallicity stars in the NSC. This can be predicted from
the fact that as the jet ram pressure removes upper hydrogenand
helium-rich parts of the stellar atmosphere, the lower
metal-rich parts as well as the denser core are exposed. In fact,
two late-type stars at ~0.5 pc from SgrA*
were reported as
having a supersolar metallicity (Do et al. 2018) with an
anomalous abundance of scandium, vanadium, and yttrium. A
detailed modeling of the stellar evolution in combination with
the treatment of the jet–star interaction is needed to confirm or
exclude the previous interaction with the jet for these and
similar candidate stars with supersolar metallicities.
14
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
139
6.4. A Collimated Jet or a Broad-angle Disk Wind?
In the current analysis, we took into account mainly highly
collimated nuclear outflow—jet—with the small half-opening
angle close to ∼10°. The analysis of the UV ionization cones
by Bland-Hawthorn et al. (2019) indicates a half-opening angle
of ∼30°, which could be a signature of jet precession as we
discussed in Section 6.1 or alternatively disk winds with a
larger opening angle. In case the jet would be absent and the
disk wind would be present with the larger half-opening angle,
the expected stagnation radius would be proportionally larger
because qµR tanstag . Assuming the same kinetic luminosity
= -L 10 erg sj
42 1 and the outflow velocity close to c (ultrafast
outflows), the ratio of the stagnation radii is =R Rstag
wind
stag
jet
q q »tan tan 2.6wind jet , which yields for ~R R70stag
wind
using
Equation (6). The ablation effect would still take place but only
for the largest red giants with  R R100 at the outer radius
of the S cluster. The stagnation radius of 30 Re would be
reached at the distance of z∼0.017 pc for the same stellar
parameters as we assumed in Equation (6) and a larger outflow
half-opening angle of 30◦.
6.5. Recurrent Seyfert-like Activity and TDEs
The X-ray/γ-ray Fermi bubbles were created during the
increased Seyfert-like activity about 3.5±1 Myr ago (BlandHawthorn
et al. 2019) with total duration of ∼0.1–0.5 Myr
(Guo & Mathews 2012). Currently, it is unclear whether this
increased activity is related to the star formation event that led
to the formation of massive OB/Wolf–Rayet stars a few
million years ago, a fraction of which forms a stellar disk that is
a remnant of a former massive gaseous disk (Levin &
Beloborodov 2003). In case a correlation between the episodic
star formation and the accretion activity exists, the Seyfert-like
phase could occur every 100 million years based on the
currently observed stellar populations in the Galactic center
region (Pfuhl et al. 2011). In the context of this work, this could
provide a mechanism for the recurrent depletion of large red
giants by the increased jet activity. However, the most relevant
episode in terms of currently observed stellar populations is the
most recent episode a few million years ago. There is evidence
for even more recent activity ∼400 yr ago, which is inferred
from the X-ray reflections or propagating brightening of
molecular clouds in the Central Molecular Zone (Sunyaev
et al. 1993; Sunyaev & Churazov 1998). However, these
repetitive events occur stochastically based on the presence of
infalling clumps and lead to the increase by only several orders
of magnitude and last for several years depending on the exact
viscous timescale (Czerny et al. 2013).
Another possibility of a recurrent launching of the jet is a TDE,
which can occur in the Galactic center every ∼104
–105
yr
depending on the stellar type (Syer & Ulmer 1999; Alexander
2005; Komossa 2015). For completeness, we note that the jet is
not always formed during the TDE (Komossa 2015). However,
for a few months to years, the TDE can trigger a jet activity
similar to the Seyfert sources (Hills 1975). Due to the short
duration of the TDE between several months to years given
by the steep dependency of the luminosity on time, µ -L t 5 3,
the average number of interacting stars would be given by the
estimates calculated in Section 4. In general, the number
of ablated red giants in the S cluster would be of the order of
unity. The jet precession driven by the Lense–Thirring effect
(Lodato & Pringle 2006) could enlarge this number depending on
the precession period and Ωp (see Section 6.1).
6.6. Comparison with Other Mechanisms—the Region of
Efficiency
The jet-induced alternation of the population of late-type
stars is not necessarily an alternative to other proposed
mechanism, listed in the introductory, Section 1. In reality, it
could have coexisted simultaneously during the past few
million years with other previously proposed mechanisms, in
particular the tidal disruption of red giant envelopes as well as
direct star–disk interactions. This follows from the fact that
these mechanisms have different length scales of their
efficiency, as we further outline in the paragraphs below.
First, the tidal disruption of red giant envelopes takes place
on the smallest scales—less than 1 mpc from SgrA*
—as given
by the tidal radius, ( )»  r R M m2t •
1 3,
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
( )
  

´
= =


r
R
R
m
M
M
M
R
R
6000
30 1 4 10
0.14 mpc 354 . 32
t
•
6
Schw
1
3
1
3
The resonant relaxation process (discussed in Section 4), in
particular the scalar resonant relaxation, can cause an increase
in orbital eccentricities and thus effectively induce the tidal
disruption of giants as their orbital distance decreases below rt
close to the pericenter of their orbits. This could have
contributed to the dearth of brighter red giants in the inner
∼0.1 pc (Madigan et al. 2011), which is a larger scale than
given by rt but still smaller than the total extent of 0.5 pc of the
red giant hole.
Then, the jet-induced mass removal is clearly the most efficient
in the S-cluster region, z 0.04 pc, according to the cumulative
mass removal distance profile in Figure 5. Another way to
constrain the region of the maximum efficiency is to use the
relation in Equation (6) for the stagnation radius, from which
we derive the distance z. It follows that for the maximum
jet luminosity of = -L 10 erg sj
44 1
and the stagnation radius
range of – =R R4 30stag , we obtain the distance range
–=z 0.06 0.44 pcjet . Hence, within the S cluster, z 0.04 pc,
Rstag would be effectively below 4 Re, which corresponds to
K∼16 mag stars for a typical age of 5 Gyr. Therefore, the jet
luminosities close to the Eddington limit for SgrA*
are required
to truncate the atmospheres of late-type stars of K  16 mag. For
the moderate jet luminosity of = -L 10 erg sj
42 1
, the distance
range decreases by an order of magnitude to zj=0.006–0.04 pc;
hence, only brighter giants with Rå=30 Re (K∼13.5 mag)
would be effectively truncated within the S cluster, while the
smaller and fainter giants with K∼16 mag would remain largely
unaffected by the jet.
Finally, the star–clumpy disk collisions are the most efficient
for the disk surface densities S > -10 g cm4 2
typical of selfgravitating
clumps (Kieffer & Bogdanović 2016; Amaro-Seoane
et al. 2020), which can form at larger distance scales where
the condition for gravitational instability is met as given by
the Toomre instability criterion (Milosavljević & Loeb 2004). In
the Galactic center, this region likely corresponds to 0.04  z
0.5 pc, where the disk population of young massive stars is
observed, and they are believed to have formed in situ in a massive
gaseous disk (Levin & Beloborodov 2003).
15
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
140 CHAPTER 4. PAPER 3: RED-GIANT DEPLETION IN THE GALACTIC CENTER
Hence, we speculate that the dearth of bright red giants for
z  0.5 pc is due to the combination of the three processes—
tidal stripping, jet-induced atmosphere ablation, and star–disk
interactions—that operated the most efficiently at complementary
length scales up to ∼0.5 pc.
6.7. Observational Signatures and Falsifiability
The jet-ablation mechanism likely operated in the central
S-cluster region (<0.04 pc) for stars of large atmosphere radii
of 10 Re, and especially for supergiants of ∼100 Re even at
larger distances up to ∼0.1 pc. However, as the enhanced jet
activity and the resulting atmosphere ablation took place a few
million years ago, any direct observational trace of the jet–star
interaction is difficult to find. Here we list tentative observational
signatures of the jet ablation on the preexisting cusp of
late-type stars. Some of them have more possible interpretations
due to other mechanisms operating simultaneously in the
complex NSC around SgrA*
. The signatures proposed here
can serve as a guideline toward confirming the jet activity and
in particular the jet–star interaction in the central parsec. On the
other hand, if other explanations become more likely, these can
also serve as suitable falsifiability criteria for the jet-ablation
theory. The signatures can be outlined as follows:
(i) Flattening of the density distribution for brighter late-type
stars. This is a classical signature of the preferential bright
late-type star depletion, which has more interpretations due
to mechanisms, which likely operated on different scales;
see Section 6.6. Therefore, this signature should be treated
with caution. However, we have shown in Section 5 that the
jet active for a sufficiently long time can have an impact on
the surface-brightness profile of the NSC when it reaches
the kinetic luminosity at least -10 erg s ;42 1
see also
Section 5 and Figure 10. In particular, brighter giants with
mK<14 mag could exhibit a flat profile due to the jet
activity inside the inner arcsecond (z  0.04 pc). Such a
trend has also been recently reported by the high-sensitivity
photometric analysis of Schödel et al. (2020).
(ii) Detection of high-metallicity stars. The jet ablation of red
giant and supergiant shells could reveal deeper metal-rich
layers. A jet-ablation mechanism can be considered as
one of the explanations for the occurrence of stars with
anomalous metal concentrations in their atmospheres, as
was found by Do et al. (2018); see also Section 6.3.
(iii) Cluster of remnant white dwarfs at millipasec scales. In
relation to point (ii), an extreme case of jet ablation could
lead to the exposure of degenerate cores for asymptotic
giant branch (AGB) stars. This is analogous to the
ablation by tidal stripping (King 2020); however, the jet
ablation has a larger length scale for SgrA*
. As we
derived in Section 3, the AGB stars could be jet-ablated
down to the white-dwarf cores for z<0.015–0.15 mpc
for –= -L 10 10 erg sj
42 44 1
. The tidal stripping to the size
of 10−2
Re is only possible essentially below the event
horizon. There has not been a direct observation of white
dwarfs at such small distances from SgrA*
; however, the
hard X-ray flux peaking at SgrA*
was hypothesized to
originate in the cluster of accreting white dwarfs (Perez
et al. 2015).
(iv) Cusp of remnant blue OB stars. As we have shown in
Section 3, the late-type stars could be turned to blue stars
of spectral type OB by the jet-ablation mechanism. In
Table 1, we show that the effective temperature could be
of a few ×104
K, and with the stagnation radius of
Rstag=4.45 Re, the K-band magnitude was estimated to
reach mK∼13 mag, which is comparable to an S2 star
(mK∼14.1 mag, Habibi et al. 2017). In this sense, we
hypothesize that the fraction of S stars could be produced
via the jet ablation of older stars; however, the production
rate within the S cluster was of the order of unity, as we
showed in Section 4. Hence, the majority of B-type S
stars was most likely formed in situ in the circumnuclear
gaseous material (Mapelli & Gualandris 2016), and the
current location and the kinematic structure of the S
cluster are a result of different dynamical processes, most
likely the Kozai–Lidov mechanism and the resonant
relaxation (Ali et al. 2020).
(v) Presence of bow-shock and comet-shaped sources. The
presence of bow-shock sources X3 and X7 (Mužić et al.
2010) as well as X8 (Peißker et al. 2019) in the mini
cavity implies the interaction of these sources with a
nuclear outflow in the current state of activity of SgrA*
.
The present nuclear outflow could be a signature of a
low-surface-brightness jet (Yusef-Zadeh et al. 2020),
which was much more luminous a few million years ago.
The infrared-excess sources X3, X7, and X8 thus directly
reveal the interaction of a nuclear outflow/jet with stars at
the scale of ∼0.2 pc.
(vi) Nonspherical distribution of stars. In the broader context,
the activity of the Seyfert-like jet at the scales of ∼0.1 pc
could be imprinted on the nonspherical stellar structures,
e.g., by affecting the distribution of denser star-forming
material and its temperature via the jet feedback. Recently,
Ali et al. (2020) revealed an X-shape structure of the S
cluster formed by two, nearly perpendicular stellar disks.
Because S stars formed a few million years ago, their
formation could be linked to the phase of higher accretion
and enhanced jet activity. Also, the X-structure implies that
the resonant relaxation process (see Section 4), in particular
the VRR, is not as fast; otherwise, the kinematic structure
of the S cluster would be rather isotropic. However,
the potential relation between the jet activity and the
stellar kinematics needs to be verified via the detailed
hydrodynamical/N-body or smooth-particle-hydrodynamics
simulations.
(vii) Nonspherical distribution of ionization tracers around
SgrA*
. In a similar way as we discussed in point (vi) in
terms of the nonspherical stellar distribution, the jet
interaction with the surrounding gas could also be
revealed via the nonisotropic distribution of ionization
tracers. In particular, the shock-tracer line [Fe III] seems
to be preferentially located in the direction of the mini
cavity (Peißker et al. 2020), which suggests either current
or past interaction of the gas with the high-velocity
outflow/jet (Yusef-Zadeh et al. 2020). On scales larger
than 1 pc, the nonisotropic distribution is manifested by
bipolar radio lobes (Heywood et al. 2019) and X-ray
(Ponti et al. 2019) and γ-ray bubbles (Su et al. 2010;
Ackermann et al. 2014). Recently, the analysis of the
tilted, partially ionized disk in the inner Galactic latitudes
has shown that its optical line ratios are characteristic of
low-ionization nuclear emission regions (LINERs; Krishnarao
et al. 2020). The bipolar ionization structure is
energetically in favor of the Seyfert-like jet activity rather
16
The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
141
than the star formation event (Bland-Hawthorn et al.
2019).
In summary, the jet-activity signs listed in points (i)–(vii)
indicated the past enhanced activity of the jet and its interaction
with the surrounding circumnuclear medium, including the
nuclear star cluster. Although each of the above-mentioned
points can have alternative explanations, the absence of all of
these signatures would suggest that the jet did not operate in the
past, and our hypotheses would then be strongly disfavored.
Future detailed observations by the Extremely Large Telescope
(ELT) in combination with detailed numerical simulations of
the jet–star interactions close to SgrA*
will help to reveal the
signatures of current and past jet–star interactions.
7. Summary and Conclusions
We presented a novel scenario to explain the lack of bright red
giants in the inner regions of the Galactic center in the sphere of
influence of the currently quiescent, but previously active, radio
source SgrA*
. Taking this increased activity into account, we
focused on the effect of the jet on late-type stars at 0.3 pc. By
adopting the scenario of the recent active period of Sgr Aå
, we
considered the interaction of red giants with a jet of a typical
active Seyfert-like nucleus with the expected kinetic luminosity
–= -L 10 10 erg sj
41 44 1
. Given that red giants have a very slow
wind, the jet can significantly ablate the stellar envelope down to
at least ∼30 Re within the S cluster (z  0.04 pc) after repetitive
encounters. Specifically, at z=0.02 pc, the stagnation radius is
4„Rstag/Re„30 for ´ ´- L2.0 10 erg s 1.1 1041
j
1 43.
Hence, the higher luminosity end that corresponds to the less
frequent events that formed the Fermi bubbles can ablate the
stellar atmospheres of late-type giants by a factor of ∼7.5 more
than the more frequent, less energetic outbursts of SgrA*
.
This truncation is accompanied by the removal of a large
fraction of matter, reaching as much as D » ´ »-M M3 101
5
M10 Earth for red giants with radii Rå>200 Re at distances
smaller than 0.01 pc for a single encounter. After at least a
thousand red giant–jet encounters, we expect the cumulative mass
loss of at least ΔM≈10−4
Me at the orbital distance of 0.01 pc.
This is comparable to the values inferred from red giant–
accretion-clump simulations. The proposed mechanism can thus
help to explain the presence of late-type stars with the maximum
atmosphere radius of ∼30Re within the S cluster as inferred from
the near-infrared observations.
The reduction in the mass and radius of the red giant
atmosphere after repetitive jet–star crossings will produce an
estimated decrease in the near-infrared K-band magnitude by
1.9, 5.3, and 8.9 mag with respect to the normal evolution at
0.1, 0.01, and 0.001 pc from SgrA*
, respectively. Simultaneously,
the color index would decrease to negative values, i.e.,
the stars should appear bluer with a higher effective
temperature. The mean expected number of red giant–jet
crossings per orbital period is 3.5 within 0.04 pc, and 82.5
within 0.3 pc, respectively. For the jet kinetic luminosity of
-10 erg s44 1, ∼26.5% of currently detectable late-type stars
located at z=0.04 pc (S cluster) with radii larger than 2.7 Re
and K-band magnitudes smaller than ∼16 mag could be
affected by the jet ablation. The estimated numbers of
interacting giants can be considered as lower limits because
various dynamical effects, such as the coherent resonant
relaxation within the nuclear star cluster as well as a potential
jet precession would enlarge the number of affected giants.
Constructed surface-brightness profiles of the mock NSC
affected by the jet with the luminosity of – -10 10 erg s42 44 1
show that profiles of mainly brighter late-type stars with
mK<14 mag (dereddened, <16 mag with the foreground
extinction included) are flattened by the jet inside the inner
arcsecond (0.04 pc). Fainter stars keep the initially assumed
cusp-like projected profile.
In summary, the interaction of red giants with the jet of SgrA*
during its enhanced activity could contribute to the observed lack
of bright red giants and hence affect their surface-brightness
profile in the central parts of the NSC. More likely, this
mechanism operated in parallel with other previously proposed
mechanisms, such as the star–disk interactions, star–star collisions,
and TDEs that have different spatial scales of efficiency. Detailed
numerical computations of red giant–jet interactions in combination
with a modified stellar evolution will help to verify our
analytical estimates.
We thank the referee for constructive comments that helped
us improve our manuscript. M.Z., B.C., and V.K. acknowledge
the continued support by the National Science Center, Poland,
grant No. 2017/26/A/ST9/00756 (Maestro 9), and the CzechPolish
mobility program (MSMT 8J20PL037). A.A. and V.K.
acknowledge the Czech Science Foundation under grant
GACR 20-19854S titled “Particle Acceleration Studies in
Astrophysical Jets,” and the European Space Agency PRODEX
project eXTP in the Czech Republic. This work was carried out
partly also within the Collaborative Research Center 956, subproject
[A02], funded by the Deutsche Forschungsgemeinschaft
(DFG) project ID184018867. The work on this
project was partially carried out during the short-term stay of
M.Z. within the Polish-Czech bilateral exchange program
supported by NAWA under agreement PPN/BCZ/2019/1/
00069. M.Z. also acknowledges the NAWA financial support
under agreement PPN/WYM/2019/1/00064 to perform a
three-month exchange stay at the Astronomical Institute of the
Czech Academy of Sciences in Prague.
ORCID iDs
Michal Zajaček https://orcid.org/0000-0001-6450-1187
Anabella Araudo https://orcid.org/0000-0001-7605-5786
Vladimír Karas https://orcid.org/0000-0002-5760-0459
Bożena Czerny https://orcid.org/0000-0001-5848-4333
Andreas Eckart https://orcid.org/0000-0001-6049-3132
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The Astrophysical Journal, 903:140 (18pp), 2020 November 10 Zajaček et al.
143
Chapter
5
Paper 4: Reverberation-Mapping of
HE 0435-4312
From the studies of the spatial distribution of late-type stars in the Galactic center, we
refocused on distant luminous quasars, specifically HE 0435-4312 (z = 1.2231). We analyzed
the variability of the broad MgII line (in the UV part of the spectrum in the rest frame) and
mainly how this variability is driven by the photoionizing continuum at 300 nm.
We found that, despite some predictions, MgII line is quite variable with the fractional
variability of ∼ 5.4%, which is comparable to the continuum variability of 4.8%. Using seven
time-delay methodologies, we inferred the MgII time delay of 296+13
−14 days in the rest frame.
We dedicated some effort to the removal of false peaks and aliases using the bootstrap method
and the light-curve pair weighting probability function.
With its high luminosity at 300 nm (L3000 = 1046.4
erg s−1
), the source is beneficial for
decreasing the rms scatter of the RBLR − L relation, while at the same time, it increases
its correlation. Using 58 SDSS-RM sources (Homayouni et al. 2020), we put together a
sample of 69 sources including HE 0435-4312. For the whole sample, the MgII relation is
surprisingly flat with the best-fit RBLR − L relation, log (τ/lt.day) = (1.67 ± 0.05) + (0.30 ±
0.05) log (L3000/1044
erg s−1
), which has a considerable scatter of 0.30 dex.
When we restrict ourselves to the high-accreting sources (dimensionless accretion rate ˙M
larger than the median value), the scatter of the high-accreting sources around their best-fit
RBLR − L relation, log (τ/lt.day) = (1.37 ± 0.08) + (0.42 ± 0.06) log (L3000/1044
erg s−1
) is
significantly smaller, σ ∼ 0.20, than the scatter for the whole sample. This indicates that
the RBLR − L relation for especially high-accreting quasars could be applied for constraining
cosmological parameters. For the current sample of 27 high-accreting sources (with 8
outliers removed), the fitting of general non-flat ΛCDM model yields the best-fit parameters
(Ωm, ΩΛ) = (0.19, 0.62), which is within 1σ confidence interval consistent with the values
based on better established cosmological probes (CMB; Planck Collaboration et al. 2020).
Credit: Zajaˇcek et al. (2021), ApJ 912, 10. Reproduced with permission ©AAS.
145
Time Delay of Mg II Emission Response for the Luminous Quasar HE 0435-4312: toward
Application of the High-accretor Radius–Luminosity Relation in Cosmology
Michal Zajaček1
, Bożena Czerny1
, Mary Loli Martinez–Aldama1
, Mateusz Rałowski2
, Aleksandra Olejak3
,
Robert Przyłuski1
, Swayamtrupta Panda1,3
, Krzysztof Hryniewicz4
, Marzena Śniegowska1,3
, Mohammad-Hassan Naddaf1
,
Raj Prince1
, Wojtek Pych3
, Grzegorz Pietrzyński3
, Catalina Sobrino Figaredo5
, Martin Haas5
, Justyna Średzińska3
,
Magdalena Krupa2
, Agnieszka Kurcz2
, Andrzej Udalski6
, Vladimír Karas7
, Marek Sarna3
, Hannah L. Worters8
,
Ramotholo R. Sefako8
, and Anja Genade8
1
Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland; zajacek@cft.edu.pl
2
Astronomical Observatory of the Jagiellonian University, Orla 171, 30-244 Cracow, Poland
3
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland
4
National Centre for Nuclear Research, Pasteura 7, 02-093 Warsaw, Poland
5
Astronomisches Institut—Ruhr Universitaet Bochum, Germany
6
Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warsaw, Poland
7
Astronomical Institute of the Czech Academy of Sciences, Boční II 1401, CZ-14100 Prague, Czech Republic
8
South African Astronomical Observatory, P.O. Box 9, Observatory, 7935 Cape Town, South Africa
Received 2020 December 21; revised 2021 February 10; accepted 2021 February 23; published 2021 April 29
Abstract
Using six years of spectroscopic monitoring of the luminous quasar HE 0435-4312 (z = 1.2231) with the Southern
African Large Telescope, in combination with photometric data (CATALINA, OGLE, SALTICAM, and BMT),
we determined a rest-frame time delay of -
+
296 14
13
days between the Mg II broad-line emission and the ionizing
continuum using seven different time-delay inference methods. Time-delay artifact peaks and aliases were
mitigated using the bootstrap method and prior weighting probability function, as well as by analyzing unevenly
sampled mock light curves. The Mg II emission is considerably variable with a fractional variability of ∼5.4%,
which is comparable to the continuum variability (∼4.8%). Because of its high luminosity (L3000 = 1046.4
erg s−1
),
the source is beneficial for a further reduction of the scatter along the Mg II-based radius–luminosity relation and its
extended versions, especially when the highly accreting subsample that has an rms scatter of ∼0.2 dex is
considered. This opens up the possibility of using the high-accretor Mg II-based radius–luminosity relation for
constraining cosmological parameters. With the current sample of 27 reverberation-mapped sources, the best-fit
cosmological parameters (Ωm, ΩΛ) = (0.19; 0.62) are consistent with the standard cosmological model within the
1σ confidence level.
Unified Astronomy Thesaurus concepts: Accretion (14); Galaxy accretion disks (562); Active galactic nuclei (16);
Quasars (1319); Emission line galaxies (459); Reverberation mapping (2019); Galaxy spectroscopy (2171); Galaxy
photometry (611)
1. Introduction
Broad emission lines with line widths of several thousand
km s−1
are one of the main characteristic features of the optical
and UV spectra of active galactic nuclei (AGNs; Seyfert 1943;
Woltjer 1959; Schmidt 1963), specifically of type I, where the
broad-line region (BLR) is not obscured by the dusty molecular
torus (Antonucci 1993; Urry & Padovani 1995). However, the
scattered polarized light can reveal broad lines even for obscured
type II AGNs (type II NGC 1068 was the first case, Antonucci &
Miller 1985), which implies the universal presence of the BLR for
accreting supermassive black holes (SMBHs). Low-luminosity
systems, such as the Galactic Center (Genzel et al. 2010;
Eckart et al. 2017; Zajaček et al. 2018) or M87 (Sabra et al. 2003),
do not reveal the presence of broad lines. But broad lines
can be present even for some sources with lower accretion rates
(Bianchi et al. 2019), and the exact accretion limit for their
appearance was analyzed to some extent by, e.g., Elitzur &
Ho (2009), who estimated a bolometric luminosity limit of
´ -M M5 10 10 erg s39
•
7 2 3 1( ) , where M• is the black hole
mass in units of 107
solar masses (Me). However, several crucial
questions remain unanswered. Mainly the transition from
geometrically thin disk accretion flows to geometrically thick
advection-dominated accretion flows at lower accretion rates is
still unclear and is likely related to the boundary conditions, the
ability of the flow to cool, the feeding mechanism (warm stellar
winds or an inflow of cold gas from larger scales), the associated
initial angular momentum, and the resulting circularization radius.
In addition, not only the formation of the BLR but also its
properties seem to depend on the accretion rate, which motivates
the study of more highly accreting sources (Du et al. 2015, 2018),
such as HE 0413-4031 in particular (Zajaček et al. 2020).
The BLR has mostly been studied indirectly via reverberation
mapping, i.e., by inferring the time delay between the
ionizing UV continuum emission of an accretion disk and the
broad-line emission (Blandford & McKee 1982; Peterson &
Horne 2004; Gaskell 2009; Czerny 2019; Popović 2020) using
typically the interpolated cross-correlation function (Peterson
et al. 1998, 2004; Sun et al. 2018) or other methods (see, e.g.,
Zajaček et al. 2019, 2020, for an overview and an application
of seven methods in total). The high correlation between the
continuum and the line-emission fluxes implies that the line
emission is mostly reprocessed thermal emission from an
accretion disk. From the rest-frame time delay τBLR, it is
straightforward to estimate the size of the BLR, RBLR = cτBLR,
and in combination with the single-epoch line FWHM or the
line dispersion σ, which serve as proxies for the BLR virial
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 https://doi.org/10.3847/1538-4357/abe9b2
© 2021. The American Astronomical Society. All rights reserved.
1
146 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
velocity, one can infer the central black hole mass,
M• = fcτBLRFWHM2
G−1
. The factor f is known as the virial
factor and takes into account the geometrical and kinematic
characteristics of the BLR. Although f is typically of the order
of unity, it introduces a factor of ∼2–3 uncertainty in the black
hole mass. By comparing the black hole masses inferred from
accretion-disk spectra with the masses from single-epoch
spectroscopy, Mejía-Restrepo et al. (2018) found that the value
of f is approximately inversely proportional to the broad-line
FWHM,9
which provides a way to better estimate f for
individual sources.
Optical reverberation mapping studies using the Hβ line
showed that there is a simple power-law relation between the
size of the BLR and the monochromatic luminosity of AGNs at
5100 Å (Kaspi et al. 2000; Peterson et al. 2004), the so-called
radius–luminosity (RL) relation. After a proper removal of the
host galaxy starlight (Bentz et al. 2013), the slope of the power
law is close to 0.5, which is expected from simple
photoionization arguments. The importance of the radius–
luminosity relation lies in its application to infer black hole
masses from single-epoch spectroscopy, where FWHM or the
line dispersion σ serves as a proxy for the velocity of virialized
BLR clouds, and the monochromatic luminosity of the source
serves as a proxy for the rest-frame time delay, and hence the
BLR radius, via the RL relation.
Another, more recent application of the RL relation is the
possibility to utilize it for obtaining absolute monochromatic
luminosities. From the measured flux densities, one can
calculate luminosity distances and use them for constraining
cosmological parameters (Haas et al. 2011; Watson et al.
2011; Czerny et al. 2013, 2020; Martínez-Aldama et al. 2019;
Panda et al. 2019). The problem for cosmological applications
is that the RL relation exhibits a scatter, which has increased
with the accumulation of more sources, especially those with
higher accretion rates (super-Eddington accreting massive
black holes—SEAMBHs; Du et al. 2015, 2018).
The scatter is present both for lower-redshift Hβ sources
(Grier et al. 2017) and for higher-redshift Mg II sources, which
follow an analogous RL relation (Czerny et al. 2019;
Homayouni et al. 2020; Zajaček et al. 2020). The scatter was
attributed to the accretion-rate intensity, with the basic trend
that the largest departure from the nominal RL relation is
exhibited by the highly accreting sources (Du et al. 2018). The
correction to the time delay was proposed based on the
Eddington ratio and the dimensionless accretion rate (MartínezAldama
et al. 2019); however, these two quantities depend on
the time delay via the black hole mass. To break down the
interdependence, Fonseca Alvarez et al. (2020) proposed to
make use of independent, observationally inferred quantities
related to the optical/UV spectral energy distribution (SED).
The relative Fe II strength correlated with the accretion-rate
intensity is especially efficient in reducing the scatter for Hβ
sources to only 0.19 dex (Du & Wang 2019; Yu et al. 2020a).
The same effect is observed for the extended radius–luminosity
relations for Mg II reverberation-mapped sources (68 sources;
Martínez-Aldama et al. 2020). Martínez-Aldama et al. (2020)
divide the sources into low and high accretors, where the high
accretors show a much smaller scatter of only ∼0.2 dex. The
extended RL relation including the relative Fe II strength
further reduces the scatter down to 0.17 dex for the highly
accreting subsample.
Large reverberation monitoring campaigns are currently
performed by several groups, for instance the Australian Dark
Energy Survey (OzDES, Hoormann et al. 2019), the Sloan
Digital Sky Survey Reverberation Mapping project (SDSSRM,
Shen et al. 2015, 2019), the Dark Energy Survey (DES,
Abbott et al. 2018; Diehl et al. 2018; Yang et al. 2020), the
SEAMBHs (Du et al. 2015, 2018), but monitoring of an
individual source can also contribute significantly, especially if
its luminosity is an extreme value in the radius–luminosity
relation. This is because the most luminous quasars have very
low sky densities, so they are not suitable for reverberation
mapping multi-object spectroscopy (MOS-RM) programs, and
instead require monitoring of individual objects. This is why
programs such as the one presented here are necessary.
Luminous sources are expected to be beneficial in terms of
increasing the RL correlation coefficient, and this can also lead
to a reduction in the scatter. In the current paper, we present
results of the time delay of the Mg II line for the last of three
very luminous quasars at intermediate redshift monitored for
several years with the Southern African Large Telescope
(SALT). The source HE 0435-4312 (z = 1.2231) hosts a
supermassive black hole of 2.2 × 109
Me that is highly
accreting with an Eddington ratio of 0.58 according to the
SED best-fit of Sredzińska et al. (2017). The peculiarity of the
source is a smooth shift of the peak of the Mg II line first
toward longer wavelengths, while currently the shift proceeds
toward shorter wavelengths. This line shift could hint at
the presence of a supermassive black hole binary (Sredzińska
et al. 2017).
In this paper, we measure the time delay of HE 0435-4312
using seven methods. Subsequently, we study the position of
the source in the RL relation, including its extended versions,
and how the source affects the correlation coefficient as well as
the scatter. Finally, we look at the potential applicability of the
Mg II highly accreting subsample for cosmological studies.
The paper is structured as follows. In Section 2, we describe
observations including both spectroscopy and photometry. In
Section 3, we analyze the mean and the rms spectra, spectral
fits of individual observations, and the variability of the
continuum and the line-emission light curves. The core of the
paper is Section 4, where we summarize the mean rest-frame
time delay between the Mg II emission and the continuum as
inferred from seven different methods. The position of the
source in the RL relation and its extended versions is also
analyzed in this section. Subsequently, in Section 5, we discuss
the aspect of variability of the Mg II emission as well as the
application of the highly accreting Mg II subsample in
cosmology. Finally, we present our conclusions in Section 6.
2. Observations
Here we present the optical photometric and spectroscopic
observations of the quasar HE 0435-4312 (z = 1.232,
V = 17.1 mag) with J2000 coordinates R.A. = 04h
37m
11 8,
decl. = −43°06′04ʺ according to the NED database.10
Due to
its large optical flux density, it was found during the Hamburg
ESO quasar survey (Wisotzki et al. 2000). Previously,
9
More precisely, using the general dependence of f on the line FWHM
in the form = bf FWHM line FWHMobs obs
0
( ( ) ) , with FWHMobs
0
and β being
the searched parameters, Mejía-Restrepo et al. (2018) obtained =FWHMobs
0
 -3200 800 km s 1
, β = −1.21 ± 0.24 for Mg II and = FWHM 4550obs
0
-1000 km s 1
, β = −1.17 ± 0.11 for Hβ measurements.
10
NASA/IPAC Extragalactic Database: http://ned.ipac.caltech.edu/.
2
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
147
Sredzińska et al. (2017) reported ten spectroscopic observations
performed by SALT Robert Stobie Spectrograph (RSS) over
the course of three years (from 2012 December 23/24 to 2015
December 7/8). The main result of their analysis was the
detection of the fast displacement of the Mg II line with respect
to the quasar rest frame by 104 ± 14 km s−1
yr−1
. In this paper
the number of spectroscopic observations increased to 25,
which together with 81 photometric measurements allows for
the analysis of the time-delay response of the Mg II line with
respect to the variable continuum. Previously we detected a
time delay for two other luminous quasars: -
+
562 68
116
days for
CTS C30.10 (Czerny et al. 2019) and -
+
303 33
29
days for HE
0413-4031 (Zajaček et al. 2020), both in the rest frames of the
corresponding source. These intermediate-redshift sources are
very important for constraining the Mg II-based radius–
luminosity relation. Especially sources with either low or high
luminosities are needed to constrain the slope of the RL relation
and evaluate the scatter along it (Martínez-Aldama et al. 2020).
2.1. Photometry
The photometric data were combined from a few dedicated
monitoring projects, described in more detail in Zajaček et al.
(2020). The source has been monitored in the V band as part of
the OGLE-IV survey (Udalski et al. 2015) done with the 1.3 m
Warsaw telescope at the Las Campanas Observatory, Chile.
The exposure times were typically around 240 s, and the
photometric errors were small, of the order of 0.005 magnitude
(see Table 3). In the later epochs the quasar was observed,
again in the V band, with the 40 cm Bochum Monitoring
Telescope (BMT).11
These data showed a systematic offset of
0.2 magnitudes toward larger magnitudes with respect to the
overlapping OGLE data, which we corrected for by the shift of
all of the BMT points. SALT spectroscopic observations were
also supplemented, whenever possible with SALTICAM
imaging in the g band. We have analyzed all of these data;
however, two data sets (2013 August 20 and 2019 January 27)
showed a significant discrepancy with the other measurements.
The first of the two sets of observations was done during full
moon, and with the moon–target separation relatively large;
spectroscopic observations were not affected, but the photometric
observations were. During the second set of observations
the night was dark but seeing was about 2 5 during the
photometry, dropping down to 2″ during the spectroscopic
exposures. We were unable to correct the data for these effects,
and we did not include these data points in further considerations.
Because of the collection of the data in the g band, we
allowed for the grayshift of all the SALTICAM data, and the
shift was determined using epochs when they coincided with
the more precise OGLE set collected in the V band. Finally, we
supplemented our photometry with the light curve from the
Catalina Sky Survey,12
which is not of a very high quality
(with uncertainties of 0.02–0.03 mag) but nicely covers the
early period from 2005 until 2013. We have binned these data
to reduce the scatter. Table 3 contains only the data points that
were used in time-delay measurements. All the data points are
presented in the upper panel of Figure 1.
Recently, the quasar was monitored in the V band with a
median sampling of 14 days using Lesedi, a 1 m telescope at
the South African Astronomical Observatory (SAAO), with the
Sutherland High Speed Optical Camera (SHOC). SHOC has a
5.7 × 5.7 arcmin2
field of view (FoV). Each observation
consists of nine dithered 60 s exposures. They are corrected for
bias and flatfields (using dusk or dawn sky flats). Astrometry is
obtained using the SCAMP tool.13
The resulting mediancombined
image has a 7.5 × 7.5 arcmin2
FoV centered on the
quasar. The light curves were created using five calibration
stars located on the same image as the quasar. The preliminary
results are consistent with the last photometric point from
SALT/SALTICAM.
2.2. Spectroscopy
Spectroscopic observations of HE 0435-4312 were performed
with the 11 m telescope SALT, with the RSS (Burgh
et al. 2003; Kobulnicky et al. 2003; Smith et al. 2006) in a
long-slit mode and a slit width of 2″. We used the RSS PG1300
grating with a grating tilt angle of 26°.75. Order blocking was
done with the blue PC04600 filter. Two exposures were always
made, each of about 820 s. The same setup has been used
throughout the whole monitoring period, from 2012 December
23 until 2020 August 20. Observations were always performed
in the service mode.
The raw data reduction was performed by the SALT
observatory staff, and the final reduction was performed by
us with the use of the IRAF package. All the details were given
in Sredzińska et al. (2017), where the results from the first three
years of this campaign were presented. We followed exactly
the same procedure for all 25 observations to minimize the
possibility of unwanted systematic differences.
In order to get the flux calibration, we performed a weighted
spline interpolation of the first order (with inverse measurement
errors as weights) between the epochs of photometric and
spectroscopic observations, thus an apparent V magnitude was
assigned to each spectrum. Taking as a reference the composite
spectrum and the continuum with a slope of αλ = −1.56 from
Vanden Berk et al. (2001), we just normalized each spectrum to
the V magnitudes (5500 Å).
2.3. Spectroscopic Data Fitting
The reduced and calibrated spectra were fitted in the
2700–2900 Å range in the rest frame. The basic model
components were as in Sredzińska et al. (2017). The data
were represented by (i) continuum in the form of a power law
with arbitrary slope and normalization, (ii) the Fe II
pseudocontinuum, and (iii) two kinematic components representing
the Mg II line; each of the kinematic components was
represented by two doublet components. The line is unresolved,
and the doublet ratio could not be well constrained, so it
was fixed at 1:1 (see Sredzińska et al. 2017 for the discussion).
For the kinetic shapes we used Lorentzian profiles since they
provided somewhat better representation of the data in χ2
terms
than Gaussian ones. All the parameters were fitted simultaneously.
In order to determine the redshift and the most
appropriate Fe II template, we studied in detail observation 23,
which also covered the region around 3000 Å in the rest frame
(see Appendix B). Thus for the adopted redshift z = 1.2231, the
Fe II template was very slightly modified in comparison with
Sredzińska et al. (2017), and the pseudocontinuum was kept at11
BMT is a part of the Universitaetssternwarte Bochum located near Cerro
Armazones in Chile. For more information, see Ramolla et al. (2013).
12
http://nunuku.caltech.edu/cgi-bin/getcssconedb_release_img.cgi
13
https://www.astromatic.net/software/scamp
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148 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
FWHM of 3100 km s−1
. Thus there were eight free parameters
in the model: power-law normalization and slope, normalization
of the Fe II pseudocontinuum, the width and normalizations
of the two kinematic components of Mg II, and the
position of the second component, with the other one set at the
quasar rest frame, together with Fe II.
3. Results: Spectroscopy
3.1. Determination of the Mean and the rms Spectra
We determined the mean and the rms spectra for HE 0435-
4312 as we did previously for quasar HE 0413-4031 (Zajaček
et al. 2020). Due to the particularly low signal-to-noise ratio
(∼7.5) shown by spectrum no. 19, which is clearly an outlier in
the light curve (Figure 1), we do not consider it for the
estimation of the mean and rms spectra. We followed the
methodology for constructing the mean and the rms spectra as
outlined in Peterson et al. (2004). In particular, we formed the
mean spectrum (without spectrum no. 19) using
ål l=
=
F
N
F
1
, 1
i
N
i
1
( ) ( ) ( )
where Fi(λ) is the ith spectrum out of a total of N spectra in the
measured database. Subsequently, the rms spectrum, initially
taking into account all spectral components (Mg II line +
continuum + Fe II pseudocontinuum), was constructed using
ål l l=
-
-
=
S
N
F F
1
1
. 2
i
N
i
1
2
1 2
⎧
⎨⎩
⎫
⎬⎭
( ) [ ( ) ( )] ( )
The constructed mean and rms spectra are shown in Figure 2
(black solid lines) in the upper and upper middle panels,
respectively. The quasar is not strongly variable, so the
normalization of the rms is very low, and the spectrum is
noisy, with visible effects of occasional imperfect sky
subtraction. However, the overall quality of the rms spectrum
is still suitable for the analysis. In both the mean and the rms
spectra, the Mg II line modeling required two kinematic
components, since line asymmetry is clearly visible. The result
is shown in Figure 2 with spectral components depicted with
different colored lines described in the figure caption. For the
fitting, we finally used the redshift as determined by Sredzińska
et al. (2017), but with a slightly modified Fe II template based
on the d11 template of Bruhweiler & Verner (2008). We also
compared and analyzed other Fe II templates based on the
updated CLOUDY model (Ferland et al. 2017) as well as the
six-transition model by Kovačević-Dojčinović & Popović
(2015) and Popović et al. (2019). For a detailed discussion of
different Fe II templates—a total of eight setups with different
redshifts as well as Lorentzian or Gaussian line component
profiles—see Appendix B.
The overall shapes of the mean and the rms spectra are
similar (see Figure 2). The FWHM of the Mg II line in the
mean spectrum is +
-3695 km s21
21 1; the line in the rms spectrum
might be slightly broader, +
-3886 km s341
143 1, but is consistent
within the error margins. A much larger difference is seen in
the line dispersion, which is much smaller in the mean
spectrum than in the rms spectrum ( -
+
2707 6
10
km s−1
versus
-
+
3623 412
76
km s−1
). The FWHM and σ are larger in the rms
spectrum, most likely due to its noisy nature, although there is
an indication of a trend of both Mg II FWHM and σ being
larger in the rms spectrum than in the mean spectrum based on
the analysis of the SDSS-RM sample (Wang et al. 2019).
However, the ratio of FWHM to σ for both the mean and the
rms spectra is far from the value 2.35 expected for a Gaussian
shape. The source can be classified as A-type according to the
classification of Sulentic et al. (2000). This is consistent with
the Eddington ratio 0.58 determined by Sredzińska et al. (2017)
for this object. There is also an interesting change in the line
position between the mean and the rms spectra, as determined
from the first moment of the distribution: 2805 Å versus
2792 Å.
Figure 1. Light curves and the time evolution of emission line properties
measured in the rest frame. Points marked with a black circle (obs. 19) were
removed from the analysis.
4
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
149
Following the spectral studies by Barth et al. (2015) and
Wang et al. (2019), we show in Figure 2 (lower middle and
lower panels) the mean and the rms spectra constructed taking
into account all the spectral components (black lines; Mg II
line + continuum + Fe II pseudocontinuum), the mean and
the rms spectra that have the continuum power law subtracted
from each spectrum (red lines), and finally the spectra with Fe
II pseudocontinuum subtracted from individual spectra, which
represents the true, line-only mean and the rms spectrum (blue
lines). For the rms spectra, we do not detect any significant
difference in the line width, which is expected to be smaller
for the total-flux rms than for the line-only rms spectrum
(Barth et al. 2015; Wang et al. 2019). This can be attributed to
the overall noisy nature of our rms spectra, which are
constructed from only 24 individual spectra. According to
Barth et al. (2015) and Wang et al. (2019), the difference in
the line width becomes smaller for a sufficiently long duration
of the campaign. However, in our case, the spectroscopic
monitoring was only ∼4.25 times longer than the emissionline
time lag in the observer’s frame (see Section 4). For
such a short duration, the distribution of the ratios of line
width between the total-flux and the line-only rms spectra is
broad—between 0.5 and 1.0, with the peak close to 1.0; see
Appendix C in Barth et al. (2015).
3.2. Spectral Fits of Individual Observations
The fits to individual spectroscopic data sets were done in
the same way as for the mean spectrum. In all 25 data sets, two
kinematic components of the Mg II line were needed to
represent the line shape well. The normalization of Fe II
pseudocontinuum was allowed to vary for each individual
spectrum, while the Fe II width was fixed to
FWHM = 3100 km s−1
. The Mg II component kinematically
related to the Fe II is slightly narrower, having an average
FWHM of 2128 ± 28 km s−1
, while the second shifted
component is somewhat broader, with FWHM of 2262 ±
90 km s−1
. However, we stress here that the broadband
modeling by Sredzińska et al. (2017) did not support any
identification of these components with separate regions, so
the two components are just a mathematical representation of
the slightly asymmetric line shape.
The parameters for observation 19 were considerably
different, but as we already mentioned in Section 3.1, this
observation was of a particularly low quality despite the fact
that actually three exposures were made this time. Cirrus clouds
were present during the whole night, and even more clouds
started arriving during the second exposure of the quasar, so the
third exposure was done. Nevertheless, all the parameters were
determined with errors a few times larger than for the
remaining observations.
The average value of the equivalent width of the Mg II line is
23.6 ± 0.5 Å if observation 19 is included. If observation 19 is
not taken into account, the mean value increases to
24.1 ± 0.6 Å, and this is similar to the value determined from
the mean spectrum: 23.9 Å. Such values are perfectly in
agreement with the properties of the bright quasar sample
studied by Forster et al. (2001), where the mean EW of the Mg
II broad component was found to be -
+
27.4 6.3
8.5
Å. We do not see
any traces of the narrow component in either the mean
spectrum or the individual data sets.
The average value of the EW of Fe II, 18.2 ± 0.7 Å, is also
similar to the value in the mean spectrum, 18.9 Å. The relative
error is larger than for the Mg II line since Fe II
pseudocontinuum is more strongly coupled to the power-law
continuum during the fitting procedure.
The dispersion in the measurements between observations
partially represents the statistical errors, but partially reflect the
intrinsic evolution of the source in time. This evolution is
studied in the next section.
3.3. Light Curves: Variability and Trends
The quasar HE 0435-4312 is not strongly variable in terms
of the continuum emission. The whole photometric light curve,
including the CATALINA data, covers 14 yr, and the fractional
Figure 2. Upper panel: mean spectrum (red curve) obtained without
observation 19. We also show its decomposition into two Lorentzian
components of the Mg II line (dotted magenta), Fe II pseudocontinuum
(dotted blue line), and a power law (green dashed line). Upper middle
panel: rms spectrum and its decomposition. The notation of spectral
components is the same as for the mean spectrum in the upper panel.
Lower middle panel: the mean spectrum in absolute calibration. The solid
black line denotes the mean spectrum including all the components (line,
continuum, and Fe II pseudocontinuum). The red solid line indicates the mean
spectrum constructed after removal of the continuum contribution from each
spectrum. The blue solid line indicates the line-only mean spectrum after the
additional removal of Fe II pseudocontinuum. Lower panel: a properly
calibrated rms spectrum, with the black line denoting the total rms (line +
continuum + Fe II pseudocontinuum). The rms spectrum after the subtraction
of the continuum is shown by the red line, while the line-only rms is depicted
by the blue line.
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150 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
variability amplitude for the continuum is 8.9% in flux. During
the period covered by SALT data (7 yr) it is ∼4.9%.
Fortunately, the Mg II line flux shows significant variability,
comparable to the continuum, at the level of 5.4% during this
period. We do not observe a suppressed Mg II variability in this
source, unlike that seen in much larger samples (Goad et al.
1999; Woo 2008; Zhu et al. 2017). Yang et al. (2020) also
detect the response of Mg II emission to the continuum for 16
extreme-variability quasars, but with a smaller variability
amplitude, D =  DL Llog Mg 0.39 0.07 log 3000II( ) ( ) ( Å).
A low Mg II variability was modeled to be the result of a
relatively large Eddington ratio (Guo et al. 2020) but HE 0435-
4312 is also a source with a rather large Eddington ratio of 0.58
(Sredzińska et al. 2017). Overall, the fractional variability of
the Mg II line for our source is comparable to a variability
of ∼10% on 100 day timescales as inferred for the SDSS-RM
ensemble study (Sun et al. 2015).
The variations in quasar parameters are smooth overall. The
quality of observation 6 was not very high, as discussed in
Sredzińska et al. (2017), but it still allowed the Mg II line
parameters to be obtained properly. However, observation 19
created considerable problems. The registered number of
photons was much lower (by a factor of a few) than in typical
observations, even the background was rather low, and clouds
were apparently present in the sky. We did the data fitting, and
the derived values of the model parameters form clear outliers
when compared with the trends (see Figure 1). Therefore, we
did not use this observation in the remaining analysis and the
determination of the time delay.
In Sredzińska et al. (2017) the change of the line position
was discussed in much detail, since during the first three years
the Mg II line seems to move systematically toward longer
wavelength with a surprising speed of 104 ± 14 km s−1
yr−1
with respect to the quasar rest frame. However, now this trend
has seemingly stopped, and in recent observations it seems to
have reversed. Such emission line behavior is frequently
considered as a signature of a binary black hole (e.g.,
Popović 2012 for a review). However, to claim such a
phenomenon would require extensive tests that are beyond the
current paper, which is aimed at measurement of the time delay
of the Mg II line.
4. Results: Time-delay determination
To determine the most probable time delay between the
continuum and Mg II line emission, we applied several
methods as previously in Czerny et al. (2019) and Zajaček
et al. (2020), namely:
1. interpolated cross-correlation function (ICCF),
2. discrete correlation function (DCF),
3. z-transformed discrete correlation function (zDCF),
4. the JAVELIN package,
5. measures of data regularity/randomness—von Neumann
and Bartels estimators,
6. χ2
method.
These seven methods are described in detail in Appendix C,
including their strengths over other methods. It is beneficial to
compare more methods since our light curves are irregularly
sampled and the continuum light curve is heterogeneous, i.e.,
coming from four different instruments (CATALINA, OGLE,
SALTICAM, and BMT). After the exclusion of low-quality
data points and outliers, we finally obtained 79 continuum
measurements with a mean cadence of 69.0 days (maximum
597.6 days, minimum 0.75 days) and 24 Mg II light-curve data
points with a mean cadence of 121.6 days (maximum 398.9
days, minimum 25.9 days).
For our set of light curves, there were several candidate time
delays present for different methods. A significant time delay
between 600 and 700 days in the observer’s frame was present
for all the methods and we summarize the obtained values for
this peak in Table 1 for the d11mod Fe II template and the
redshift of z = 1.2231. The time delay is not affected
significantly by a different Fe II template, in particular the
template of Kovačević-Dojčinović & Popović (2015) and
Popović et al. (2019) (hereafter denoted as KDP15) with a
slightly different best-fit redshift of z = 1.2330. The ICCF peak
for KDP15 is at 692 days for the observer’s frame; see
Figure 13 in Appendix C.
The significance of the peak between 600 and 700 days was
evaluated using the bootstrap method for several time-delay
techniques, i.e., by randomly selected light-curve subsets. In
addition, for the JAVELIN method, we applied alias mitigation
using downweighting by the number of overlapping data
points; see Appendix C.4. With this technique (see also Grier
et al. 2017), secondary peaks for a time delay longer than 700
days could effectively be suppressed. For the assessment of
other time-delay artifact peaks, we generated mock light curves
using the Timmer–Koenig algorithm (Timmer & Koenig 1995)
with the same light-curve cadence as the observed one; see
Appendix D for a detailed discussion. From the constructed
time-delay probability distributions for all the seven methods,
we could identify clear artifacts due to the sampling for time
delays 200 days as well as for 800 days in the observer’s
frame. The recovery of the true time delay appears to be
challenging for the given cadence and the duration of the
observations, but the combination of more methods is
beneficial in identifying the best candidate for the true time
delay.
4.1. Final Time Delay for the Mg II Line
Combining all the seven methods listed in Table 1, the mean
value in the observer’s frame is t = -
+
658obs 31
29
days. We
visually compare the continuum light curve and the original as
Table 1
Overview of the Best Time Delays for Different Methods
Method Time Delay in the Observer’s Frame (days)
ICCF -
+
672 37
49
DCF -
+
656 73
18
zDCF -
+
646 57
63
JAVELIN -
+
645 41
55
von Neumann estimator -
+
635 66
32
Bartels estimator -
+
644 45
27
χ2
method -
+
706 61
70
Observer’s frame mean -
+
658 31
29
Rest-frame mean (z = 1.2231) -
+
296 14
13
Note. The time delay is expressed in light-days in the observer’s frame. The
last two rows contain the mean time delays in the observer’s frame and in the
rest frame for a redshift of z = 1.2231.
6
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
151
well as the time-shifted light curve of the Mg II line in Figure 3.
For an easier comparison, the Mg II line is shifted toward larger
magnitudes by the difference in the mean values of the two
light curves (1.74 mag). The correlation between the continuum
and the shifted Mg II light curve, although present, is not
visually improved with respect to the zero time lag. This is not
unexpected since our source does not exhibit such a large
variability amplitude as sources with a low Eddington ratio. In
addition, even when the line-emission light curve is shifted by
the fiducial time delay, it can intrinsically exhibit periods when
the line emission is decorrelated with respect to the continuum
emission, which is referred to as the emission-line or the BLR
holiday (studied in more detail for NGC 5548, Dehghanian
et al. 2019). This justifies the need to use several robust
statistical methods to assess the best time delay. We also tried
to subtract a linear trend from both light curves, but since for
both of them the slope is consistent with zero within fitting
uncertainties, it did not yield an improvement. Even for a
noticeable linear trend, as for instance for HE 0413-4031
(Zajaček et al. 2020), detrending actually led to a decrease in
the correlation coefficient at the fiducial time delay. Hence, the
subtraction of a linear trend should be tested on a larger set of
sources to assess statistical relevance in terms of time-delay
determination.
Subsequently, we obtain the mean rest-frame value of
t t= + = -
+
z1 296rest obs 14
13
( ) days for the redshift of
z = 1.2231. The light-travel distance of the Mg II emission
zone can then be estimated as t~ =R cMg restII
´ =-
+
-
+
7.7 10 cm 0.249 pc0.4
0.3 17
0.012
0.011
. The rest-frame time delay
is comparable within uncertainties to the time delay of the
previously analyzed highly accreting quasar HE 0413-4031
(z = 1.38, Zajaček et al. 2020).
4.2. Estimate of Black Hole Mass
Taking into account the rest-frame time delay of
t = -
+
296rest 14
13
days and the Mg II FWHM in the mean
spectrum of = +
-FWHM 3695 km sMg 21
21 1
II , we can estimate
the central black hole mass under the assumption that Mg II
emission clouds are virialized. Using the anticorrelation
between the virial factor and the line FWHM according to
Mejía-Restrepo et al. (2018),
=
 -

f
FWHM
3200 800 km s
, 3MR
Mg
1
1.21 0.29
II
⎛
⎝
⎞
⎠
( )
we obtain fMR ∼ 0.84. The virial black hole mass can then be
calculated using the Mg II FWHM in the mean spectrum
and the measured time delay as = ´-
+
M f 6.6vir
FWHM
MR 0.3
0.3
( ) ( )
M108
. Adopting the virial factor according to Woo et al.
(2015), fWoo = 1.12 (based on FWHM of the Hβ line), we
obtain the virial black hole mass = ´-
+
M f 8.8vir
FWHM
Woo 0.4
0.4
( ) ( )
M108
. Here we adopted the FWHM from the mean spectrum
since it is better constrained than the rms FWHM. The mean
values, however, are consistent within uncertainties, which is in
agreement with the general correlation of Mg II line widths
measured in the mean and the rms spectra using the SDSS-RM
sample (Wang et al. 2019).
Using instead the Mg II line dispersion in the mean
spectrum, s = +
-2707 km s6
10 1, and the associated virial factor
fσ = 4.47 (based on the Hβ line dispersion) according to Woo
et al. (2015), the black hole mass is estimated as
= ´s
s -
+
M f M1.89 10vir 0.09
0.08 9( ) ( ) . This value is consistent with
the value inferred from the broadband SED fitting using the
model of a thin accretion disk according to Sredzińska et al.
(2017), where they obtained MSED = 2.2 × 109
Me. Hence for
our source, using the line dispersion inferred from the mean
spectrum (the rms spectrum is too noisy to reliably measure σ)
appears to be beneficial for constraining the virial SMBH mass.
Using the FWHM yields a virial mass below that inferred from
broadband fitting.
Next, we estimate the Eddington ratio. Using our continuum
light curve, the mean V-band magnitude is 17.15 ± 0.09 mag.
With the redshift of z = 1.2231 and the mean Galactic
foreground extinction in the V band of 0.045 mag according
to NED,14
we determine the luminosity at 3000 Å,
=-
-
+
Llog erg s 46.3593000
1
0.034
0.038
( [ ]) , for which we apply the
conversions of Kozłowski (2015). To estimate the bolometric
luminosity, the corresponding bolometric correction can be
obtained via the simple power-law scaling by Netzer (2019),
k = ´ ~- -L25 10 erg s 3.36bol 3000
42 1 0.2[ ] , which yields
Lbol = 3.36L3000 ∼ 7.68 × 1046
erg s−1
. The Eddington limit
can be estimated for M• ; 2 × 109
Me, which was obtained
via the SED fitting as well as the virial mass using the line
dispersion, LEdd ; 2.5 × 1047
× (M•/(2 × 109
Me)) erg s−1
.
Finally, the Eddington ratio is η = Lbol/LEdd ∼ 0.31, which is
about a factor of two smaller than the Eddington ratio of 0.58
obtained by Sredzińska et al. (2017) using the SED fitting. Still,
the source is highly accreting, with η comparable to HE 0413-
4031 (η = 0.4, Zajaček et al. 2020).
The highly accreting sources exhibit the largest scatter with
respect to the standard RL relation, with a trend of shorter
time delays by a factor of a few than expected based on their
monochromatic luminosity. This was studied for the Hβ
reverberation-mapped sources (Du et al. 2015, 2016; MartínezAldama
et al. 2019), and confirmed for the higher-redshift Mg II
reverberation-mapped sources as well (Homayouni et al. 2020;
Martínez-Aldama et al. 2020; Zajaček et al. 2020), which
suggests a common mechanism for time-delay shortening driven
by the accretion rate. The relation between the rest-frame time
Figure 3. Comparison of the continuum and the shifted Mg II light curves.
Top: the continuum and the original Mg II light curve. Bottom: the continuum
and the Mg II light curve shifted by the mean time delay of 658 days in the
observer’s frame.
14
https://ned.ipac.caltech.edu/
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152 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
delay of the Hβ line and the linear combination of the
monochromatic luminosity at 5100 Å and the relative strength
of the Fe II line (flux ratio between Fe II and Hβ lines) yields a
low scatter of only σrms = 0.196 dex (Du & Wang 2019),
which suggests that the relative Fe II strength and hence the
accretion rate can account for most of the scatter.
In addition, highly accreting Mg II reverberation-mapped
sources exhibit a generally lower scatter along the multidimensional
RL relations (Martínez-Aldama et al. 2020). This
motivates us to further study how high-luminosity and highly
accreting sources such as HE 0435-4312 affect the scatter along
the radius–luminosity relation on their own as well as in
combination with independent observables, such as the Mg II
line FWHM, the Fe II strength RFe II, and the fractional
variability Fvar of the continuum, where the latter two
parameters are correlated with the accretion rate.
4.3. Position in the Radius–Luminosity Plane
The high luminosity of HE 0435-4312 is expected to be
beneficial for constraining the Mg II-based radius–luminosity
relation. We add HE 0435-4312 to the original sample of 68
Mg II reverberation-mapped sources studied in MartínezAldama
et al. (2020). To characterize the accretion rate of
our source and in order to compare it with other sources, we
make use of the dimensionless accretion rate  expressed
specifically for 3000 Å as (Wang et al. 2014; Martínez-Aldama
et al. 2020)
q
= -

L
m26.2
cos
, 444
3 2
7
2⎛
⎝
⎞
⎠
( )
where L44 is the luminosity at 3000 Å expressed in units of
1044
erg s−1
and m7 is the central black hole mass expressed in
units of 107
Me. The angle θ is the inclination angle with
respect to the accretion disk and we set q =cos 0.75, which
represents the mean inclination angle for type I AGNs
according to studies of the covering factor of the dusty torus
(see, e.g., Lawrence & Elvis 2010; Ichikawa et al. 2015).
Using Equation (4) and the estimate of black hole mass
based on the line dispersion in the mean spectrum and the
broadband SED fitting, we obtain = -
+
 4.0 0.6
0.7 or =log 
-
+
0.61 0.06
0.07
for HE 0435-4312, which puts it into the highaccretor
category according to Martínez-Aldama et al. (2020),
where all the Mg II reverberation-mapped sources with
>log 0.2167 belong (median value of their Mg II sample).
Using the smaller SMBH mass based on Mg II FWHM in
the mean spectrum yields a larger  by a factor of a few,
= -
+
log 1.51 0.06
0.07 (based on fMR) and = -
+
log 1.26 0.06
0.07
(based on fWoo). In the further analysis, we adopt the  value
based on the line dispersion in the mean spectrum because of
the consistency of s
sM fvir ( ) with the SMBH mass inferred from
the broadband fitting of Sredzińska et al. (2017). In Figure 4
(left panel), we plot the RL relation for all 69 sources including
HE 0435-4312 (green circle). In the right panel of Figure 4, we
restrict the RL relation to only highly accreting sources, which
results in a significantly reduced rms scatter of σrms = 0.1991
dex versus σrms = 0.2994 dex for the full sample. Adding HE
0435-4312 results in a small but detectable reduction of scatter
for both the full sample (0.2994 versus 0.3014) and the highly
accreting subsample (0.1991 versus 0.2012) with respect
to the original Mg II sample of 68 sources (Martínez-Aldama
et al. 2020).
In the extended RL relations that include other independent
observables in the linear combination of logarithms, namely
Mg II line FWHM, the relative Fe II strength with respect to
the Mg II line RFe II, and the continuum fractional variability
Fvar, HE 0435-4312 lies within 1σ of the mean relation for
both the full sample and the highly accreting subsample; see
Figure 5 for the combination with FWHM, Figure 6 that
includes RFe II, and Figure 7 that utilizes the continuum Fvar.
When one restricts the analysis to the highly accreting
subsample, the rms scatter drops below 0.2 dex in all
combinations, with the smallest scatter exhibited by the RL
relation including RFe II (σrms = 0.1734 dex). In Table 2, we
summarize the best-fit parameters as well as the rms scatter for
all the RL relations for the highly accreting subsample
including HE 0435-4312. Our high-luminosity source is
Figure 4. Left panel: Mg II-based radius–luminosity relation including all 68 Mg II reverberation-mapped sources studied in Martínez-Aldama et al. (2020) and the
new source HE 0435-4312 denoted by a green circle. The relative UV Fe II strength RFe II is color-coded for each source according to the color axis on the right (except
for NGC 4151 and CTS 252, for which RFe II was not available, and these sources are denoted by empty circles). For HE 0435-4312, we obtained RFe II = EW(Fe II)/
EW(Mg II) ∼ 2.36. Right panel: the same as the left panel, but for highly accreting sources with >log 0.2167 , where the division of high accretors was taken from
Martínez-Aldama et al. (2020) according to the median value of their full sample. The scatter along the RL relation is noticeably lower for high accretors than for the
full sample. In both panels, dashed and dotted lines denote the 68% and 95% confidence intervals, respectively.
8
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
153
Figure 5. Rest-frame time delay expressed as a function of Llog 44( ) and log FWHM3( ). Left panel: the linear combination studied for all 68 Mg II reverberationmapped
sources studied in Martínez-Aldama et al. (2020) and a new source HE 0435-4312 denoted by a green circle. Right panel: as in Figure 4, the linear
combination is restricted to highly accreting sources with the same division according to  . In both panels, each source is color-coded according to the corresponding
Mg II FWHM.
Figure 6. Rest-frame time delay expressed as a function of Llog 44( ) and Rlog Fe II( ). Left panel: the linear combination studied for all 68 Mg II reverberation-mapped
sources studied in Martínez-Aldama et al. (2020) and a new source HE 0435-4312 denoted by a green circle. Right panel: as in Figure 4, the linear combination is
restricted to highly accreting sources with the same division according to  . In both panels, each source is color-coded according to the corresponding relative UV Fe
II strength RFe II.
Figure 7. Rest-frame time delay expressed as a function of Llog 44( ) and Flog var( ). Left panel: the linear combination studied for all 68 Mg II reverberation-mapped
sources studied in Martínez-Aldama et al. (2020) and a new source HE 0435-4312 denoted by a green circle. Right panel: as in Figure 4, the linear combination is
restricted to highly accreting sources with the same division according to  . In both panels, each source is color-coded according to the corresponding continuum
fractional variability Fvar.
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The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
154 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
beneficial for the reduction of rms scatter, except for the
combination including RFe II, where the rms scatter marginally
increases in comparison with the best-fit result of MartínezAldama
et al. (2020). For all RL relations, adding the new
quasar leads to an increase in the Pearson correlation
coefficient. For the comparison of the rms scatter and the
correlation coefficients with and without the inclusion of HE
0435-4312, see the last four columns of Table 2.
The dimensionless accretion rate  of Mg II sources
defined by Equation (4) is intrinsically correlated with the
rest-frame time delay via the black hole mass ( tµ - 2 ,
while the Eddington ratio η ∝ τ−1
) as discussed by MartínezAldama
et al. (2020). Therefore we do not use  in extended
RL relations, because the correlation would be artificially
enhanced. We merely use  for the division of the sample
into the high and low accretors. For the extended RL relations,
we prefer the independent observables Mg II FWHM, UV
RFe II, and Fvar. Characterizing the accretion-rate intensity by
 is justified by its correlation with the relative UV Fe II
strength RFe II, which in turn is related to the accretion rate
(Dong et al. 2011; Martínez-Aldama et al. 2020), which was
analogously shown for optical Fe II strength (Shen &
Ho 2014; Du & Wang 2019). For the whole sample of Mg
II sources, including HE 0435-4312, for which RFe II can be
estimated (in total 66 sources), the Spearman correlation
coefficient between  and RFe II is positive with ρ = 0.440
(with a p-value of 2.19 × 10−4
). For the same sample, the
relative Fe II strength is in turn positively correlated with the
Eddington ratio η = Lbol/LEdd with ρ = 0.447 (p = 1.71 ×
10−4
). This justifies the division into low and high accretors
according to  .
On the other hand,  is anticorrelated with respect to the
continuum variability Fvar with ρ = −0.480 (p = 2.97 × 10−5
,
69 sources). Furthermore, the parameter  is anticorrelated
with Mg II FWHM, although the (anti)correlation is weaker
than for RFe II and Fvar with ρ = −0.386 (p = 1.05 × 10−3
, 69
sources). The anticorrelation between Mg II FWHM and  ,
and hence also RFe II, is expected from optical studies of
eigenvector 1 of the quasar main sequence (Boroson &
Green 1992; Sulentic et al. 2000), which can be traced in the
UV plane as well (Kozłowski et al. 2020). These (anti)
correlations between  and other quantities across classical
and extended RL relations are also apparent in the color-coded
plots in Figures 4–7. The reduction in scatter for the high-
subsample could therefore arise due to a lower variability and
the stabilisation of the luminosity and black hole mass ratio for
the sources accreting close to the Eddington limit as discussed
in detail in Martínez-Aldama et al. (2020); see also Ai et al.
(2010) and Marziani & Sulentic (2014).
In order to clarify our idea of the sample division
quantitatively, we divided the sample analyzed by MartínezAldama
et al. (2020), with the studied source HE 0435-4312
included, considering the median values of RFe II and Fvar
( =Rlog 0.02Fe II , = -Flog 1.05var ) instead of  ( =log 
0.23). Since the correlation between  and RFe II is positive,
we expect that the high Fe II emitters show the highest 
values, i.e., above the corresponding median value. On the
other hand, the correlation between Fvar and  is negative,
hence highly accreting AGNs show a lower variability or Fvar
values with respect to the median value of each parameter. In
the case of the  –RFe II correlation, we find that ∼70% of the
sample satisfies the criteria with respect to the median values of
RFe II and  . Meanwhile, for the  –Fvar correlation, ∼72% of
our sources are within the median values considered. This is
graphically shown in Figure 8, where we depict the correlation
 –RFe II (left panel) and the anticorrelation  –Fvar (right
panel) for the studied sample of Mg II sources. Therefore,
we can conclude that the division into low and high accretors
based on  is analogous to a division based on the
independent parameters RFe II and Fvar. To illustrate this, in
Figure 4 we use RFe II for color-coding individual sources in
the RL relation for the whole sample (left panel) and the
high-accretor subsample (right panel).
5. Discussion
By combining the SALT spectroscopy and the photometric
data from more instruments, we were able to determine the restframe
time delay of -
+
296 14
13
days between the Mg II broad line
and the underlying continuum at 3000 Å. Fitting the Mg II line
with the underlying continuum and Fe II pseudocontinuum is
rather complex, but we show in Appendix B that the time-delay
distribution for a different Fe II template is comparable and
does not affect the main time-delay analysis presented in
this paper.
The rest-frame time delay is essentially the same as for
another luminous and highly accreting quasar, HE 0413-4031,
analyzed in Zajaček et al. (2020). While the RL relation for the
collected sample of 69 Mg II reverberation-mapped sources has
a relatively large scatter of ∼0.3 dex, it is significantly reduced
to 0.2 dex when we consider only high accretors, where
HE 0435-4312 also belongs with an Eddington ratio
of ∼0.31–0.58 (the corresponding dimensionless accretion rate
is = -
+
 4.0 0.6
0.7 ). Further reduction of the scatter is achieved in
the 3D RL relations that include independent observables
(FWHM, RFe II, and Fvar). Especially, the linear combination
including the relative strength of Fe II leads to the smallest
scatter of 0.17 dex. Because of the correlation between RFe II
and  (Martínez-Aldama et al. 2020), this indicates that the
Table 2
Parameters for The Standard RL Relation as Well as Multidimensional RL Relations Including Independent Observables, Namely FWHM, RFe II, and Fvar, for the
Highly Accreting Subsample (35 Sources Including HE 0435-4312)
tlog obs K1 K2 K3 σrms [dex] r σrms [dex] (without) r (without)
+K L Klog1 44 2 0.422 ± 0.055 1.374 ± 0.082 L 0.1991 0.80 0.2012 0.78
+ +K L K Klog logFWHM1 44 2 3 3 0.43 ± 0.06 −0.13 ± 0.31 1.44 ± 0.17 0.1986 0.80 0.2007 0.78
+ +K L K R Klog log1 44 2 Fe 3II 0.45 ± 0.05 0.84 ± 0.29 1.28 ± 0.08 0.1734 0.85 0.1718 0.84
+ +K L K F Klog log1 44 2 var 3 0.39 ± 0.06 −0.38 ± 0.18 0.99 ± 0.19 0.1861 0.83 0.1863 0.82
Note. The last four columns show rms scatter and Pearson’s correlation coefficient with and without HE 0435-4312 for comparison.
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The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
155
scatter along the RL relation is driven by the accretion rate, as
we already showed in Zajaček et al. (2020) for a sample of only
11 Mg II sources.
In the following subsection, we further discuss some aspects
of the Mg II variability, focusing on the interpretation of a
relatively large variability of the Mg II line for our source.
Then, using the sample of 35 high accretors that exhibit a small
scatter along the RL relation, we show how it is possible to
apply the radius–luminosity relation to constrain cosmological
parameters.
5.1. Variability of Mg II Emission
The fractional variability of the Mg II line of HE 0435-4312
is F 5.4%var
line
 (excluding observation 19). The continuum
fractional variability is larger, F 8.8%var
cont
 over 14.74 yr.
However, when the continuum light curve is separated into the
first 7 yr (CATALINA), F 4.8%var
cont1
 , and the last 6 yr
(SALT monitoring), F 4.8%var
cont2
 , then both values are
comparable to the fractional variability of Mg II emission.
This implies that Mg II-emitting clouds reprocess the
continuum emission very well for our source. In other words,
the triggering continuum and a line echo have similar
amplitudes, suggesting that sharp echoes are present and that
the Mg II-emitting region lies on (or close to) an isodelay
surface, which is an important geometrical condition. In
addition, the variability timescale of the continuum must be
long enough, i.e., longer than the light-travel time through the
locally optimally emitting cloud (LOC) model of the BLR. It
seems that both conditions are fulfilled for our source.
This is in contrast with the study of Guo et al. (2020), who
used the CLOUDY code and the LOC model to study the
response of Mg II emission to the variable continuum. They
found that at the Eddington ratio of ∼0.4, the Mg II emission
saturates and does not further increase with the rise in the
continuum luminosity. Observationally, Yang et al. (2020)
found for extreme-variability quasars that Mg II emission
responds to the continuum but with a smaller amplitude,
D =  DL Llog Mg 0.39 0.07 log 3000II( ) ( ) ( Å). Although
our source has a high Eddington ratio comparable to that
studied in Guo et al. (2020), η ∼ 0.3–0.6, its Mg II emission
responds very efficiently to the variable continuum. For the
previous highly accreting luminous quasar HE 0413-4031 that
we studied (Zajaček et al. 2020), we also showed that the Mg II
line can respond strongly to the increase in the continuum,
D =  DL Llog Mg 0.82 0.26 log 3000II( ) ( ) ( Å), as shown by
the intrinsic Baldwin effect.
A possible interpretation of the discrepancy between the
saturation of Mg II emission at larger Eddington ratios modeled
nominally by Guo et al. (2020) and our two highly accreting
sources, HE 0435-4312 and HE 0413-4031, which exhibit a
strong response of the Mg II emission to the continuum, is an
order-of-magnitude difference in the black hole mass as well as
in the studied luminosity at 3000 Å. In Guo et al. (2020), they
used M• = 108
Me and L3000 = 1044
–1045
erg s−1
as well as
(Rout, Γ) = (1017.5
, −2) for the outer radius and the slope of the
LOC model, respectively. For our source, all of the
characteristic parameters are increased: M• ; 2 × 109
Me,
L3000 ; 1046.36
erg s−1
, and RMg II = 1017.9
cm. Mainly the
larger outer radius implies that not all of the Mg II-emitting
gas is fully ionized at these scales and can exhibit “partial
breathing,” as is also shown by Guo et al. (2020) for the case
with Rout = 1018
cm, when the Mg II line luminosity continues
to rise with the increase in the continuum luminosity.
Figure 8. Relation between the dimensionless accretion rate  and the relative UV Fe II strength RFe II and the continuum fractional variability Fvar. Left panel: the
positive correlation between  and RFe II (Spearman correlation coefficient ρ = 0.44; p = 2.2 × 10−4
). The dashed lines mark the median values of each
parameter. When the sample is divided according to the median of RFe II, ∼ 70% of high-/low- sources are present. The star symbol marks HE 0435-4312. Right
panel: the anticorrelation between  and Fvar (Spearman correlation coefficient ρ = −0.48; p = 2.9 × 10−5
). The dashed lines mark the median values of
each parameter. When the Mg II sample is divided according to the median value of Fvar, ∼72% of high-/low- sources are included. The star symbol depicts
HE 0435-4312.
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156 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
5.2. Constraining Cosmological Parameters Using an Mg II
Highly Accreting Subsample
Since the RL relation for a highly accreting Mg II subsample
showed a relatively small scatter of ∼0.2 dex, we attempt to
use it for cosmological purposes. We adopt the general
approach outlined in Martínez-Aldama et al. (2019), that is
we assume a perfect relation between the absolute luminosity
and the measured time delay, and having absolute luminosity
and the observed flux we can determine the luminosity distance
for each source. We do not use here the best-fit relation given in
Figure 4, right panel, since this relation was calibrated for a
specific assumed cosmology. Therefore we assume a relation in
a general form,
a t b= - +Llog log 44, 53000 ( )
and we treat α and β as free parameters. We consider first the
case of a flat cosmology, and we assume the value of the
Hubble constant H0 = 67.36 km s−1
Mpc−1
adopted from
Planck Collaboration et al. (2020), and we minimize the fits
to the predicted luminosity distance by varying Ωm, α, and β.
The preliminary fit was highly unsatisfactory, and we used a
sigma-clipping method to remove the outliers (eight sources).
The final sample was well fitted with the standard ΛCDM
model for W = -
+
0.252m 0.044
0.051
(1σ error). This result is fully
consistent with the data from Planck Collaboration et al. (2020)
with W = 0.3153 0.0073m
Planck
. The values obtained for the
remaining two parameters were α = 1.8 and β = 2.1, which
would correspond to a slightly different RL relation,
t = +Llog 0.56 log 1.183000 . The results are illustrated in
Figure 9, left panel. We also attempted to constrain both ΩΛ
and Ωm, waiving the assumption of a flat space. The parameters
α and β in Equation (5) were kept fixed to the values inferred
from the flat-cosmology fit, i.e., α = 1.8 and β = 2.1. The result
is given in the right panel of Figure 9. The best fit in this case
implies a slightly lower Ωm, but the contour error is large and
covers the best fit from Planck Collaboration et al. (2020)
within the 1σ confidence level. The data do not yet tightly
constrain the cosmological parameters, but the Mg II highly
accreting subsample does not imply any departures from the
standard model, and the data quality is much higher, and
constrains the parameters better than the larger sample based on
the Hβ line and discussed in Martínez-Aldama et al. (2019),
and somewhat better than the mixed sample discussed in
Czerny et al. (2020).
6. Conclusions
Our main conclusions from the reverberation mapping
analysis of the source HE 0435-4312 (z = 1.2231,
=-
-
+
Llog erg s 46.3593000
1
0.034
0.038
( [ ]) ) can be summarized as
follows.
1. Using seven different methods, we determined the mean
rest-frame time delay of -
+
296 14
13
days, with all the
methods giving a consistent time-delay peak within
uncertainties that were determined using the bootstrap or
the maximum-likelihood method. By combining the
bootstrap method, the weighting by the number of
overlapping data points, and the analysis of mock light
curves, we could classify the other prominent time-delay
peaks as artifacts due to the particular sampling and a
limited observational duration.
2. The fractional variability of Mg II emission (∼5.4%) is
comparable to the continuum variability, hence the Mg II
line flux for our source has not reached the saturation
level despite the high Eddington ratio of ∼0.3–0.6. This
is most likely due to the large black hole mass
of ∼2 × 109
Me and the large extent of the Mg IIemitting
region, RMg II = 1017.9
cm.
Figure 9. Constraining cosmological parameters using the highly accreting subsample of Mg II reverberation-mapped sources, including HE 0435-4312. Left panel:
the quasar Hubble diagram using 27 sources (red points), after removal of eight outliers, with the best-fit standard ΛCDM model (black solid line; W = -
+
0.252m 0.044
0.051
with fixed H0 = 67.36 km s−1
Mpc−1
according to Planck Collaboration et al. 2020). The bottom panel shows the residuals D =D D DlogL L
exp
L( ), where DL
exp
is the
expected luminosity distance and DL is the measured one. HE 0435-4312 is marked by a black circle. Right panel: contour plot showing the confidence levels at 68%
(orange) and 95% (brown) for the general ΛCDM model based on χ2
fitting. The yellow star depicts the best-fit (Ωm, ΩΛ) = (0.19, 0.62) and the blue filled circle
shows the cosmological constraints as provided by Planck Collaboration et al. (2020).
12
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
157
3. The large luminosity of HE 0435-4312 is beneficial for
decreasing the scatter and increasing the correlation
coefficient for the Mg II-based radius–luminosity
relation. The scatter is ∼0.2 dex for the highly accreting
subsample of Mg II sources, where HE 0435-4312
belongs. A further reduction in the scatter is achieved
using linear combinations with independent observables
(FWHM, relative Fe II strength, and fractional variability),
which indicates that the scatter along the radius–
luminosity relation is mainly driven by the accretion
rate.
4. A low scatter of the radius–luminosity relation for the
highly accreting subsample motivates us to apply these
sources for constraining cosmological parameters. Given
the current number of sources (27, after removal of eight
outliers) and the data quality, the best-fit values of the
cosmological parameters (Ωm, ΩΛ) = (0.19; 0.62) are
consistent with the standard cosmological model within
the 1σ confidence level.
The project is based on observations made with the
SALT under programs 2012-2-POL-003, 2013-1-POL-RSA-
002, 2013-2-POL-RSA-001, 2014-1-POL-RSA-001, 2014-2SCI-004,
2015-1-SCI-006, 2015-2-SCI-017, 2016-1-SCI-011,
2016-2-SCI-024, 2017-1-SCI-009, 2017-2-SCI-033, 2018-1MLT-004
(PI: B. Czerny). The authors acknowledge the
financial support by the National Science Centre, Poland,
grant No. 2017/26/A/ST9/00756 (Maestro 9), and by the
Ministry of Science and Higher Education (MNiSW) grant
DIR/WK/2018/12. G.P. acknowledges the grant MNiSW
DIR/WK/2018/09. K.H. acknowledges support by the
Polish National Science Centre grant 2015/18/E/ST9/
00580. M.Z. was supported by the NAWA under the
agreement PPN/WYM/2019/1/00064 to perform a
three-month exchange stay at the Charles University and the
Astronomical Institute of the Czech Academy of Sciences in
Prague. M.H. and C.S.F. are supported by Deutsche
Forschungsgemeinschaft grants CH71/33 and CH71/34.
The OGLE project has received funding from the National
Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/
00121. The Polish participation in SALT is funded by
grant No. MNiSW DIR/WK/2016/07. M.Z., V.K., and
B.C. acknowledge PPN/BCZ/2019/1/00069 (MŠMT
8J20PL037) for the support of the Polish-Czech mobility
program. This paper uses observations made at the South
African Astronomical Observatory (SAAO).
Software: IRAF (Tody 1986, 1993), JAVELIN (Zu et al.
2011, 2013, 2016), PyCCF (Sun et al. 2018), vnrm.py
(Chelouche et al. 2017), zdcf_v2.f90 (Alexander 1997),
plike_v4.f90 (Alexander 1997), delay_chi2.f (Czerny et al.
2013), sklearn (Pedregosa et al. 2011), statsmodels (Seabold &
Perktold 2010), numpy (Oliphant 2015), matplotlib (Hunter
2007).
Appendix A
Photometric and Spectroscopic Data
Continuum magnitudes with uncertainties are shown in
Table 3.
Table 3
Continuum Magnitudes with Uncertainties
JD Magnitude (V band) Error Instrument
− 2,450,000 [mag] [mag] No.
3696.98828 16.8733330 2.51584481E-02 1
4067.76562 16.9422932 1.88624337E-02 1
4450.48828 16.9090614 2.42404137E-02 1
4837.18359 17.0258694 1.94998924E-02 1
5190.14453 17.0322189 2.00808570E-02 1
5564.26562 16.9177780 2.75434572E-02 1
5889.63672 16.8666668 2.98607871E-02 1
6296.05078 16.9212513 2.82704569E-02 1
6893.60449 17.1165180 1.20000001E-02 2
6986.31592 17.1647282 1.20000001E-02 2
7032.45020 17.1936970 1.20000001E-02 2
7035.63428 17.1329994 4.00000019E-03 3
7047.64209 17.1079998 4.00000019E-03 3
7058.61475 17.1240005 8.00000038E-03 3
7083.54346 17.1119995 4.99999989E-03 3
7116.50684 17.1089993 8.00000038E-03 3
7253.89209 17.1749992 4.00000019E-03 3
7261.88330 17.1779995 4.00000019E-03 3
7267.91504 17.1630001 4.99999989E-03 3
7273.84717 17.1849995 4.99999989E-03 3
7283.84912 17.1779995 4.00000019E-03 3
7295.84277 17.1889992 6.00000005E-03 3
7306.78125 17.1690006 4.00000019E-03 3
7317.74023 17.1889992 4.99999989E-03 3
7327.77490 17.1959991 6.00000005E-03 3
7340.70654 17.2140007 4.00000019E-03 3
7355.69482 17.1860008 4.99999989E-03 3
7363.66650 17.2159996 4.00000019E-03 3
7364.53760 17.2753944 1.20000001E-02 2
7374.70947 17.2080002 4.00000019E-03 3
7385.55762 17.2049999 4.00000019E-03 3
7398.61768 17.2269993 4.00000019E-03 3
7415.58545 17.2229996 4.00000019E-03 3
7426.56641 17.2010002 4.00000019E-03 3
7436.52539 17.2049999 4.99999989E-03 3
7447.52783 17.2080002 4.00000019E-03 3
7457.52246 17.2089996 4.00000019E-03 3
7655.49414 17.1270580 1.20000001E-02 2
7692.38037 17.1313496 1.20000001E-02 2
7717.70557 17.1089993 4.00000019E-03 3
7754.46582 17.0703278 1.20000001E-02 2
7803.32959 17.1150951 1.20000001E-02 2
7973.91357 17.2000008 1.30000003E-02 3
7984.59424 17.2056389 1.20000001E-02 2
8038.86182 17.1779995 6.00000005E-03 3
8091.25000 17.2399998 9.99999978E-03 4
8102.25000 17.2199993 4.00000019E-03 4
8104.25000 17.2430000 8.99999961E-03 4
8105.00000 17.2430000 4.99999989E-03 4
8107.25000 17.2509995 6.00000005E-03 4
8112.48926 17.2262497 1.20000001E-02 2
8130.25000 17.2639999 8.99999961E-03 4
8138.00000 17.2459984 7.00000022E-03 4
8147.00000 17.2319984 8.00000038E-03 4
8166.00000 17.2319984 2.00000009E-03 4
8182.00000 17.2519989 8.00000038E-03 4
8206.00000 17.2309990 8.99999961E-03 4
8410.25000 17.1949997 8.99999961E-03 4
8540.00000 17.2019997 8.00000038E-03 4
8568.24609 17.1906471 1.20000001E-02 2
8585.50000 17.2489986 8.00000038E-03 4
8775.75000 17.1980000 7.00000022E-03 4
8778.75000 17.2049999 4.00000019E-03 4
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158 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
Appendix B
Redshift and Fe II Template
Precise determination of the redshift for quasar HE 0435-
4312 is challenging, although its spectrum is not affected by
absorption. The original redshift for the quasar, z =
1.232 ± 0.001, was reported by Wisotzki et al. (2000) from
the position of the Mg II line. Marziani et al. (2009) measured
the redshift on the basis of the Hβ line from VLT/ISAAC IR
spectra, deriving z = 1.2321 ± 0.0014. A narrow [O III] line
was also visible in the spectrum, but it was strongly affected by
atmospheric absorption, so it could not serve as a reliable
redshift mark. Sredzińska et al. (2017) determined the redshift
as z = 1.2231 using the data from SALT collected during the
first three years of the SALT monitoring of this source. In this
paper, two kinematic components were used to fit the Mg II
line: one component at the systemic redshift, together with the
Fe II template, and the shift of the second was a model
parameter. What is more, Sredzińska et al. (2017) showed that
the Mg II line position systematically changes with time. Thus
the redshift was mostly determined by the location of the strong
Fe II emission at 2750 Å.
In the currently available set of observations, one set,
obtained on 2019 December 5 (observation 23), was obtained
with a slightly shifted setup, so it covered the spectral range
almost up to 3000 Å in the rest frame (in all other observations,
this region overlaps with a CCD gap). Observed quasar spectra
usually have a clear gap just above 2900 Å, which could serve
as additional help in constraining the redshift, as well as the
optimum Fe II template.
The basic template d11-m20-20.5-735 (marked later as d11)
of Bruhweiler & Verner (2008) (with parameters: plasma
density 1011
cm−3
, turbulence velocity 20 km s−1
, and log of
ionization parameter in cm−2
s−1
of 20.5) favored by
Sredzińska et al. (2017) does not fit well the dip in the region
of 2900 Å (see Figure 10). We also checked other theoretical
templates provided by Bruhweiler & Verner (2008), but all of
them predicted considerable emissivity in that spectral region.
Since the CLOUDY code has been modified over the years, we
calculated new Fe II templates using the newest version of the
code (Ferland et al. 2017), but with the same input as in the
template d11, including the spectral shape of the incident
continuum. New results did not solve the problem, and actually
gave a much worse fit (see Table 4), if the two-Lorentzian
model was assumed for the Mg II line, as in Sredzińska et al.
(2017). If, instead, we used two Gaussians for the line fitting,
the resulting χ2
became much better (see Table 4) but still
higher than with the older template, and the emission above
2900 Å was still overproduced. We thus experimented with
simple removal of a few transitions from the original d11
template. We removed transitions at λλ2896.32, 2901.96,
2907.61, and 2913.28, creating the d11mod template. This
clearly allowed a satisfactory representation of the data to be
achieved, and favored the same redshift as in Sredzińska et al.
(2017).
Next, we tried the KDP15 Fe II templates (KovačevićDojčinović
& Popović 2015; Popović et al. 2019), which have
fewer transitions but an additional flexibility of arbitrarily
changing the normalization of each of the six transitions. This
template provided a good fit for another of the quasars
monitored with SALT (Zajaček et al. 2020). The clear
disadvantage is that fitting these templates is much more
time-consuming, since then the spectral model has 13 free
parameters instead of eight, when the Fe II template has just
one normalization as a free parameter. Nevertheless, we fitted
all parameters at the same time, as in our standard approach.
The KDP15 template gave a rather poor fit for the low values
of redshift favored by Sredzińska et al. (2017), but the model
gave much lower χ2
values for the redshift range suggested by
Marziani et al. (2009) (see Table 4). The best fit for this
template was achieved for the redshift z = 1.2330, even slightly
higher than in Marziani et al. (2009). However, formal χ2
is
still higher than for the d11mod template. Since the two redshifts
and the Fe II templates used for modeling in these two cases are
so different, we checked how this difference in the spectrum
decomposition actually affects the Mg II line. For that purpose,
we subtracted the fitted Fe II template and continuum from the
original spectrum. The result is displayed in Figure 11 (left
panel) in the observer’s frame. As we see, the difference in the
actual Mg II shape is not large, despite large differences in the
Fe II templates. The FWHM of the line is only slightly broader
for KDP15, 3632 km s−1
versus 3507 km s−1
, as determined
from the total line shape. Line dispersion σ measured
as the second moment differs more (3060 km s−1
versus
Table 3
(Continued)
JD Magnitude (V band) Error Instrument
− 2,450,000 [mag] [mag] No.
8788.75000 17.1889992 4.99999989E-03 4
8797.75000 17.2469997 4.99999989E-03 4
8802.50000 17.1669998 1.09999999E-02 4
8805.50000 17.1959991 3.00000003E-03 4
8823.55176 17.1121445 1.20000001E-02 2
8834.75000 17.1529999 9.99999978E-03 4
8838.75000 17.1910000 4.00000019E-03 4
8878.75000 17.1229992 3.00000003E-03 4
8883.50000 17.0970001 2.00000009E-03 4
8892.50000 17.0909996 8.99999961E-03 4
8906.50000 17.1269989 6.00000005E-03 4
8909.50000 17.0479984 8.99999961E-03 4
8913.50293 17.0949993 4.99999989E-03 3
8920.50293 17.1130009 4.00000019E-03 3
8928.26728 17.1011489 0.012 2
9081.58692 17.1188643 0.012 2
Note. The epoch is given as the Julian Dates (−2,450,000). The last column
denotes four different instruments used to obtain the photometric data: 1.
CATALINA, 2. SALTICAM, 3. OGLE, 4. BMT. The BMT photometric points
were shifted by 0.2 mag toward lower magnitudes to optimize the match with
the OGLE photometry.
Table 4
Summary of the Redshift and Fe II Templates Used to Fit Observation 23
Mg II
Model Fe II Template Redshift
FWHM
(Fe II) χ2
Panel in
Figure 10
LL d11 1.2231 3100 1377.59436 a
LL d11BV08-C17 1.2231 3100 1818.21631 b
GG d11BV08-C17 1.2231 3100 1505.38 c
GG d12-MaFer-C17 1.2321 2800 1517.13757
LL d11mod 1.2231 3100 1296.09912 d
LL KDP15 1.2321 3600 1408.91748
LL KDP15 1.2321 4000 1400.57812 e
LL KDP15 1.2330 4000 1370.64978 f
14
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
159
3423 km s−1
) but in both cases the ratio FWHM/σ is much
smaller than expected for a Gaussian profile.
Since fitting the full six-transition KDP15 template is timeconsuming,
and we do not expect considerable changes in Fe II
shape in the SALT data, we constructed a new single-parameter
template based on KDP15, taking the relative values of the six
components from the best fit of observation 23 in the extended
wavelength range, and using the (best) Fe II broadening of
4000 km s−1
. With this new template KDP15, we refitted all
SALT observations in the range 2700–2900 Å . For 17
observations c c<d11
2
KDP15
2
mod
, and for eight KDP15 fitted
the data better, but generally not significantly; see Figure 11
(right panel). We thus perform most of the time-delay
computations with the d11mod template, and we illustrate the
role of the template in the time-delay determination for the
ICCF method—see Appendix C.1, where we show that the
Figure 11. Comparison between the fits of the observed Mg II and Fe II complexes performed using d11mod and KDP15 models. Left panel: Mg II line shape in the
observer’s frame after subtraction of Fe II and a power law with models d11mod from panel (d) of Figure 10 (red line) and KDP15 from panel (f) (blue line). The
normalization is the same as in Figure 10, so the slight difference in the line normalization between the two models is visible. Right panel: the ratio of χ2
values
between the fits performed using the d11mod model (z = 1.2231) and the KDP15 model (z = 1.2330) for available observational epochs. For 17 epochs out of
25, c c<d11
2
KDP15
2
mod
.
Figure 10. Selected models of observation 23 from Table 4.
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160 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
KDP15 template is associated with a comparable crosscorrelation
function and similar peak and centroid distributions
as those for d11mod; see Figure 13.
Appendix C
Overview of Methods for Time-delay Determination
C.1. Interpolated Cross-correlation Function
We first analyzed the continuum and Mg II line-emission
light curves using the interpolated cross-correlation function,
which is a standard and well-tested method for assessing the
time delay between the continuum and the line emission flux
density (Peterson et al. 1998). Light curves are typically
unevenly sampled, while the ICCF works with the continuum–
line emission pairs with a certain time step of Δt = ti+1 − ti.
The cross-correlation function for two light curves, xi and yi,
with the same time step of Δt achieved by interpolation,
evaluated for a time shift of τk = kΔt (k = 1, K, N − 1), is
defined as
å
å å
t
=
- -
-
=
-
+
= =
N x x y y
N x x N y y
CCF
1
1 1
.
C1
k
i
N k
i i k
i
N
i i
N
i
1
1
2
1 2
1
2
1 2
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
( )
( ) ( )( )
( ) ( ) ( ) ( )
( )
/
/ /
The same time step Δt can be achieved by interpolating the
continuum light curve with respect to the line-emission light
curve and vice versa (asymmetric ICCF). Typically, both
interpolations are averaged to obtain the symmetric ICCF.
For the time-delay analysis, we use the Python implementation
of ICCF in code PYCCF by Sun et al. (2018), which is
based on the algorithm by Peterson et al. (1998). The code
allows one to perform both asymmetric and symmetric
interpolation. Based on the Monte Carlo techniques of random
subset selection and flux randomization, one can obtain the
centroid and the peak distributions and their corresponding
uncertainties.
We studied the time delay between the continuum light
curve consisting of 81 measurements, with eight Catalinasurvey
averaged detections, 16 SALTICAM measurement, 27
BMT data, and 30 OGLE data. Two SALTICAM measurements
were excluded based on their poor quality. The
emission-line light curve consists of 25 SALT measurements,
where the 19th measurement has a poor quality due to weather
conditions and is excluded from the further analysis. Hence, we
have 79 continuum points with a mean cadence of 69.0 days
and 24 Mg II flux-density measurements with a mean cadence
of 121.6 days. We set the interpolation interval to one day. For
the redshift of z = 1.2231 and the d11mod template, we display
the ICCF as a function of time delay in the observer’s frame in
Figure 12 (left panel) for both asymmetric and symmetric
interpolation. In the middle and right panels, we show the
centroid and the peak distributions for the symmetric
interpolation based on 3000 Monte Carlo realizations of
random subset selection and flux randomization. The centroid
and the peak are generally not well defined. The peak value of
the correlation function for the symmetric interpolation is 0.32
for a time delay of 635 days, which is less than for our previous
quasars CTS C30.10 (peak CCF of ∼0.65, Czerny et al. 2019;
Zajaček et al. 2019) and HE 0413-4031 (peak CCF of 0.8,
Zajaček et al. 2020). In the next step, we focus on the
surroundings of this peak and we analyze the CCF centroid and
peak distributions in the interval between 500 and 1000 days.
The results for all interpolations are summarized in Table 5.
For the symmetric interpolation, we obtain a centroid time
delay of t = -
+
663cent 40
66
days and a peak time delay of
t = -
+
672peak 37
49
days.
We also performed the time-delay analysis using the ICCF
for the Mg II light curve derived using the KDP15 template
(case f in Table 4). For the symmetric ICCF, the CCF peak
value is 692 days with CCF = 0.36, which is comparable to the
analysis performed for the d11mod template. The CCF peak and
centroid distributions also contain the same subpeaks, with the
peak close to 700 days being the most prominent; see
Figure 13.
Figure 12. The interpolated cross-correlation function as a function of the time delay expressed in days in the observer’s frame. The calculation is performed for the
d11mod template and the redshift of z = 1.2231. Left panel: the ICCF as a function of the time delay expressed in days in the observer’s frame for three types of
interpolation: interpolated continuum light curve (green solid line), interpolated line light curve (blue solid line), and the symmetric interpolation (black solid line).
Middle panel: the distribution of the cross-correlation centroids for the symmetric interpolation. Right panel: the distribution of the cross-correlation peaks for the
symmetric interpolation.
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161
C.2. Discrete Correlation Function
For unevenly sampled and sparse light curves, the ICCF can
distort the best time delay by adding additional data points to
one or both light curves. In that case, the discrete correlation
function (DCF) introduced by Edelson & Krolik (1988) is
better suited to determine the best time lag.
In general, the DCF value is determined for any pair of light
curves (xi, yj) whose time difference Δtij falls into the timedelay
bin of size δτ, τ − δτ/2 < Δtij < τ + δτ/2, where τ is a
given time delay. First, one calculates the unbinned DCF,
s s
=
- -
-
x x y y
s s
UDCF , C2ij
i j
x x y y
2 2
( )( )
( )
where x and y are light-curve means in a given time-delay bin,
sx and sy are corresponding light curve variances, and σx and σy
are the mean measurement errors of the light-curve points in
the given time-delay interval.
The DCF is then calculated as a mean over M light-curve
points that are located in a given bin,
åt =
M
DCF
1
UDCF . C3
ij
ij( ) ( )
The uncertainty can be estimated using the relation
ås t=
-
-
M
1
1
UDCF DCF . C4ijDCF
2[ ( )] ( )
We made use of the Python script pyDCF (Robertson et al.
2015), where the general procedure described using
Equations (C2), (C3), and (C4) is implemented. We searched
for the DCF peak in the time interval from 100 to 1000 days,
with a time step of 50 days. We obtained a better defined DCF
peak using the Gaussian weighting scheme than using the slot
weighting. In Figure 14 (left panel), we show the DCF versus
time delay in the observer’s frame. The time delay with the
highest DCF value of 0.41 ± 0.16 is at 675 days. To determine
the uncertainty of the peak, we ran 1000 bootstrap simulations,
where at each step we constructed a pair of new light curves by
randomly selecting a light-curve subset. The histogram of peak
DCF time delays constructed from 1000 bootstrap realizations
is shown in Figure 14 (right panel). The peak of the distribution
is at t = -
+
656DCF 73
18
days in the observer’s frame. The left and
right uncertainties represent standard deviations, where we
included the area within 30% of the main peak.
C.3. z-Transformed Discrete Correlation Function
In the following, we applied the z-transformed discrete
correlation function (Alexander 1997), which improves the
classical DCF by replacing equal time binning by equal
population binning. This is achieved by applying Fisher’s ztransform.
With this property, the zDCF processes satisfactorily
especially undersampled, sparse, and heterogeneous light
curves, which to some extent is the case here, since the
continuum light curve originates from three different instruments
and the Mg II light curve is relatively sparse with respect
to the continuum (24 versus 79 points). In our analysis, we
applied the zDCF method several times, changing the
minimum number of light-curve pairs per population bin.
Finally, we set the minimum number of light-curve pairs to
eight and used 5000 Monte Carlo-generated pairs of light
curves to determine the errors in each bin. In Figure 15, we
show the zDCF values as a function of time delay in the
observer’s frame. There are some peaks with a large DCF value
within the first 200 days in the rest frame, e.g., 190.3 days
Table 5
Summary of the Time-delay Determination for the Quasar HE 0435-4312
Using the ICCF
Interpolation Method Time Delay (z = 1.2231)
Interpolated continuum—centroid [days] -
+
635 34
31
Interpolated continuum—peak [days] -
+
630 46
42
Interpolated line—centroid [days] -
+
673 50
60
Interpolated line—peak [days] -
+
683 48
38
Symmetric—centroid [days] -
+
663 40
66
Symmetric—peak [days] -
+
672 37
49
Note. We list the centroids as well as the peaks for the interpolated continuum
light curve, the interpolated line emission light curve, and the symmetric
interpolation. Time delays are expressed in days in the observer’s frame of
reference.
Figure 13. The same ICCF analysis as in Figure 12 but for the KDP15 template (case f in Table 4) and the redshift of z = 1.2330.
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162 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
(DCF = 0.69). These are, however, too short to correspond to
the realistic rest-frame time delay for our highly luminous
quasar. The most prominent peak at larger time delays is at 646
days (DCF = 0.46).
Next we calculate the maximum likelihood (ML) using the
zDCF values and we focus on the prominent peak in the
interval between 500 and 800 days. From the ML analysis, we
obtain the ML peak of t = -
+
646zDCF 57
63
days in the observer’s
frame. This peak and the corresponding uncertainties are also
highlighted in Figure 15 by vertical lines.
C.4. The JAVELIN Package
Another technique to evaluate the time-delay distribution is
to model the continuum variability of AGNs as a stochastic
process using the damped random walk process (Kelly et al.
2009; Kozłowski et al. 2010; MacLeod et al. 2010;
Kozłowski 2016). Subsequently, the line emission is assumed
to be time-delayed, smoothed, and a scaled version of the
continuum emission. This method is implemented in the
JAVELIN package (Just Another Vehicle for Estimating
Lags in Nuclei; Zu et al. 2011, 2013, 2016)15
. The package
uses Markov Chain Monte Carlo (MCMC) methods to first
determine the posterior probabilities for the continuum
variability timescale and the amplitude. Based on that, the
variability of the line emission is modeled to obtain the
posterior probabilities for the time lag, smoothing width of
the top-hat function, and the scaling ratio (the ratio between the
line and the continuum amplitudes, Aline/Acont).
First, we searched for the time delay in the longer interval
between 0 and 2000 days in the observer’s frame. There are
four distinct peaks (see Figure 16, left panel) at ∼100, ∼650,
∼1300, and ∼2000 days. The first peak is too short, while the
last two appear too long for our data set. In the zDCF analysis
in Section C.3, the time-delay peaks at 1000 days and more
also have large uncertainties. Therefore, in the next search, we
perform a time-delay search in the narrower interval between 0
and 1000 days to focus on the intermediate peak at ∼650 days.
We obtain a prominent peak at ∼652 days; see Figure 16 (right
panel).
To determine the precise position of the time-delay peak, we
performed 200 bootstrap simulations—i.e., generating 200
subsets of the original continuum and Mg II light curves. Then
we applied the JAVELIN to determine the peak time delay for
each individual pair of light curves. From 200 best time delays,
we first construct a density plot in the plane of the time delay
and the scaling factor; see Figure 17 (left panel). We see that
there is a peak in the distribution close to 600 days in the
observer’s frame. In Figure 17 (right panel), we show the
histogram of the best time delays with the peak value of
t = -
+
645peak 41
55
days, where the uncertainties were determined
within 30% of the peak value.
For the JAVELIN time-delay determination, we typically
notice several narrow comparable peaks in the histogram of
time delays for a single MCMC run as can be seen in Figure 16.
These secondary peaks typically arise due to a limited duration
of observational runs and a sparse and/or nonuniform sampling
of continuum and line-emission light curves. However, they
might also reflect the complex BLR geometry seen in advanced
Figure 14. Discrete correlation function vs. a time delay in the observer’s frame using the d11mod template. Left panel: a DCF vs. time delay in the observer’s frame. A
red vertical line denotes the peak DCF. Right panel: histogram of peak DCF time delays constructed from 1000 bootstrap realizations. The red and dashed green
vertical lines denote the histogram peak and its left and right standard deviations within 30% of it, respectively.
Figure 15. The zDCF as a function of the time delay in the observer’s frame.
The uncertainties in each population bin were inferred from 5000 Monte Carlogenerated
pairs of light curves (using the observed measurement errors). The
red vertical line marks the most prominent, maximum-likelihood peak of
-
+
646 57
63
days, while the green vertical dashed lines mark the uncertainties.
15
http://www.astronomy.ohio-state.edu/~yingzu/codes.html#javelin
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The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
163
data analysis or models (e.g., Grier et al. 2017; Hu et al. 2020;
Horne et al. 2021; Naddaf et al. 2021). As mentioned in Grier
et al. (2017), these alias peaks can be of a comparable
significance to the true peak in the time-delay distribution,
which is also the case here; see Figure 18 (right panel, black
line), where time delays at ∼105, ∼1300, and ∼1980 days
appear to have a larger significance than the fiducial peak of
∼650 days in the observer’s frame.
Following Grier et al. (2017), we weight the posterior
probability distribution of time delays by the number of
overlapping light-curve points, where the prior probability
distribution is given by P(τ) = [N(τ)/N(0)]2
, where N(τ)
denotes the number of overlapping light-curve points for the
time delay τ, and N(0) is the number of data points in the
overlap region for zero time lag. Hence, the weight is P(τ) = 1
by definition for zero time lag and it will decrease for larger
positive and negative time lags, being zero when there is no
overlap. For our light curves, we construct the prior probability
distribution P(τ), which is shown in Figure 18 (left panel).
Using P(τ), we weight the posterior time-delay distribution
based on the number of overlapping light-curve points. This is
demonstrated in Figure 18 (right panel, red line). The alias
mitigation based on P(τ) helps to effectively suppress longer
time-delays, which drop in significance below the fiducial time
lag at ∼655 days. However, this technique is not efficient to
suppress aliases at shorter time delays of ∼100 days, where the
decrease is negligible due to the definition of P(τ). This peak at
smaller time delays is effectively mitigated by the bootstrap or
random subset selection technique. As we showed in Figure 17,
this peak is not further represented in the posterior time-delay
Figure 16. The time-delay determination for HE 0435-4312 using the JAVELIN package. Left panel: the time-delay search in the interval between 0 and 2000 days in
the observer’s frame. There are four distinct peaks at ∼100, ∼650, ∼1300, and ∼2000 days. Right panel: the time-delay search in the narrower interval between 0 and
1000 days yields a clear peak at ∼652 days.
Figure 17. Bootstrap analysis of the BLR time delay in HE 0435-4312 using the JAVELIN package. Left panel: the distribution of 200 best time delays in the plane of
the time delay (in the observer’s frame) and the scaling factor Aline/Acont. There is a prominent peak in the distribution close to 600 days. Right panel: the histogram of
200 best time delays. The peak value is at t = -
+
645peak 41
55
days, which is marked by the vertical red and green dotted lines. The uncertainty is determined as the
standard deviation within 30% of the main peak.
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164 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
distribution, which leaves us with the fiducial peak close to
∼650 days. In addition, in Appendix D we show that the
artifact peaks at 200 days arise in the probability density
distributions (see Figures 22 and 23) constructed from mock
light curves that are sampled with the same cadence as the
original continuum and line-emission light curves.
C.5. Measures of Data Regularity/Randomness—von Neumann
and Bartels Estimators
We also analyzed the time- delay between the continuum
and Mg II light curves using a novel technique of the measures
of the data regularity or randomness (Chelouche et al. 2017),
which were previously applied extensively in cryptography and
data compression. The advantage of these regularity measures
is that they do not require the interpolation as for the ICCF or
χ2
technique and neither do they require binning in the
correlation space like the DCF and zDCF methods. In addition,
no AGN variability model is needed for the continuum light
curve as for the JAVELIN.
One of the suitable estimators to analyze the time delay
between two light curves is the optimized von Neumann
scheme, which works with the combined light curve
Èt = = t
=F t t f F F, ,i i i
N
1 1 2( ) ( ) , where F1 is the continuum
light curve and t
F2 is the time-shifted line-emission light curve.
The optimized von Neumann estimator for a given time delay τ
is defined as the mean of the successive differences of F(t, τ),
åt =
-
-
=
-
+E
N
F t F t
1
1
. C5
i
N
i i
1
1
1
2( ) [ ( ) ( )] ( )
The aim of the von Neumann scheme is to find the minimum
t¢E( ), where t t¢ ~ 0 is supposed to correspond to the actual
time delay.
In Figure 19 (left panel), we calculate E(τ) for HE 0435-
4312 using the Python script based on Chelouche et al.
(2017).16
The minimum is reached for a time delay between
300 and 400 days in the observer’s frame (333–334 days and
391–392 days), and then for 690 days, which is consistent with
the results of previous methods. To determine the peak value
and its uncertainty close to this minimum, we performed
∼10,000 bootstrap realizations, from which we constructed the
histogram of the best von Neumann time delays; see Figure 19
(right panel). In this histogram, we detect two prominent peaks
at ∼27 days and ∼1200 days and a smaller peak at ∼635 days.
After focusing on the interval between 150 and 1100 days, the
best peak is at -
+
635 66
32
days in the observer’s frame, where the
uncertainties correspond to standard deviations within 30% of
the best peak.
For comparison, we also applied the Bartels estimator to
both light curves; it uses the ranked version of the combined
light curve FR(t, τ). In Figure 20 (left panel), we show the
Bartels estimator as a function of the time delay in the
observer’s frame. The minimum is clearer than for the von
Neumann estimator and is located at 690 days. After running
10,000 bootstrap realizations, we detect three peaks as for the
von Neumann estimator. Between 100 and 1100 days, there is a
peak of -
+
644 45
27
days (see Figure 20, right panel), where the
uncertainties were calculated within 30% of this timedelay
peak.
C.6. The χ2
Method
Inspired by the time-delay analysis in quasar lensing studies,
we applied the χ2
method to our set of light curves. The χ2
method performed well and consistently in comparison with
other time-delay analysis techniques for the previous two
SALT quasars—CTS C30.10 (Czerny et al. 2019) and HE
0413-4031 (Zajaček et al. 2020). It also performs better than
the classical ICCF for the case when the AGN variability can
be interpreted as a red-noise process (Czerny et al. 2013). We
subtracted the mean from both the continuum and the lineemission
light curves, and subsequently they were normalized
by their corresponding variances. The similarity between the
continuum and the time-shifted line-emission light curves is
evaluated using χ2
. We make use of symmetric interpolation.
In Figure 21 (left panel), we show χ2
as a function of the
time delay in the observer’s frame. There is a global minimum
at 696 days. The exact position and the uncertainty of this peak
are inferred from the histogram of the best time delays
Figure 18. Alias mitigation for the JAVELIN time-delay distribution. Left panel: prior probability distribution P(τ) = [N(τ)/N(0)]2
based on the number of
overlapping data points for a given time delay. Right panel: posterior time-delay distributions before alias mitigation (black line) and after alias mitigation by using P
(τ) as an effective weight for individual time-delay peaks.
16
For the script and the corresponding documentation, see www.pozonunez.
de/astro_codes/python/vnrm.py.
20
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
165
Figure 19. The results of the time-delay analysis using the von Neumann estimator. Left panel: the value of the von Neumann estimator as a function of the time delay
in the observer’s frame. The red vertical line denotes the minimum at 690 days. Right panel: the histogram of best von Neumann time delays constructed from 10,000
bootstrap simulations of random subset selections of both continuum and line-emission light curves. The red and green dotted vertical lines mark the peak value of
-
+
635 66
32
days and the corresponding uncertainties.
Figure 20. The results of the time-delay analysis using the Bartels estimator. Left panel: the value of the Bartels estimator as a function of the time delay in the
observer’s frame. The minimum estimator value is reached for a time delay of 690 days. Right panel: the histogram of best Bartels time delays constructed from
10,000 bootstrap simulations of random subset selections of both continuum and line-emission light curves. The red and green dotted vertical lines mark the peak
value of -
+
644 45
27
days and the corresponding uncertainties.
Figure 21. Time-delay determination using χ2
method. Left panel: the χ2
value as a function of the time delay in the observer’s frame. The global minimum is at
∼696 days, which is marked by a red vertical line. Right panel: the histogram of best time delays constructed from 10,000 bootstrap simulations around the global χ2
minimum of ∼700 days. The peak value is -
+
706 61
70
days, which is shown using vertical red and green dotted lines.
21
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
166 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
constructed from 10,000 bootstrap realizations. We obtain
-
+
706 61
70
days, where the uncertainties were determined as the
left and the right standard deviations from the time delays that
are positioned within 30% of the main peak; see Figure 21
(right panel).
Appendix D
Alias Mitigation Using Generated Light Curves
In this appendix, we investigate the alias problem, i.e., the
occurrence of secondary peaks in the time-delay distribution
from a different perspective than presented in Appendix C.4,
where we applied the downweighting technique on the
posterior time-delay distribution based on the number of data
points in the overlap region. Here we instead generate a large
set of synthetic light curves similar in basic temporal properties
to those of our studied quasar, while the line-emission light
curve has a known prior time delay with respect to the
continuum light curve. Then we apply several methods for
time-delay determination to see how well we can recover the
true time delay and what the distribution width is close to the
assumed time delay.
To generate mock light curves, we use the method of
Timmer & Koenig (1995) (hereafter TK) to produce synthetic
light curves from the assumed shape and the normalization of
the power density spectrum (PDS). The TK method can
generate mock light curves based on any shape of PDS, unlike
the damped random walk approach (Kelly et al. 2009;
MacLeod et al. 2010; Zu et al. 2011, 2013, 2016), which
generates light curves with the PDS slope close to −2. The
assumed shape of the PDS is a broken power-law function with
two break frequencies corresponding to ∼10,000 days at lower
frequencies and to ∼700 days at higher frequencies. The slopes
from lower to higher frequencies vary consequently from 0.0,
through −1.2, up to −2.5. The line-emission light curve is first
time-shifted by the assumed time delay, here fixed to 600 days
in the observer’s frame. Then the line emission is smeared by a
timescale equal to 10% of the time delay, where we adopt the
Gaussian shape of the BLR transfer function. Finally, dense
continuum and line emission light curves are interpolated to the
actual observational epochs of our observed light curves. We
generate in total 1000 mock light curves with the actual
observational cadence, which has the potential to reveal artifact
peaks in the time-delay probability distributions due to the
particular sampling pattern of our observations (see also MaxMoerbeck
et al. 2014, for a similar analysis of cross-correlation
artifacts). These corresponding continuum–line pairs are further
analyzed by seven different time-delay methods. Subsequently,
we construct histograms of best time delays, which are utilized
as probability density distributions to determine the peak time
delays and the corresponding 1σ uncertainties; see Figure 22
for the ICCF method and Figure 23 for the zDCF, JAVELIN,
von Neumann, Bartels, DCF, and χ2
methods. In particular, we
focus on how well we can determine the prior (true) time delay
and what its uncertainty is. In Table 6, we list for individual
methods the most prominent peaks and their uncertainties in the
interval between 500 and 800 days in the observer’s frame.
In general, the cadence of our observed light curves appears
to produce two or three secondary peaks besides the prior peak
close to 600 days, which are often more prominent than the
assumed peak. Two peaks at 200 days and ∼900–1000 days
are especially apparent. For the ICCF, DCF, and zDCF
methods, the prior time-delay peak is not well defined, i.e.,
the distribution is highly smeared and broad in the interval
between 500 and 800 days. For other methods, the peak close
to 600 days is better defined, however, with a large standard
deviation of the order of 100 days. The true peak at ∼600 days
is best recovered using the JAVELIN method, which also
suppresses effectively the secondary peaks detected in other
methods. This result is consistent with the study of Yu et al.
(2020b), who report that the JAVELIN outperforms the ICCF
in terms of estimating time-delay error. Furthermore, Li et al.
(2019) used mock light curves to compare the time-lag
recovery and error estimation of the JAVELIN, ICCF, and
zDCF and concluded that the JAVELIN produces higher
quality time-delay estimations than both the ICCF and the
zDCF. In Table 6, we list the inferred peaks in the range
between 500 and 800 days, i.e., close to the true peak of 600
days in the observer’s frame. We see that due to the sparse
cadence of our observations, the detected peak can be shifted
by as much as ∼100 days shortward or longward of the
assumed peak.
The time-delay analysis of the generated light curves thus
shows that secondary peaks can be created in the time-delay
distribution due to the specific cadence and duration of the
observed light curves. The secondary peaks longward of the
Figure 22. Best time-delay distribution constructed from the analysis of 1000
pairs of light curves generated using the Timmer–Koenig algorithm (Timmer &
Koenig 1995) and subsequently analyzed by the interpolated cross-correlation
function. The histogram of the best time delays has a bin size of 50 days. The
dashed vertical line marks the time delay of 600 days in the observer’s frame
assumed for the time-shifted line-emission light curve.
Table 6
Peaks Close to τ = 600 days (in the Range between 500 and 800 days in the
Observer’s Frame) in the Time-delay Distributions (see Figure 23) for
Individual Methods
Method Time-delay peak (days)
ICCF -
+
720 218
79
zDCF -
+
724 221
79
JAVELIN -
+
564 165
131
Von Neumann -
+
594 115
143
Bartels -
+
707 199
78
DCF -
+
525 109
127
χ2
-
+
632 178
128
22
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
167
true peak at 600 days can be mitigated using the downweighting
technique as we showed in Appendix C.4 for the
JAVELIN method; see also Grier et al. (2017). Here we show
that the prominent peaks between 0 and ∼200 days, which are
not mitigated by the downweighting due to a large number of
overlapping light-curve pairs, can arise due to a lower cadence
Figure 23. Best time-delay distributions constructed from 1000 pairs of light curves generated using the Timmer–Koenig algorithm (Timmer & Koenig 1995). Top
left: the histogram of the best time delays constructed for the zDCF method. The bin size is 50 days. The dashed vertical line marks the time delay of 600 days in the
observer’s frame assumed for the time-shifted line-emission light curve. The other panels show analogous histograms of the best time delays constructed for the
JAVELIN method (top right), the von-Neumann estimator (middle left), the Bartels estimator (middle right), the DCF method (bottom left), and the χ2
method
(bottom right).
23
The Astrophysical Journal, 912:10 (25pp), 2021 May 1 Zajaček et al.
168 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
of our light curves, especially the line-emission light curve with
only 24 points. Hence, they do not reflect the physical response
of the BLR transfer function. In this sense, the reported mean
peak time-delay of -
+
658 31
29
days in the observer’s frame ( -
+
296 14
13
days in the rest frame for z = 1.2231) for the quasar HE 0435-
4312 can be considered as the best candidate for the true time
delay, albeit with a large uncertainty up to ∼100 days. The
other peaks appear to be aliases due to the specific cadence and
the duration of our light curves.
ORCID iDs
Michal Zajaček https://orcid.org/0000-0001-6450-1187
Bożena Czerny https://orcid.org/0000-0001-5848-4333
Mary Loli Martinez–Aldama https://orcid.org/0000-0002-
7843-7689
Mateusz Rałowski https://orcid.org/0000-0002-0297-3346
Aleksandra Olejak https://orcid.org/0000-0002-6105-6492
Swayamtrupta Panda https://orcid.org/0000-0002-
5854-7426
Krzysztof Hryniewicz https://orcid.org/0000-0002-
2005-9136
Marzena Śniegowska https://orcid.org/0000-0003-
2656-6726
Mohammad-Hassan Naddaf https://orcid.org/0000-0002-
7604-9594
Grzegorz Pietrzyński https://orcid.org/0000-0002-
9443-4138
Catalina Sobrino Figaredo https://orcid.org/0000-0001-
9704-690X
Martin Haas https://orcid.org/0000-0002-7284-0477
Andrzej Udalski https://orcid.org/0000-0001-5207-5619
Vladimír Karas https://orcid.org/0000-0002-5760-0459
Marek Sarna https://orcid.org/0000-0003-4745-3923
Ramotholo R. Sefako https://orcid.org/0000-0003-
3904-6754
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170 CHAPTER 5. PAPER 4: REVERBERATION-MAPPING OF HE 0435-4312
Chapter
6
Paper 5: Enhanced Doppler Beaming
Most spiral and elliptical galaxies with the total stellar mass larger than 108
M⊙ host dense
nuclear star clusters in their centers (Neumayer et al. 2020). The Galactic center is the only
galactic nucleus where one can study the motion and variability of individual stars as well as
the properties of the nuclear star cluster as a whole. The closest stars to the supermassive black
hole Sgr A*, so-called S stars, move at the velocities of several thousand km/s. During the last
30 years, several of them have already completed at least one orbit around the supermassive
black hole. In this sense, these are special or rather extreme-mass binary systems, where the
heavier component is the supermassive black hole of 4 × 106
M⊙.
When being close enough, the S stars can move around the common center of mass, which
is close to the supermassive black hole, at the fraction of a light speed. More specifically, to
reach ∼ 3% of the light speed, the star needs to be at ∼ 44 AU or ∼ 1100 gravitational radii.
When the star is located at ∼ 4 AU or 100 gravitational radii, it already reaches as much as
∼ 10% of the light speed. There are stellar candidates in the S cluster that can reach such a
fraction of the light speed close to their pericenters (Peißker et al. 2020a, 2022).
Rafikov (2020) suggested that due to high velocities, the stellar light is expected to be
Doppler-boosted, hence the star would appear temporarily brighter or fainter in a narrow
infrared photometry band. The variability amplitude due to Doppler boosting for the S2 star
is about 2%, while for some of the newly discovered S stars (S62 and S4714), it can reach
∼ 6%.
In this paper, we investigated the possibility that the broad-band continuum spectral energy
distribution of S cluster objects does not necessarily have to correspond to main-sequence
stars (positive spectral indices close to α = 2), but also to colder objects (dust-enshrouded
objects, brown dwarfs) or pulsars with generally negative spectral indices in the infrared
domain. In that case, the photometric variability is significantly enhanced by a factor of
∼ 4 for pulsars and by an order of magnitude for dust-enshrouded stars, which can reach
the variability amplitude due to Doppler beaming of ∼ 10%. One of the main applications,
given that future instruments have a sufficient photometric precision, is to infer the nature of
S cluster objects in case their orbits have already been precisely determined. The photometric
variability amplitude can thus provide important clues whether the object is a main-sequence
star, a dust-enshrouded object, or an exotic pulsar.
Credit: Zajaˇcek (2021), ApJ 915, 111. Reproduced with permission ©AAS.
171
Enhanced Doppler Beaming for Dust-enshrouded Objects and Pulsars in the Galactic
Center
Michal Zajaček1,2,3
1
Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland; zajacek@cft.edu.pl
2
Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
3
L. Novomeského 4, 901 01 Malacky, Slovakia
Received 2021 April 5; revised 2021 May 7; accepted 2021 May 21; published 2021 July 15
Abstract
Stars within the innermost part of the nuclear star cluster can reach orbital velocities up to a few percent of the light
speed. As analyzed by Rafikov, Doppler boosting of stellar light may be of relevance at the pericenter of stellar
orbits, especially with the upcoming high-precision photometry in the near- and mid-infrared bands. Here we
analyze the previously neglected effect of the infrared spectral index of monitored objects on the Doppler-boosted
continuum emission in a narrow photometric band. In contrast to main-sequence stars, the detected compact
infrared-excess dust-enshrouded objects have an enhanced Doppler-boosting effect by as much as an order of
magnitude, with the variability amplitude of the order of 10% for the most eccentric orbits. In a similar way,
pulsars dominated by nonthermal synchrotron emission are also expected to exhibit a stronger Doppler-boosted
signal by a factor of at least 4 in comparison with canonical S stars. In case the stellar orbit is robustly determined,
the relative flux variation can thus provide hints about the nature of the objects. For extended dust-enshrouded
objects, such as G1, that are variable due to tidal, ellipsoidal, bow-shock, and irradiation effects, the subtraction of
the expected Doppler-boosting variations will help to better comprehend their internal physics. In addition, the
relative flux variability due to higher-order relativistic effects is also modified for different negative spectral indices
in a way that it can obtain both positive and negative values with the relative variability of the order of 1%.
Unified Astronomy Thesaurus concepts: Galactic center (565); Stellar photometry (1620); Relativistic binary
stars (1386)
1. Introduction
The Galactic center nuclear star cluster (NSC) is a unique
dynamical testbed, where it is possible to monitor the motion of
stars in the potential of the compact radio source Sgr A*
(Balick
& Brown 1974), which is associated with the supermassive
black hole of ∼ 4 × 106
Me (SMBH; Genzel et al. 2010;
Schödel et al. 2014; Eckart et al. 2017). In particular, the
innermost part of the NSC, the S cluster, contains several tens
of bright B-type stars with inferred orbits (Ghez et al. 2005;
Gillessen et al. 2009, 2017; Ali et al. 2020), which has been
utilized for tests of gravitational theories in the strong-field
regime (Hees et al. 2017; Parsa et al. 2017) as well as for Nbody
cluster dynamics in the potential dominated by the SMBH
(see, e.g., Merritt 2013, and references therein).
For the S2 star on a highly elliptical orbit with the period of
∼16 yr, the combined general relativistic gravitational redshift
and transverse Doppler shift of ∼200 km s−1
/c was measured
using its spectral absorption lines (Gravity Collaboration et al.
2018; Do et al. 2019b). The general theory of relativity was
also confirmed to a high precision by the measurement of its
Schwarzschild precession of 12df ~ ¢ per orbital period (Parsa
et al. 2017; Gravity Collaboration et al. 2020).
Recently, Rafikov (2020) analyzed the effect of nonrelativistic
and relativistic Doppler boosting on the detected
photometric flux density of S stars. The study was inspired
by the analysis of the photometric light curve of the S2 star in
L′-band (Hosseini et al. 2020) that found no intrinsic variability
at the level of ∼2.5%. Rafikov (2020) concluded that the
Doppler boosting of the continuum stellar light is especially of
relevance for stars that reach the pericenter velocities of a few
percent of the light speed. The amplitude of the relative flux
change due to the Doppler beaming is ∼2.0% for the S2 star
(Δm ∼ 0.02 mag), and reaches ∼5.6% for the newly analyzed
S62 (Δm ∼ 0.06 mag) and ∼6.4% for the recently discovered
S4714 star (Δm ∼ 0.07 mag) (Peißker et al. 2020a, 2020b).
This is at the sensitivity limit of ∼0.01 mag of current infrared
adaptive optics instruments. The detection and the timing of the
Doppler beaming for these sources is achievable with an order
of magnitude improved sensitivity of 30 + meter telescopes
(Do et al. 2019a; Hosseini et al. 2020). The higher-order
corrections to the Doppler-beamed stellar light due to general
relativistic redshift and transverse Doppler shift have the
amplitude of the relative flux change at the level of
0.7 × 10−3
mag for S2, ∼ 2.6 × 10−3
mag for S62,
and ∼ 2.6 × 10−3
mag for S4714, which is close to the
sensitivity limit of upcoming infrared instruments. However,
they will hardly be detectable due to stellar crowding and
confusion in the innermost parts of the NSC (Rafikov 2020). In
principle, if the Doppler boosting effect and its temporal profile
is detected, it could be utilized to verify and constrain orbital
elements in case the photometry and the spectroscopy of the
source is confused (Rafikov 2020).
However, the overall uncertainty of the infrared spectral
index of the Galactic center sources was not quantitatively
analyzed by Rafikov (2020). Since their study focused on
B-type stars, such as S2, fixing the spectral index to α = 2
(using the convention for the radiation intensity as Iν ∝ ν+ α
)
can be justified in the infrared domain. However, the S cluster
also hosts several dust-enshrouded objects with a negative
spectral index in the near-infrared domain due to the dust
emission with the effective temperature of ∼ 500–600 K
(Ciurlo et al. 2020; Peißker et al. 2020c). In addition, the
emission of compact remnants, in particular energetic pulsars,
The Astrophysical Journal, 915:111 (7pp), 2021 July 10 https://doi.org/10.3847/1538-4357/ac043a
© 2021. The American Astronomical Society. All rights reserved.
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172 CHAPTER 6. PAPER 5: ENHANCED DOPPLER BEAMING
is expected to be dominated by optically thin synchrotron
emission in infrared bands with α ∼ − 1 (see, e.g., Zajaček
et al. 2017, and references therein). Future surveys using
30 + meter telescopes will likely reveal cold brown dwarfs
with infrared spectral properties similar to dusty objects (Do
et al. 2019a). Since the relative flux change due to the Doppler
boosting is F F v c3em 1 LOS( ) ( )aD » - (Rafikov 2020),
where vLOS is a line-of-sight velocity (positive for receding
objects), dust-enshrouded objects as well as pulsars are
expected to exhibit a larger variability due to the beaming
effect by at least a factor of a few in comparison with mainsequence
stars.
In this study, we consider different negative values of a
stellar spectral index in the infrared domain to quantify the
relative flux variability due to the Doppler boosting. Since the S
cluster hosts different types of objects, we focus on the
enhanced variability with respect to main-sequence stars.
The paper is structured as follows. In Section 2, we introduce
the basic formalism of the continuum Doppler boosting and
compare the relative flux variability among dust-enshrouded
objects, pulsars, and main-sequence stars. Subsequently, we
evaluate the relative variability due to the Doppler boosting for
four monitored dust-enshrouded objects in Section 3 to
demonstrate the importance of the spectral index for the actual
objects in the S cluster. In Section 4, we discuss other internal
processes for extended dust-enshrouded objects that can lead to
significant continuum variations. We also consider the potential
detection of longer beaming flares and dimming events.
Finally, we conclude in Section 5.
2. Doppler Boosting of Stellar Light: Effect of Spectral
Index
Stars orbiting the SMBH in the Galactic center can reach
pericenter distances of a few 1000 gravitational radii (rg),
reaching velocities of a few percent of the light speed. Two
stars, S62 and S4714, are candidates to reach only a few 100 rg
with pericenter velocities up to ∼10% of the light speed
(Peißker et al. 2020b). As stars approach the SMBH, they are
subject to time dilation, light aberration, and the frequency shift
due to a stellar motion and a general relativistic redshift as well
as a special relativistic transverse Doppler shift. All of these
effects add up and lead to the Doppler boosting of stellar
emission (Zucker et al. 2006, 2007; Rafikov 2020) that can
make a star appear both fainter and brighter depending on the
line-of-sight velocity.
The flux density of a star as detected by an observer on the
Earth in a narrow frequency band w(ν) can be expressed as a
power-law function of the ratio of observed and emitted
frequencies νobs and νem, respectively, as
F Fobs em obs em
3( )n n= a- , where F I w dem
0
em ( ) ( )ò n n n=
¥
is
the emitted flux density.
As shown by Rafikov (2020), the relative flux variability due
to v c( ) terms (nonrelativistic Doppler beaming) for v = c
can be expressed as,
F
F
v
c
3 . 1
em 1
LOS
⎜ ⎟
⎛
⎝
⎞
⎠
( ) ( )a
D
» If
we consider main-sequence B-type stars with α ∼ 2, in
particular S2, the variability amplitude is 2.13% and 2.07% in
K (2.2 μm) and L (3.8 μm) bands, respectively, see Table 1.
More exotic objects within the S cluster, namely monitored
dusty objects (Ciurlo et al. 2020; Peißker et al. 2020c) as well
as putative pulsars (Pfahl & Loeb 2004; Wharton et al. 2012),
have a broadband spectral energy distribution (SED) with the
negative spectral index α < 0. Hence, the variability amplitude
due to the Doppler boosting will be increased for them as the
factor in Equation (1) is at least ∼3 in absolute terms while for
main-sequence stars with α ∼ 2 it is effectively equal to unity.
As soon as more sensitive near- and mid-infrared detectors
mounted at 30 + telescopes are operational, it will be possible
to probe the stellar initial mass function toward the low-mass
end where brown dwarfs of spectral type L and T are
positioned (Do et al. 2019a). Old brown dwarfs have effective
temperatures 1000 K (Basri 2000) and their SED slopes are
thus comparable to dust-enshrouded objects and therefore the
presented analysis is relevant for them as well.
We take into account different negative values of the spectral
index in the infrared K and L bands. First, we take into account
the SED of dust-enshrouded objects D2, D23, D3, and DSO/
G2 as analyzed by Peißker et al. (2020c). Their SEDs are
plotted in Figure 1. In most cases, for D2, D23, and D3 sources,
the broadband SED can be described well as a one-component
blackbody spectrum with the effective temperature of ∼ 500 K
and the radius of ∼ 1 au. For the DSO/G2 source, the twocomponent
blackbody fit is preferred since at the shortest
wavelengths the stellar emission appears to dominate, see
Figure 1 for the spectral decomposition and Peißker et al.
(2020c) for a detailed discussion. The dominant contribution in
K, L, and M bands is due to the optically thick dusty envelope
with the temperature of T ∼ 500 K. The corresponding spectral
indices between K and L bands as well as L and M bands—αKL
and αLM—are listed in Table 1. The mean values for the four
studied dust-enshrouded objects are 6.31 1.23KLa = -  and
4.30 2.75LMa = -  . We use these average values for a
representative case of a dust-enshrouded object orbiting the
SMBH on the S2 orbit, for which we obtain the variability
amplitude of 18.16% and 14.24% in K and L bands,
respectively. Hence, the variability due to the Doppler boosting
is increased by a factor of ∼9 and ∼7 in K and L bands,
respectively. If we define the characteristic half-maximum
timescale τ1/2 between the epochs where the relative flux
variability reaches half of the maximum value, we obtain
τ1/2 = 2.8 yr independent of the spectral index, which by
definition affects only the amplitude of the relative flux
variability.
Furthermore, the higher-order corrections to the Doppler
boosting due to v c2 2( ) terms (gravitational redshift and the
transverse Doppler shift) are also affected by the spectral index.
If we consider the relative flux variability ΔF/Fem up to
v c2 2( ) terms, then we get (Rafikov 2020),
F
F
F F
F
v c
1
1 2
1, 2
v
c
em
obs em
em
BH
2 2
3LOS
⎛
⎝
⎜
⎞
⎠
⎟( )
( )
f
D
=
-
=
=
+
+ -
-
awhere
fBH = − GM•/r is the gravitational potential of the
SMBH. Using Equations (2) and (1), the higher-order
corrections to the first-order Doppler boosting can be calculated
as F F F F F Fem 2 em em 1( ) ( )D = D - D . In contrast to α = 2
considered by Rafikov (2020), F Fem 2( )D can reach positive
2
The Astrophysical Journal, 915:111 (7pp), 2021 July 10 Zajaček
173
values (negative magnitude change), which is unique for exotic
objects within the S cluster, such as dusty objects, pulsars or
brown dwarfs. The overall amplitude of the relative flux
variability is also increased. For 6.31KLa = - on the S2 orbit,
we obtain F F 0.98%em 2( )D = , while for 4.30LMa = - , we
get F F 0.65%em 2( )D = .
In Figure 2, we show the line-of-sight velocity, vLOS (top
panel), the relative flux variability due to the Doppler boosting
F Fem 1( )D (middle panel) for different spectral indices, and the
associated higher-order relative flux variability F Fem 2( )D as a
function of time for the exemplary orbit of the S2 star.
Finally, we also consider a putative case of an energetic
pulsar orbiting within the S cluster, which could mimic nearinfrared
excess sources in terms of the broadband SED
(Zajaček et al. 2017). As an analog, we adopt the energetics
of PSR B0540-69 that has a prominent near-infrared emission
(Mignani et al. 2012) with the K-band luminosity of
LK ≈ 1034
erg s−1
. For the spectral index, we adopt α = −1
that is typical of synchrotron-dominated young pulsars
(Mignani et al. 2012). The SED of such a putative pulsar is
shown in Figure 1. The amplitude of the relative flux variability
is 7.80%, hence by about a factor of 4 larger than for the mainsequence
star. The temporal evolution of F Fem 1( )D is shown
among other cases in Figure 2. The amplitude of the relative
variability due to higher-order corrections is also increased by a
factor of ∼4% to ∼0.26%. The flux density minimum of
F Fem 2( )D is at + 2.63 × 10−3
magnitudes, while the maximum
is at − 0.23 × 10−3
magnitudes. The characteristic
amplitudes of the Doppler boosting for both the first- and the
second-order effects in K and L bands are summarized in
Table 1 for the case of a main-sequence star, a dust-enshrouded
object, as well as a pulsar assuming the same S2 orbit.
3. Results
In this section, we describe the analysis of the relative flux
variability due to Doppler beaming for monitored dustenshrouded
objects within the S cluster, specifically D2, D23,
D3, and DSO/G2 objects. We adopt the infrared flux densities
as determined by Peißker et al. (2020c). The SEDs of these
sources and the corresponding blackbody fits are shown in
Figure 1. All of these sources are on long-period orbits with
periods of a few hundred years. Therefore the detection of a
significant Doppler-boosted signal within the observational
duration of a few years is unlikely with the upcoming
monitoring or in archival data. However, we estimate the
Doppler beaming effect for these sources to illustrate that the
overall photometric amplitude of relative variations can be
comparable to or even exceed the values expected for a shortperiod
star S2 on a tight orbit. This is especially relevant in case
such an infrared-excess source will be approaching or going
through its pericenter during the future more sensitive
photometric monitoring, such as previous G1 and DSO/G2
sources (Witzel et al. 2014; Valencia-S. et al. 2015).
Below we list relevant values of F Fem 1( )D , F Fem 2( )D and
their amplitudes for individual objects.
Table 1
Near-infrared Spectral Indices between K and L Bands and L and M Bands for the Selected Infrared-excess Sources Analyzed by Peißker et al. (2020c)
Source αKL αLM F F KL
em 1( )d D [%] F F LM
em 1( )d D [%] F F KL
em 2( )d D [%] F F LM
em 2( )d D [%]
D2 −6.02 −2.64 3.95 2.47 0.026 0.011
D23 −5.69 −8.59 3.65 4.86 0.019 0.033
D3 −8.38 −1.32 4.30 1.63 0.032 0.0056
DSO/G2 −5.15 −4.65 16.79 15.76 0.66 0.60
G1 (−9.07, 1.17) (−5.50, 0.89) 18.33 12.51 1.02 0.49
S2 +1.91 +1.94 2.13 2.07 0.066 0.064
Pulsar (S2 orbit) −1.00 −1.00 7.80 7.80 0.26 0.26
Dust-enshrouded object (S2 orbit) −6.31 −4.30 18.16 14.24 0.98 0.65
Dust-enshrouded object (S62 orbit) −6.31 −4.30 60.27 47.26 12.25 7.86
Dust-enshrouded object (S4714 orbit) −6.31 −4.30 59.15 46.38 12.56 7.61
Note. For comparison with main-sequence stars, we also include the S2 star whose blackbody SED was calculated using the radius and the effective temperature from
Habibi et al. (2017). We also modified the spectral index of S2 to demonstrate the impact on the beamed flux density for a dust-enshrouded object (slopes determined
as mean values of four studied objects: D2, D23, D3, and DSO/G2) as well as a pulsar. In a similar way, we also estimated the Doppler beaming for putative dustenshrouded
objects on S62- as well as S4714-like orbits. The amplitudes of relative flux variability due to v c( ) terms, F Fem 1( )d D , as well as v c2 2( ) terms,
F Fem 2( )d D , are calculated for both K and L infrared bands.
Figure 1. Representative spectral energy distributions (SED) of four dusty
sources in the S cluster (D2, D23, D3, and DSO/G2) studied in Peißker et al.
(2020c), see the legend. We include measured flux densities in H, K, L, and M
bands as well as best-fit blackbody SEDs characterized by the temperature and
the radius of the optically thick photosphere. For the DSO/G2 source, a twocomponent
blackbody fit is preferred consisting of a stellar blackbody emission
as well as a more extended dusty envelope. Hot main-sequence B-type stars in
the S cluster are represented by the S2 star (dotted-dashed orange line; Habibi
et al. 2017). A putative pulsar, whose energetic analog is PSR B0540-69
(Mignani et al. 2012), with the spectral slope α = −1.0 is depicted by a cyan
dashed line. Spectral slopes between K and L bands as well as L and M bands
are listed in Table 1 for selected sources.
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174 CHAPTER 6. PAPER 5: ENHANCED DOPPLER BEAMING
D2. The source is on a mildly eccentric orbit with the
eccentricity of e ∼ 0.15 and the semimajor axis of a ∼ 30 mpc.
The pericenter distance is rp ∼ 130,000 rg and the corresponding
velocity is vp ∼ 900 km s−1
. Therefore the resulting
continuum variations are rather small, with the amplitudes
F F 3.95%KL
em 1( )d D = and F F 2.47%LM
em 1( )d D = for the
first-order Doppler boosting. The amplitudes for the higherorder
flux variations in the near-infrared K and L bands are
F F 0.026%KL
em 2( )d D = and F F 0.011%LM
em 2( )d D = ,
respectively.
D23. This dusty source is the least eccentric from the
selected sources, with e = 0.06 ± 0.01. Orbiting the SMBH
with the long period of ∼431 yr, its pericenter distance is as
much as ∼ 212,000 rg with the corresponding velocity of
∼670 km s−1
. The first-order Doppler-boosting flux variations
have the amplitude of 3.65% and 4.86% in K and L bands,
respectively, while the relativistic corrections are 2 orders of
magnitude smaller, F F 0.019%KL
em 2( )d D =
and F F 0.033%LM
em 2( )d D = .
D3. This dusty source is on a mildly eccentric orbit with
e = 0.24 ± 0.02 and the semimajor axis of
a = 35.20 ± 0.01 mpc (orbital period of ∼306 yr). Its smallest
distance to Sgr A*
is ∼ 137,000 rg and the corresponding
maximum velocity is ∼904 km s−1
. Because of the measured
steep slope between K and L bands, implying α ∼ − 8.4, the
amplitude of the first-order flux variability is
F F 4.30%KL
em 1( )d D = . Between L and M bands, the SED
becomes flatter, which results in the smaller amplitude of
F F 1.63%LM
em 1( )d D = . The higher-order relativistic corrections
are again at least 2 orders of magnitude smaller, with
amplitudes of 0.032% and 0.0056% in K and L bands,
respectively.
DSO/G2. The most eccentric source among the recently
monitored dusty objects is DSO/G2 with e = 0.976 (ValenciaS.
et al. 2015). Having a semimajor axis of a ∼ 33 mpc, it went
through the pericenter of its orbit around 2014.39, with the
smallest distance of rp ∼ 4042 rg and the maximum orbital
velocity of ∼6600 km s−1
. Given the high eccentricity and the
resulting small pericenter distance, the amplitudes of the
relative flux variability due to the leading-order Doppler
beaming are the largest among the monitored infrared-excess
sources, specifically F F 16.79%KL
em 1( )d D = (0.182 mag) and
F F 15.76%LM
em 1( )d D = (0.171 mag). The amplitudes of the
second-order relativistic variations are at the level of ∼1%,
F F 0.66%KL
em 2( )d D = and F F 0.60%LM
em 2( )d D = . The
relative flux variations are depicted in Figure 3 as functions
of time for the epochs close to the pericenter. The changes at
the level of ∼ 0.2 mag are still challenging to detect in the
crowded environment of the Galactic center. The L-band light
curve of the DSO/G2 as analyzed by Witzel et al. (2014) is
constant within the observational uncertainties that reach as
much as ∼0.5 mag. The mean value of the flux slightly
increased close to the pericenter and then dropped; however,
this cannot be claimed as significant (Witzel et al. 2014).
The compact dusty sources on highly eccentric orbits such as
DSO/G2 provide the best prospects for detecting longer
“beaming flares” or dimming events, i.e., the phases when the
star is expected to appear brighter or fainter for at least several
months. While for D2, D23, and D3 sources we obtain the halfmaximum
timescales of τ1/2 = 89, 143, and 111 yr, respectively,
the DSO/G2 source has τ1/2 = 3.55 yr, with the peak of
F F 8.4% 9.0%em 1( ) –D ~ (−0.088 and −0.093 mag, respectively)
at ∼2014.67 or ∼3.36 months after reaching the
pericenter.
We summarize the variability amplitudes F Fem 1( )d D and
F Fem 2( )d D for the monitored dust-enshrouded objects in
Table 1.
4. Discussion
We studied the effect of the infrared spectral index on the
Doppler-beamed continuum emission of stars within the S
cluster. The relative variability can be enhanced by a factor of a
few up to an order of magnitude for negative values of the
Figure 2. Effect of the near-infrared spectral slope on the Doppler-boosting
effect of stellar light calculated for the star on the S2 orbit. Top panel: a line-ofsight
(LOS) velocity (in km s−1
) as a function of time. The right y-axis shows
the LOS velocity in the percent of the light speed. Middle panel: the Doppler
boosting due to the leading v c( ) term (nonrelativistic) expressed as the
relative flux change in percent. Different lines stand for different types of stellar
objects present in the S cluster: B-type hot star (black solid line; α = +1.91), a
dust-enshrouded NIR-excess source observed in K band (red dotted–dashed
line; 6.31KLa = - ), a dust-enshrouded NIR-excess source observed in L band
(orange dashed line; 4.30LMa = - ), and a pulsar (blue dotted line;
α = −1.00). The y-axis on the right shows the relative flux change in
millimagnitudes (mmag). Bottom panel: the relative flux change in percent due
to v c2 2( ) terms (gravitational redshift and transverse Doppler shift). The yaxis
on the right shows the relative change in millimagnitudes (mmag).
Figure 3. The same panels as in Figure 2 for the infrared-excess source DSO/
G2. In the middle and the bottom panels, we plot the relative flux variability
separately for the spectral index between K and L bands (red solid line) and for
the spectral index between L and M bands (orange dashed line).
4
The Astrophysical Journal, 915:111 (7pp), 2021 July 10 Zajaček
175
spectral index, which is exhibited by observed dust-enshrouded
objects as well as putative young pulsars and older brown
dwarfs.
However, especially the extended dust-enshrouded objects
are prone to an order of magnitude variation due to tidal,
irradiation, bow-shock, and ellipsoidal effects. These will
prevent the detection of the clear Doppler-beamed signal. On
the other hand, the expected Doppler-beaming variations can
be subtracted to study the internal processes of these sources in
more detail. We will discuss some of those other internal
effects in the upcoming subsection. Subsequently, we also
mention the possibility of detection of beaming flares at the
position of Sgr A*
due to high-velocity dusty and other cold
objects (brown dwarfs) as well as pulsars.
4.1. Internal Variations of Dust-enshrouded Objects
There is an ongoing debate concerning the source of the
continuum emission of dust-enshrouded objects, some of which
are spatially extended. Currently, they appear to be internally
heated due to the presence of a stellar core (Witzel et al. 2017;
Zajaček et al. 2017; Ciurlo et al. 2020; Peißker et al. 2020c).
However, the contribution of an external irradiation cannot be
excluded. Below we discuss several processes that can likely
contribute to the internal photometric variations of these
objects, in particular those that are extended beyond their
corresponding tidal (Hill) radii. Subtraction of the expected flux
density changes due to Doppler beaming, provided that the
orbital trajectory is well constrained, is relevant for the further
assessment of these effects.
(a) External irradiation. Considering that there are NS ∼ 100
stars within the S cluster of radius RS ∼ 1″ ∼ 0.04 pc, we
obtain the mean stellar volume number density of
nS ∼ 4 × 105
pc−3
. The mean distance of an S star from
any dusty object thus is d n 3000 auS S
1 3( )= ~- .
Assuming that there is an embedded star inside the dusty
object, its flux is greater than the flux from an S star by a
factor of
F
F
T
T
R
R
d
R
, 3
S S
4
S
2
S
DSO
2
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
( )=  
where Få is the flux of an embedded star, Tå and Rå are its
temperature and radius, respectively, FS is the flux of an
external S star, TS and RS are its temperature and radius,
respectively, and finally RDSO is the characteristic DSO/
G2 radius. Considering Tå = 3250 K and Rå = 1Re from
the two-component blackbody fit, see Figure 1,
TS ∼ 30,000 K, RS ∼ 5 Re (Habibi et al. 2017), and
RDSO ∼ 1 au (Figure 1), we obtain using Equation (3),
Få/FS ∼ 50. The ratio Få/FS is unity for the S star
approach to the dusty object with the separation of
d 424 auS ~ . The total bolometric magnitude change due
to the external irradiation can approximately be estimated
from the extreme approach of an S star within a few
hundred astronomical units, when its flux reprocessed by
the gaseous-dusty envelope is comparable to the
embedded star, m 2.5 log 2 0.8D - ~ - mag, which is
greater than or comparable to the variations due to the
Doppler-boosting effect.
(b) Ellipsoidal variations. Due to tidal stretching and
compression of the gaseous-dusty envelope, dusty objects
are expected to have an ellipsoidal shape. As the object
orbits around SMBH, the projected area seen by the
observer changes, which leads to photometric variations.
This effect was observed for a tidally distorted star
orbiting the microquasar GRO J1655-40 (Greene et al.
2001), where the amplitude of the optical and infrared
continuum variations reaches ∼ 0.2–0.4 mag.
(c) Bow-shock radiation. Due to their supersonic motion at
the pericenter, dust-enshrouded objects are expected to
develop a bow shock, in which electrons are accelerated
in the amplified magnetic field and emit broadband
synchrotron radiation. This can lead to the flux density
enhancement close to the pericenter, which, however,
depends on the ambient density as well as magnetic field.
Hosseini et al. (2020) constrain the contribution of the
nonthermal bow-shock emission to 0.1 mag in nearinfrared
L′-band for the S2 star.
(d) Tidal truncation: Case of G1. A prominent and extended
L-band emission source passed close to Sgr A*
around
2001.0 (Clénet et al. 2004, 2005). It was subsequently
named G1 and analyzed in detail by Witzel et al. (2017)
during its post-pericenter phase; see also Pfuhl et al.
(2015). The source was more extended and resolved out
before 2006 and afterwards got more compact and
appeared as a point source, which was interpreted by
the tidal truncation of its large gaseous-dusty envelope.
Its L-band emission flux density also dropped by about
two magnitudes (Witzel et al. 2017). The first-order and
second-order Doppler beaming as a function of time is
depicted in Figure 4. We compare two cases: the Doppler
beaming for a gradually increasing spectral index (bright
red and orange lines) as indicated by the analysis of
Witzel et al. (2017) and the case that assumes fixed
spectral indices (fainter red and orange lines). The main
effect that we see is that the evolving spectral slope in the
post-pericenter phase effectively shortens the duration of
the beaming “flare” (see also Section 4.2), while the
amplitude is not significantly affected. For the leadingterm
Doppler boosting effect, we obtain the amplitudes
F F 18.33%KL
em 1( )d D = (∼0.192 mag) and
Figure 4. Effect of a variable spectral index on the Doppler beaming effect.
The same panels as in Figure 2 for the infrared-excess source G1. In the middle
and the bottom panels, we plot the relative flux variability separately for the
spectral index between K and L bands (red solid line) and for the spectral index
between L and M bands (orange dashed line). In particular, we consider
increasing spectral indices as indicated by the observations of Witzel et al.
(2017). For comparison, we also show, in fainter colors, the case with fixed
spectral indices in K and L bands.
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176 CHAPTER 6. PAPER 5: ENHANCED DOPPLER BEAMING
F F 12.51%LM
em 1( )d D = (∼0.132 mag). The higherorder
relativistic corrections have the overall amplitudes
of F F 1.02%KL
em 2( )d D = (∼0.011 mag) and
F F 0.49%LM
em 2( )d D = (∼0.005 magnitudes). Since
there is no L-band light curve of G1 close to its pericenter
passage available and the L-band flux density drops by
nearly 2 magnitudes due to structural changes in the postpericenter
phase of the orbit, the Doppler-boosting effect
cannot be practically traced for this object. On the other
hand, the subtraction of nearly ∼ 0.1–0.2 mag variations
due to the Doppler boosting is of relevance for studying
internal changes of the source close to the pericenter
passage.
For future monitoring, compact dusty sources, whose
intrinsic K- and L-band flux densities are rather stable within
at least 0.1 mag, such as the DSO/G2 object, appear suitable
for the detection of the Doppler beaming effect, especially due
to the fact that the overall amplitude of the boosting effect can
be larger by an order of magnitude in comparison with B-type
S stars. Cold brown dwarfs orbiting Sgr A*
that are even more
compact and are expected to be photometrically stable are even
more suitable for a detailed monitoring of the Doppler
beaming. Observations by future 30+ telescopes equipped
with adaptive optics in near- and mid-infrared bands should be
sensitive enough to detect faint objects orbiting Sgr A*
down to
the brown-dwarf level (Do et al. 2019a).
4.2. Beaming Flares and Dimming of ∼0.1–1 mag Close
to Sgr A*
Faint dust-enshrouded objects, pulsars, and brown dwarfs on
highly eccentric orbits observed in near-infrared bands are
expected to cause brightening events or beaming “flares” with
an increase of ∼ 0.1–1 magnitudes and lasting for a few days to
years, depending on the pericenter distance. Having these
properties, the events would be unique and could be
distinguished from the near-infrared flares of Sgr A*
that last
approximately 1 hour and occur a few times per day (Witzel
et al. 2020).
Specifically, focusing on K-band observations, for a dustenshrouded
object on the S2 orbit we get the peak relative flux
of 5.83% (Δm = − 0.062 mag) with the timescale of
τ1/2 = 2.79 yr. For a pulsar on the same orbit, we get the
relative flux maximum of 2.50% (Δm = −0.027 mag) with the
same timescale. For the DSO/G2 object, the relative flux
density increases up to 8.97% (Δm = −0.093 mag) with the
half-maximum timescale of τ1/2 = 3.55 yr.
Even more prominent Doppler beaming can occur at the
pericenter distances 1 order of magnitude less than for the S2
star. Recently, Peißker et al. (2020a) and Peißker et al. (2020b)
reported the detection of faint S stars, some of which, in
particular S62 and S4714, can approach Sgr A*
at a distance as
small as ∼ 439 rg and ∼ 312 rg, respectively. Rafikov (2020)
predicted the variability of ∼6% for both S62 and S4714. In
case a dust-enshrouded object with the K-band spectral index
of 6.31KLa = - would be moving on an orbit comparable to
S62 and S4714, the variability could reach as much as ∼60%
for S62-like orbit and ∼59% for S4714-like orbit, see Table 1
for the summary of amplitudes and Figure 5 for the temporal
profiles of F Fem 1( )D and F Fem 2( )D for both stars.
As we can see in light curves of the relative variability in
Figure 5, both for S62 and S4714 orbits the Doppler dimming
by a few ∼0.1 mag would be more prominent than the Doppler
brightening. Especially for faint dusty objects, brown dwarfs,
or pulsars on similar orbits, there would be an epoch of
dimming or potentially a complete disappearance of the object
in case its infrared flux would be at the sensitivity limit. For the
S62-like orbit, the minimum relative flux is ∼−52%
(Δm ∼ 0.8 magnitudes) and the half-minimum timescale is
τ1/2 ∼ 0.036 yr or ∼13 days. In the case of S4714, the
dimming minimum is ∼59% (Δm ∼ 1 mag) and the halfminimum
timescale is τ1/2 = 4.75 days.
5. Conclusions
Motivated by the occurrence of colder dust-enshrouded
objects among main-sequence B-type stars, we explored the
effect of the infrared spectral index on the Doppler beaming
effect within the S cluster. For three dust-enshrouded objects
on mildly eccentric orbits, D2, D23, and D3, we found the
relative variability amplitudes of 3.95%, 3.65%, and 4.30% in
K band, respectively. The most prominent variability is for
highly eccentric dusty objects DSO/G2 and G1 with K-band
Figure 5. The same panels as in Figure 2 for a dust-enshrouded object on an S62-like orbit (left panel) and on an S4714-like orbit (right panel). In the middle and the
bottom panels, we plot the relative flux variability separately for the spectral index between K and L bands (red solid line) and for the spectral index between L and M
bands (orange dashed line).
6
The Astrophysical Journal, 915:111 (7pp), 2021 July 10 Zajaček
177
amplitudes of 16.79% and 18.33%, respectively, where the
latter object has a gradually increasing spectral index. In
general, dust-enshrouded objects with steep spectral indices are
expected to exhibit an enhanced Doppler beaming effect by as
much as an order of magnitude in comparison with B-type S
stars. Putative synchrotron-powered pulsars would have a
stronger Doppler-beaming variability by a factor of about 4.
Therefore, the best prospects for detecting a Doppler
beaming effect within the S cluster with future sensitive
instruments, such as Extremely Large Telescope, are for
compact dusty objects, brown dwarfs, and pulsars that are
expected to have stable intrinsic continuum flux densities. For
extended dusty objects, such as G1, variations due to tidal,
ellipsoidal, bow-shock, and irradiation effects are generally
larger. The subtraction of the expected Doppler-beaming
variations will help us to better comprehend their internal
physics, especially close to the pericenter passage.
In case the Doppler-beamed emission is detected for objects
with well-determined orbits, the temporal profiles of the firstand
second-order Doppler boosting could be utilized to
constrain the spectral index, and hence, the nature of the
objects. Moreover, with the expected detection of fainter cold
compact objects within the S cluster (dust-enshrouded objects
and brown dwarfs) using the upcoming sensitive infrared
photometry, we expect that the Doppler boosting will lead to
episodic beaming “flares” or dimming by a few 0.1 magnitudes
on the timescale of a year within ∼15 milliarcseconds of
Sgr A*
.
The author thanks the referee for constructive comments that
helped to improve the manuscript. The project was partially
supported by the Polish Funding Agency National Science
Centre, project 2017/26/A/ST9/00756 (MAESTRO 9). MZ
also acknowledges the NAWA financial support under the
agreement PPN/WYM/2019/1/00064 to perform a threemonth
exchange stay at the Charles University in Prague and
the Astronomical Institute of the Czech Academy of Sciences
in Prague. A part of the presented research was performed
within the Polish-Czech mobility program (MŠMT 8J20PL037
and NAWA PPN/BCZ/2019/1/00069.
ORCID iDs
Michal Zajaček https://orcid.org/0000-0001-6450-1187
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The Astrophysical Journal, 915:111 (7pp), 2021 July 10 Zajaček
178 CHAPTER 6. PAPER 5: ENHANCED DOPPLER BEAMING
Chapter
7
Paper 6: Effect of Extinction on
Quasar Distances
Currently, they are two methods that are used to standardize quasars, i.e. use them as standard
candles in analogy to type Ia supernovae: one method is based on the BLR radius-luminosity
(RBLR − L) relation and the other on the correlation between X-ray (2 keV) and UV (250 nm)
luminosities or LX − LUV relation. These two methods were previously applied to quasar
samples separately. In Khadka et al. (2023), we collected for the first time a sample of 58 X-ray
emitting reverberation-mapped quasars, which allowed to compare luminosity distances based
on LX − LUV and RBLR − L relations as well as the corresponding cosmological constraints.
Quite surprisingly, luminosity distances to the same quasars were not identical within uncertainties.
The distribution of the luminosity distance differences ∆ log DL ≡ log DL,LX−LUV
−
log DL,R−L for this sample deviates from the Gaussian distribution - the distribution peak is
positively shifted and the whole distribution is significantly asymmetric. These are common
characteristics for all the six cosmological models we have considered (flat and non-flat
ΛCDM, XCDM, and ϕCDM models, i.e. cold dark matter models with different equations of
state for dark energy: PDE = wDEϵDE).
In this paper, we propose that the properties of the ∆ log DL distribution can be explained
by invoking standard extinction due to dust in host galaxies. In other words, the extinction
of X-ray and UV emission always contributes to the non-zero difference by the term we
derive: (∆ log DL)ext = (τX − τUV) log e/[2(1 − γ′
)], where τX − τUV is the difference in
the optical depths between X-ray and UV domains, e is the Euler number, and γ′
is the
slope of the LX − LUV relation for a given sample of galaxies. Inversely, since we measured
the positive shift of the distribution, we can estimate the average X-ray/UV colour index
EX−UV ≡ AX − AUV ∼ 5(1 − γ′
)(∆ log DL)ext, which is between 0.03 and 0.28 mag when the
median and the peak values of the distributions are considered, respectively. This amount of
extinction is rather moderate and corresponds to the extrapolated standard optical reddening
of the population of quasars. It can arise due to the presence of dust in the circumnuclear
media of galaxies. When we make use of standard hard X-ray and far UV extinction cuts,
we obtain a quasar subsample for which the extinction outliers are absent but the distribution
positive shift is nevertheless still present. We also notice that the LX −LUV relation is generally
more influenced since the effect arises due to the different amount of extinction in the UV and
the X-ray domains.
Credit: Zajaˇcek et al. (2024b), ApJ 961, 229. Reproduced with permission ©AAS.
179
Effect of Extinction on Quasar Luminosity Distances Determined from UV and X-Ray
Flux Measurements
Michal Zajaček1
, Bożena Czerny2
, Narayan Khadka3,4
, Mary Loli Martínez-Aldama5,6
, Raj Prince2
,
Swayamtrupta Panda7,9
, and Bharat Ratra8
1
Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic; zajacek@physics.muni.cz
2
Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
3
Department of Physics, Bellarmine University, 2001 Newburg Rd, Louisville, KY 40205, USA
4
Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA
5
Astronomy Department, Universidad de Concepción, Casilla 160-C, Concepción 4030000, Chile
6
Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Gran Bretaña 1111, Playa Ancha, Valparaíso, Chile
7
Laboratório Nacional de Astrofísica—MCTI, R. dos Estados Unidos, 154—Nações, Itajubá—MG, 37504-364, Brazil
8
Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506, USA
Received 2023 August 23; revised 2023 November 16; accepted 2023 December 2; published 2024 January 31
Abstract
In Khadka et al., a sample of X-ray-detected reverberation-mapped quasars was presented and applied for the
comparison of cosmological constraints inferred using two well-established relations in active galactic nuclei—the
X-ray/UV luminosity (LX–LUV) relation and the broad-line region radius–luminosity (R–L) relation. LX–LUV and
R–L luminosity distances to the same quasars exhibit a distribution of their differences that is generally asymmetric
and positively shifted for the six cosmological models we consider. We demonstrate that this behavior can be
interpreted qualitatively as arising as a result of the dust extinction of UV/X-ray quasar emission. We show that the
extinction always contributes to the nonzero difference between LX–LUV-based and R–L-based luminosity
distances and we derive a linear relationship between the X-ray/UV color index EX−UV and the luminositydistance
difference, which also depends on the value of the LX–LUV relation slope. Taking into account the median
and the peak values of the luminosity-distance difference distributions, the average X-ray/UV color index falls in
the range of –=-E 0.03 0.28X UV mag for the current sample of 58 sources. This amount of extinction is typical for
the majority of quasars and can be attributed to the circumnuclear and interstellar media of host galaxies. After
applying the standard hard X-ray and far-UV extinction cuts, heavily extincted sources are removed but overall the
shift toward positive values persists. The effect of extinction on luminosity distances is more pronounced for the
LX–LUV relation since the extinction of UV and X-ray emissions both contribute.
Unified Astronomy Thesaurus concepts: Cosmology (343); Cosmological parameters (339); Observational
cosmology (1146); Active galaxies (17); Quasars (1319); Interstellar dust extinction (837)
1. Introduction
The spatially flat ΛCDM cosmological model (Peebles 1984)
is largely consistent with most lower-redshift, z  2.3,
observations (Yu et al. 2018; eBOSS Collaboration 2021;
Brout et al. 2022) as well as with high-redshift cosmic
microwave background (CMB) data at z ∼ 1100 (Planck
Collaboration 2020). However, there are several potential
tensions between flat ΛCDM parameter values inferred using
different techniques (Abdalla et al. 2022; Moresco et al. 2022;
Perivolaropoulos & Skara 2022; Hu & Wang 2023). These can
be addressed by improving the accuracy and precision of
established cosmological probe measurements, and also by
looking for alternative cosmological probes, especially in the
redshift range between nearby data and CMB data.
Active galactic nuclei (AGN), especially bright quasars
(quasi-stellar objects (QSOs); Karas et al. 2021; Zajaček et al.
2023), appear to be promising alternative probes due to their
broad redshift coverage, ranging from the nearby Universe
(z = 0.00106 for NGC4395; Brum et al. 2019) to z ≈ 7.642
(J0313-1806; Wang et al. 2021). For cosmological applications,
so far three types of QSO data have been more widely
utilized: (i) QSO angular size observations (Cao et al. 2017;
Ryan et al. 2019; Cao et al. 2020, 2021a, 2021b; Lian et al.
2021; Cao et al. 2022b); (ii) data based on the nonlinear
relation between QSO X-ray and UV luminosities, the LX–LUV
relation (Risaliti & Lusso 2015, 2019; Khadka &
Ratra 2020a, 2020b; Lusso et al. 2020; Khadka & Ratra 2021;
Li et al. 2021; Colgáin et al. 2022; Dainotti et al. 2022; Hu &
Wang 2022; Khadka & Ratra 2022; Petrosian et al. 2022;
Rezaei et al. 2022; Khadka et al. 2023); and (iii) data based on
the correlation between the rest-frame broad-line region (BLR)
time delay and the monochromatic luminosity, the R–L relation
(Panda et al. 2019a, 2019b; Martínez-Aldama et al. 2019;
Khadka et al. 2021b, 2022a, 2022b; Czerny et al. 2021;
Zajaček et al. 2021; Cao et al. 2022c, 2023; Cao & Ratra 2022;
Panda 2022; Cao & Ratra 2023a; Czerny et al. 2023a; Panda &
Marziani 2023). In addition to these methods, Elvis &
Karovska (2002) suggested using angular diameters of the
BLR to measure the cosmological constant Λ (also see Wang
et al. 2020) and Collier et al. (1999) as well as Cackett et al.
(2007) discussed the application of continuum reverberation
mapping (RM) to measure the Hubble constant. Also, the
H0LiCOW (H0 Lenses in COSMOGRAIL’s Wellspring)
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 https://doi.org/10.3847/1538-4357/ad11dc
© 2024. The Author(s). Published by the American Astronomical Society.
9
CNPq Fellow.
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further
distribution of this work must maintain attribution to the author(s) and the title
of the work, journal citation and DOI.
1
180 CHAPTER 7. PAPER 6: EFFECT OF EXTINCTION ON QUASAR DISTANCES
program based on time delays between lensed images of QSOs
has measured the Hubble constant (Birrer et al. 2020).
QSO standardization based on the LX–LUV relation and the
constructed Hubble diagram has led to claims of strong
cosmological constraints and tension with the ΛCDM model
with the nonrelativistic matter density parameter Ωm0 ∼ 0.3
(Risaliti & Lusso 2019; Lusso et al. 2020). However, the
analyses of Risaliti & Lusso (2019) and Lusso et al. (2020)
were approximate and based on incorrect assumptions (Khadka
& Ratra 2020a, 2020b; Banerjee et al. 2021; Khadka &
Ratra 2021, 2022; Petrosian et al. 2022), i.e., cosmological
parameters and LX–LUV relation parameters were constrained
within the non-flat ΛCDM model; hence, the results were
model dependent. The correct technique for the analysis of
these data was developed by Khadka & Ratra (2020a) and here
we outline it as follows: given the current quality of these data,
one must use them to simultaneously determine the LX–LUV
relation parameters and the cosmological model parameters,
and one must also study a number of different cosmological
models to determine whether the LX–LUV relation parameter
values are independent of the assumed cosmological model. If
the LX–LUV relation parameter values are independent of the
assumed cosmological model, the QSOs are standardizable and
the circularity problem is circumvented. We emphasize,
however, that when correctly analyzed, the most recent Lusso
et al. (2020) data compilation is not standardizable (Khadka &
Ratra 2021, 2022) because the LX–LUV relation parameters
depend on the assumed cosmological model as well as on
redshift (Khadka & Ratra 2021, 2022). Khadka & Ratra (2022)
discovered that the largest of the seven subsamples in the Lusso
et al. (2020) QSO compilation, the Sloan Digital Sky Survey
(SDSS)-4XMM one that contains about 2/3 of the total QSOs,
has an LX–LUV relation that depends on the cosmological
model and on redshift and is the main source of the problem
with the Lusso et al. (2020) data.
On the other hand, the BLR R–L relation parameters
generally appear independent of the adopted cosmological
model (Khadka et al. 2021b, 2022a, 2022b; Cao et al. 2022c).
Cosmological constraints are weak, but for Mg II (at 2798 Å in
the rest frame) and C IV QSOs (at 1549 Å in the rest frame)
they are consistent with those from better established probes
(Khadka et al. 2022b; Cao et al. 2022c). However, there is a 2σ
tension between the constraints given by lower-redshift Hβ
QSOs (at 4861 Å in the rest frame) and those from the better
established probes (Khadka et al. 2022a). The Hβ QSO sample
yields weak cosmological constraints with a preference for
decelerated cosmological expansion. This tension, and possible
systematic issues, related to Hβ QSOs will need to be
addressed when more reverberation-mapped QSOs are available,
e.g., from the upcoming Vera C. Rubin telescope and its
Legacy Survey of Space and Time (LSST; see, e.g., Panda
et al. 2019a; Ivezić et al. 2019; Czerny et al. 2023b) and the
SDSS-V black hole Mapper (Almeida et al. 2023).
In summary, both the LX–LUV relation and R–L relation data
provide cosmological constraints, which is encouraging, but
they have systematic problems that require further study. To
uncover the systematic issues we looked for a sample of X-raydetected
quasars that have been reverberation mapped in the
UV domain using the Mg II line. For such a sample, in
principle, both LX–LUV and R–L relations should be applicable.
To this goal, we provided a sample of 58 X-ray-detected
reverberation-mapped Mg II QSOs in Khadka et al. (2023),
from which we measured both the LX–LUV relation and the R–L
relation parameter values that are consistent with values
measured using larger samples. The sample was quite limited
but we stress that for each of the sources we could determine
the luminosity distance from these two methods independently.
The goal was to compare cosmological constraints inferred
from the QSOs for both of these relations not just in the overall
statistical study of two independent samples but for the same
sample. Using six cosmological models, we found that both
R–L and LX–LUV relations are standardizable. The main result
of this study was that while the R–L relation measurements
favored a smaller Ωm0 value consistent with the Ωm0 ∼ 0.3
value measured using better established cosmological probes,
the LX–LUV relation measurements favored a value of Ωm0
larger than that inferred from the better established cosmological
probes.
In Khadka et al. (2023), we showed that this is in agreement
with the tendency for luminosity distances based on LX–LUV
relation data to have a mean value smaller than luminosity
distances based on R–L relation data for the same QSOs. The
median LX–LUV relation luminosity-distance values, on the other
hand, are mostly larger except for the flat and non-flat XCDM
models. We note that these results are based on the distribution of
the luminosity-distance difference ( )–--D Dlog logL R L L L L, , X UV
normalized by the square root of the quadratic sum of the
corresponding uncertainties.
Here we revisit the nonzero median (mean) of the difference
in the luminosity distances based on the LX–LUV relation and
R–L relation data sets. It is expected that, in the absence of
systematic effects, the median (mean) of the distance-difference
distribution should vanish within uncertainties since we
construct the distribution from the same sample of sources
and the luminosity distance to a particular source must be the
same for both methods. The offset from zero hints at a
systematic effect in one or both data sets and demands further
analysis.
We propose that the offset in the D ºDlog L
– - -D Dlog logL L L L R L, ,X UV
distribution may be attributed to
the extinction (absorption and scattering) of UV and X-ray
photons along the line of sight. Since the extinction curve
generally increases from the UV (2500 Å) to the soft X-ray
bands (2 keV), we evaluate the differential extinction or the
difference in optical depth between the X-ray and UV bands,
τX −τUV. Specifically, we derive a simple analytical relation
between τX − τUV and the slope g¢ of the LX–LUV relation as
well as the luminosity-distance difference D Dlog L, i.e.,
( )t t g- ¢ - D D4.6 1 logX LUV . This way the mean differential
extinction effect, or the X-ray/UV color index, can be
directly inferred for the current sample of 58 X-ray reverberation-mapped
QSOs as well as any future sample of such
sources.
We show that the asymmetry and the positive shift of
D Dlog L distributions for all the considered cosmological
models, including the flat ΛCDM model, with prevailing
positive medians, can be explained by a mild extinction of the
UV and X-ray flux densities from QSOs. From all the median
and the peak values of the D Dlog L distributions, the X-ray/
UV color index falls in the range of ∼0.03–0.28 mag for the
sample of 58 X-ray detected, reverberation-mapped sources
(Khadka et al. 2023). We demonstrate that this amount of
extinction is typical for the majority of QSOs, originates in
the circumnuclear and interstellar media of host galaxies
2
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
181
(Czerny et al. 2004), and is only slightly alleviated by standard
hard X-ray and far-UV extinction cuts (Lusso et al. 2020).
Since the LX–LUV relation employs both UV and X-ray flux
density measurements, it turns out to be more affected by
extinction, which can address some of the previously
mentioned problems with its standardization.
Our paper is structured as follows. In Section 2, we describe
the characteristics of the data set of X-ray reverberationmapped
QSOs. In Section 3, we summarize the calculation
method for luminosity distances and the different cosmological
models we utilize. Subsequently, in Section 4, we derive the
relation between the X-ray and UV optical depth difference
(color index) and the luminosity-distance difference. Our main
results are presented in Section 5. We provide an additional
discussion of the source selection and our results in Section 6
and conclude in Section 7.
The reader may also find additional derivations of luminosity
distances, including the extinction law in Appendix A, whereas
the distributions related to the luminosity-distance difference
formula are presented in Appendix B. Additional distributions
of the X-ray/UV color index for different cosmological models
are shown in Appendix C and the detailed investigation of
reddening using SDSS magnitudes is presented in Appendix D.
2. Data Description
Our sample consists of 58 sources that were both (i)
reverberation mapped using UV continuum and Mg II emission-line
light curves, and (ii) X-ray detected at 2 keV. In this
regard, the sample is complete, and due to its small size, we are
not imposing further selection criteria unless stated otherwise.
There are altogether 59 measurements of BLR time delays
since the time delay for NGC 4151 was measured twice
(Metzroth et al. 2006). The sample is described in detail in
Khadka et al. (2023), and we list the main observables, i.e., the
redshift z, the rest-frame Mg II time delay τ, 2 keV flux density
per frequency FX, 2500 Å flux density per frequency FUV, and
3000 Å flux density F3000, in Appendix A of Khadka et al.
(2023). The sample consists of 53 sources from the SDSS-RM
program (Shen et al. 2016, 2019; Homayouni et al. 2020),
NGC 4151 (Metzroth et al. 2006), and four sources from the
OzDES RM program (Yu et al. 2021). These sources are also
detected in the X-ray domain and are listed in the XMMNewton
X-ray source catalog (4XMMDR11). The sample
position on the sky to the Galactic plane and the Galactic center
(Sgr A*
; Eckart et al. 2017) is shown in Figure 1, which is color
coded using the decadic logarithm of the (B − V ) color index
-Elog B V according to Schlegel et al. (1998).
We summarize the main properties of the main sample in
Table 1. In Khadka et al. (2023), we also estimated the αOX
parameter, finding that our sample is not heavily obscured. An
alternative verification that the Mg II quasars are not intrinsically
obscured sources (or red quasars) is presented in
Appendix D using ugriz magnitudes from the SDSS database.
In addition, we analyze a subsample of 21 sources that meet
the hard X-ray index and far-UV slope criteria of Lusso et al.
(2020).10
The selection methodology and the subsample were
described in detail in Khadka et al. (2023).11
The properties of
the subsample are also described in Table 1.
3. Cosmological Models and Parameters
The application of these QSO observations in cosmology
depends on the empirical measurement of the QSO luminosity
distances. This requires the assumption of a cosmological
model. However, to determine whether or not the QSOs are
Figure 1. The position of the sample of 58 X-rays detected reverberation-mapped sources on the sky. Right ascension (R.A. expressed in hours) is along the x-axis,
while decl. (decl. expressed in degrees) is along the y-axis. The white-dotted circle in the northern hemisphere denotes the sample of 53 SDSS-RM sources (Shen
et al. 2016, 2019; Homayouni et al. 2020), while the five remaining sources (Metzroth et al. 2006; Yu et al. 2021) are more scattered to the south. The figure also
shows the dust extinction map of the Milky Way (red-orange band) color coded using the logarithm of the (B − V ) color index EB−V according to Schlegel et al.
(1998). The position of the Galactic center (Sgr A*
) is marked by a white star, while the north and the south Galactic poles are depicted by plus signs. The ecliptic
plane and the surrounding band of ± 10° are represented by the white-dashed line and the gray-shaded area, respectively.
10
The hard X-ray photon index should lie between 1.7 and 2.8 and the far-UV
spectral slope should lie between −0.7 and 1.5 (Lusso et al. 2020). The
extinction cuts are applied to the sources that are outside these limits.
11
Using the source identification (ID) of Khadka et al. (2023; see their
Appendix A), the IDs of the sources are the following: 18, 28, 44, 118, 159,
185, 260, 280, 301, 303, 338, 440, 449, 459, 522, 588, 675, J141214, J141018,
J141650, and J141644.
3
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
182 CHAPTER 7. PAPER 6: EFFECT OF EXTINCTION ON QUASAR DISTANCES
standardizable requires that we study them in several different
cosmological models to see whether or not the empirical
correlation relation used to determine their luminosities is
independent of the assumed cosmological model (Khadka &
Ratra 2020c). In this paper, we use three spatially flat and three
spatially non-flat12
cosmological models to determine QSO
luminosity distances. In any cosmological model, the luminosity
distance can be computed as a function of redshift (z) and
cosmological parameters (p) in the following way:
⎧
⎨
⎪
⎪
⎩
⎪
⎪
⎡
⎣
⎢
⎤
⎦
⎥
⎡
⎣
⎤
⎦
( )
( )
( )
( ) ( )
( )
( )
( )
∣ ∣
∣ ∣
=
+
W
W
W >
+ W =
W <
+
W
W
D z p
c z
H
H
c
D z p
z D z p
D z p
,
1
sinh , if 0,
1 , if 0,
sin , if 0.
1
L
k
k
C k
C k
c z
H
H
c C k
0 0
0 0
0
0
1
0
k
k
0 0
0 0
Here c is the speed of light, H0 is the Hubble constant, Ωk0 is
the current value of the spatial curvature energy density
parameter, and DC(z, p) is the comoving distance. DC(z, p) is
computed as a function of z and p for a given cosmological
model as follows:
( )
( )
( )ò=
¢
¢
D z p c
dz
H z p
,
,
, 2C
z
0
where H(z, p) is the Hubble parameter that is given next for the
six cosmological models we use in this paper.
In a compact form, the Hubble parameter for all the six
models (spatially flat/non-flat ΛCDM model, XCDM parameterization,
and fCDM model) can be written as
( ) ( ) ( ) ( ) ( )= W + + W + + WH z H z z z1 1 , 3m k DE0 0
3
0
2
where Ωk0 vanishes in the spatially flat models. For the
ΛCDM models and XCDM parameterizations, ΩDE(z) =
( )W + w+z1DE0
1 X , where ΩDE0 is the current value of the dark
energy density parameter and ωX is the dark energy equation of
state parameter. For the ΛCDM models ωX = −1 and the XCDM
parameterizations, ωX, is a free parameter to be determined from
observational data. For the fCDM models (Peebles &
Ratra 1988; Ratra & Peebles 1988; Pavlov et al. 2013),
ΩDE(z) = Ωf(z, α) can be obtained by solving the equations of
motion of a spatially homogeneous scalar field model
numerically. Here α is a positive parameter characterizing the
inverse power-law potential energy density of the dynamical
dark energy scalar field (f) and can be constrained by using
observational data.13
To determine QSO luminosity distances using empirical
correlation relations, in particular, those expressed by
Equations (4) and (6) below, we perform a likelihood analysis
of predicted luminosity distances in a given cosmological
model using Equation (1) and the observational luminosity
distances obtained from Equations (5)–(7) below. This allows
us to measure the nuisance parameters involved in the
correlation relation (and check whether they are independent
of cosmological model parameters), and that ultimately leads us
to the determination of the QSO luminosity distances. For a
detailed description of the computational method and the
determination of QSO luminosity distances used in this paper,
see Khadka et al. (2023).
4. UV and X-Ray Extinction and Luminosity Distances
The source intrinsic UV and X-ray flux densities (per
frequency) at 2500 Å and 2 keV are FUV,int and FX,int,
respectively, and originate in the very central parts of galaxies
during the accretion process and as such are assumed to be
unaffected by dust at the place of their origin. The corresponding
luminosities are calculated as p=L D F4 LUV,int
2
UV, int
and p=L D F4 LX,int
2
X,int, where DL is the luminosity distance of
a given QSO.
For the R–L relation, the corresponding UV luminosity is
expressed at 3000 Å, L3000,int = 4π nnD FL
2
3000, 3000 = 4π
( ) nanD F 2500 3000L
2
UV,int 3000, where αν ; −0.45 is the mean
QSO continuum slope in the frequency domain, nµn
anF (Vanden
Berk et al. 2001) and ν3000 is the frequency corresponding
to 3000 Å. Since the relation between the mean radius of the
BLR region R and the corresponding time delay τ in the rest
frame of the source is given by the light–travel relation, R = cτ,
Table 1
Selected Properties of the Main Sample of X-Ray Detected Reverberation-mapped QSOs and the Subsample of 21 Sources
Property Main Sample Subsample
Source number 58 21
Redshift range (0.0041, 1.686) (0.418, 1.587)
Redshift (16th, 50th, 84th) percentiles (0.527, 0.990, 1.454) (0.4810, 0.919, 1.3394)
2 keV luminosity range [erg s−1
] (1.9 × 1041
, 6.1 × 1044
) (1.6 × 1043
, 1.5 × 1044
)
2 keV luminosity median [erg s−1
] 4.4 × 1043
4.8 × 1043
2500 Å luminosity range [erg s−1
] (1.2 × 1043
, 1.3 × 1046
) (5.9 × 1043
, 4.8 × 1045
)
2500 Å luminosity median [erg s−1
] 9.3 × 1044
9.5 × 1044
Mg II time delay range [days] (5.3, 387.9) (17.2, 387.9)
Mg II time delay median [days] 92.0 99.1
Note. The luminosities are computed for the flat ΛCDM model with Ωm0 = 0.3 and H0 = 70 km s−1
Mpc−1
. Mg II time delays are expressed in the rest frames of the
sources. See Section 2 for the details of the subsample of 21 sources.
12
For discussions of the constraints on spatial curvature see Rana et al. (2017),
Ooba et al. (2018a), Park & Ratra (2019a), DES Collaboration (2019),
Efstathiou & Gratton (2020), Di Valentino et al. (2021), Khadka et al. (2021a),
Dhawan et al. (2021), Vagnozzi et al. (2021a, 2021b), Renzi et al. (2022), Geng
et al. (2022), Cao et al. (2022a), Mukherjee & Banerjee (2022), Glanville et al.
(2022), Wu et al. (2023), de Cruz Pérez et al. (2023), Dahiya & Jain (2023),
Stevens et al. (2023), Favale et al. (2023, and references therein).
13
For discussions of the constraints on the fCDM model see Zhai et al.
(2017), Ooba et al. (2018b, 2019), Park & Ratra (2018, 2019b, 2020), Solà
Peracaula et al. (2019), Singh et al. (2019), Ureña-López & Roy (2020), Sinha
& Banerjee (2021), Xu et al. (2022), de Cruz Perez et al. (2021), Jesus et al.
(2022), Adil et al. (2023), Dong et al. (2023), Van Raamsdonk & Waddell
(2023), Cao & Ratra (2023b, and references therein).
4
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
183
the R–L relation can be expressed in the form using τ instead
of R,
⎜ ⎟ ⎜ ⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
( )
t
b g= + h -
L
log
days
log
10 erg s
, 4
3000,int
1
where γ, β, and η represent the slope, intercept, and normalization
coefficients, respectively. From Equation (4), we can
derive an expression for the luminosity distance DL,R−L as a
function of τ, FUV, int, and the coefficients of the R–L relation
{ [ ( ) ]}
( )
g
t b g p h
=
- - + + -
-D
F
log
1
2
log log 4 log 15.04 ,
5
L R L,
UV, int
where the term 15.04 results from the evaluation of
[( ) ]nanlog 2500 3000 3000 . The LX–LUV relation considering
the intrinsic X-ray and UV luminosities of the sources LX,int
and LUV,int located at the luminosity distance –DL L L, X UV
can be
expressed as
⎜ ⎟ ⎜ ⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
( )b g= ¢ + ¢ h- - ¢ - L
L
log
erg s Hz
log
10 erg s Hz
, 6
X,int
1 1
UV,int
1 1
where b¢, g¢, and h¢ denote quantities analogous to those in
Equation (4). The luminosity distance, –DL L L, X UV
, inferred from
the LX–LUV relation given in Equation (6) is
( )
[ ( ) ( )
( ) ] ( )
–
g
b g p
g h
=
- ¢
¢ + ¢ +
¢ - ¢ -
D
F F
log
1
2 1
1 log 4
log log . 7
L L L,
UV, int X,int
X UV
Taking into account just the intrinsic UV and X-ray flux
densities, we can evaluate the luminosity-distance difference,
D Dlog L, as
( )
( )
( )
–
d
g
=
+
-
¢
-D D
F F
log log
log log
2 1
, 8
L L L L R L, , int
UV, int X,int
X UV
where the factor δ is a function of γ, β, g¢, b¢, and τ,
( )
( )d
b t
g
b g h
g
h
=
-
+
¢ - ¢ ¢
- ¢
+ -
log
2 2 1
7.52
2
, 9
where the term 7.52 results from the evaluation
of [( ) ]nan0.5 log 2500 3000 3000 .
In the following, we adopt the assumption that, in the absence of
a systematic effect, the luminosity-distance difference for a given
source, or the statistical mean (median) of the luminosity-distance
differences for a source sample, vanish, i.e., ( )D ºDlog 0L int ;
hence, ( ) [ ( )]d g+ - - ¢ =F Flog log 2 1 0UV, int X,int . However,
during the propagation of light through the circumnuclear
and interstellar medium of the host galaxy, both UV and X-ray
photons are absorbed and scattered with wavelength-dependent
optical depths τUV and τX, respectively. The observed flux
densities are therefore attenuated following the exponential law,
( )t= -F F expUV UV, int UV and ( )t= -F F expX XX,int . Hence,
the resulting luminosity-distance difference under the influence of
extinction in both the UV and X-ray domains is
( )
( )
( )
( )
( )
( )
( )
d
g
t t
g
t t
g
D
= +
-
¢
+
-
¢
=
-
¢
D
F F e
e
log
log log
2 1
log
2 1
log
2 1
, 10
X
X
L ext
UV, int X,int UV
UV
where the second equation follows because the sum of the first
two terms on the right-hand side of the first part of
Equation (10) is intrinsically zero. In Equation (10), elog
denotes the decadic logarithm of Euler’s number, i.e.,
elog 0.434. We outline a more detailed, step-by-step
derivation of Equation (10) in Appendix A. The relation
among the distributions of δ, ( ) [ ( )]g- - ¢F Flog log 2 1XUV ,
and D Dlog L for our sample is discussed in Appendix B.
Consequently, the optical depth difference τX − τUV can be
expressed as a function of the luminosity-distance difference
and the slope g¢ of the LX–LUV relation
( )
( ) ( )t t
g
- =
- ¢
D
e
D
2 1
log
log . 11X LUV ext
The extinction in magnitude at a given wavelength is directly
proportional to the optical depth, Aλ = 1.086τλ. Hence, we can
express the X-ray/UV color excess as
( ) ( ) ( )

g
º -
¢ á D ñ
-E A A
D5.001 1 log , 12
X X
L
UV UV
ext
where the angular brackets represent the median/mean/peak
value of the luminosity-distance difference for a given
population of QSOs.
5. Results
In Khadka et al. (2023), we simultaneously measured the
R–L or LX–LUV relation parameters and the cosmological
model parameters for six different cosmological models—flat
and non-flat ΛCDM, XCDM, and fCDM. Based on the
cosmological parameter values, we computed the R–L-based
and LX–LUV-based luminosity distances, DL,R−L and –DL L L, X UV
,
respectively. In Figure 2 we show the distributions of D Dlog L.
The plot shows that the difference between the luminosity
distances can be positive or negative. If extinction plays the
dominant role in measurement accuracy, the difference should
always be positive. The presence of negative values implies
that other measurement errors dominate. On the other hand, if
no extinction effect is present, the mean/median values should
be consistent with zero. Establishing the systematic shift is
important, particularly from the point of view of future
measurements coming from very large samples, when the
stochastic net error for the entire sample will become small but
the systematic shift will persist. With this aim, we concentrate
on tracing this systematic shift in the present sample.
In comparison with Khadka et al. (2023), here we
construct distributions of non-normalized luminosity-distance
differences, from which EX−UV can be inferred using
Equation (12). The normalized luminosity-distance distributions
computed in Khadka et al. (2023) are appropriate for
comparing the R–L-based and LX–LUV-based luminosity
distances for each source. For the graphical representation in
Figure 2, we binned D Dlog L using Knuth’s rule (Knuth 2006).
5
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
184 CHAPTER 7. PAPER 6: EFFECT OF EXTINCTION ON QUASAR DISTANCES
Figure 2. Distributions of the quasar luminosity-distance differences –D = - -D D Dlog log logL L L L L R L, ,X UV for 58 sources for flat and non-flat ΛCDM, XCDM, and
fCDM cosmological models (from top to bottom row). The X-ray/UV color index ( )g= - ¢ D-E D5.001 1 logX UV L is enumerated along the top x-axis in each panel.
Solid red vertical lines indicate the mean difference, red-dashed vertical lines indicate the median difference, and red-dotted vertical lines denote the 16th and 84th
percentiles. The bin width is determined based on the Knuth binning algorithm and the source number uncertainties for each bin are s = Ny i i, , where Ni is the
number of points in each bin. The orange-dashed line depicts the best-fit Gaussian function and the blue-dotted line shows the best-fit variable Gaussian function.
6
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
185
The uncertainty in the number of sources falling into the bin is
estimated as s = Ny i i, .
The distributions of the luminosity-distance differences have
several common characteristics. At first glance, the peak of
each distribution is shifted to the positive side, which hints at
positive values of τX − τUV, and hence, also EX−UV. We
summarize the main characteristics, specifically the median
distribution, 16th and 84th percentiles, mean, skewness,
Fisher’s kurtosis, kurtosis test, and the Kolmogorov–Smirnov
(K-S) test statistic, in Table 2. More specifically, for
calculating the distribution skewness, we correct for the
statistical bias and use the Fisher–Pearson standardized
moment ( ) ( )- -N N N m m1 2 3 2
3 2
, where N is the sample
size and m2 and m3 denote the second and the third central
moments, respectively. All of the distributions are positively
skewed, which is caused by the presence of tails on the positive
side. For four out of six models, the median is positive; it is
negative for the flat and non-flat XCDM models. The mean
value is positive for the flat ΛCDM, flat, and non-flat fCDM
models, while for the other cosmological models, it is negative.
Since the mean is more sensitive to the outliers in the
distribution tails, we consider the median values to be more
representative of the quasar sample. Fisher’s kurtosis, which is
also corrected for the statistical bias, is greater than zero, which
implies a heavier tail than for the normal distribution. We
verify the deviation from the normal distribution by performing
the kurtosis test, whose z-scores and the corresponding pvalues
confirm the deviation. The two-sample K-S test is
applied between each model and the flat ΛCDM model. All of
the K-S p-values are close to 1; hence, the null hypothesis that
the D Dlog L distributions are drawn from the same underlying
distribution as the one for the flat ΛCDM model is valid.
Furthermore, we analyze the D Dlog L distributions in Figure 2
by fitting a Gaussian function and a variable Gaussian function to
them.14
The comparison of the fits based on the χ2
value shows
that the variable Gaussian function fits the distributions better,
with the peak value shifted to the positive side and with
σ− > σ+, i.e., the distributions are asymmetric to the peak.
Qualitatively the same behavior is traced for the distributions of
the X-ray/UV color index EX−UV (in magnitude), which is
calculated using Equation (12) and its value is greater than the
luminosity-distance offset by about a factor of 2. We show the
corresponding histograms binned according to Knuth’s rule,
including the Gaussian and the variable Gaussian fits, for all the
flat and non-flat ΛCDM, XCDM, and fCDM cosmological
models in Figure 9 in Appendix C. In Figure 9, the distribution
means are represented by red solid vertical lines, medians are
represented by red vertical dashed lines, and the 16th and 84th
percentiles are shown with red vertical dotted lines. The basic
statistical properties of these distributions, specifically the
EX−UV median and peak values, the right and the left standard
deviations, σ+ and σ−, respectively, are summarized in
Table 3. For all the cosmological models, we obtain
σ+ < σ−, which implies a significant asymmetry. The median
values are predominantly positive (except for the flat and
non-flat XCDM models), with an average value of
Table 2
Characteristics of the Distributions –D = - -D D Dlog log logL L L L L R L, ,X UV for the Six Cosmological Models Considered in This Paper
Model Median 16th Percentile 84th Percentile Mean Skewness Fisher’s Kurtosis Kurtosis Test K-S test
Flat ΛCDM 0.0423 −0.7036 0.6080 0.0167 0.2369 1.7366 2.1136, p = 0.035 0.0000, p = 1.0000
Non-flat ΛCDM 0.0310 −0.7229 0.5806 −0.0030 0.2194 1.7271 2.1068, p = 0.035 0.0690, p = 0.9993
Flat XCDM −0.0539 −0.7911 0.5106 −0.0768 0.2418 1.7391 2.1154, p = 0.034 0.1034, p = 0.9192
Non-flat XCDM −0.0490 −0.7969 0.5003 −0.0812 0.2228 1.7290 2.1082, p = 0.035 0.1034, p = 0.9192
Flat fCDM 0.0534 −0.6766 0.6097 0.0293 0.2390 1.7376 2.1144, p = 0.034 0.0345, p = 1.0000
Non-flat fCDM 0.0556 −0.6780 0.6128 0.0307 0.2375 1.7369 2.1139, p = 0.035 0.0517, p = 1.0000
Flat ΛCDM—21 0.1869 −0.4825 0.5173 0.0114 −0.8175 0.2430 0.4899, p = 0.624 0.1552, p = 0.7855
Note. The distributions are graphically depicted in Figure 2. From the left to the right columns, we list the distribution median, 16th and 84th percentiles, mean,
skewness, and Fisher’s kurtosis parameters (both corrected for statistical bias), the kurtosis test, and the K-S test statistic including the corresponding p-values.
Table 3
Parameters of the X-Ray/UV Extinction EX−UV in Magnitude for Six Cosmological Models Inferred Using the Variable Gaussian Function That Fits the EX−UV
Distributions Better than a Normal Gaussian Function
Model g¢ EX−UV (mag) (median) EX−UV (mag) (peak) σ+ (mag) σ− (mag)
(1) (2) (3) (4) (5) (6)
Flat ΛCDM 0.616 ± 0.074 0.081 0.29 ± 0.13 1.06 ± 0.11 1.29 ± 0.12
Non-flat ΛCDM 0.609 ± 0.073 0.061 0.31 ± 0.10 0.95 ± 0.09 1.25 ± 0.10
Flat XCDM 0.614 ± 0.075 −0.104 0.17 ± 0.13 1.02 ± 0.12 1.29 ± 0.13
Non-flat XCDM 0.608 ± 0.075 −0.096 0.20 ± 0.11 0.89 ± 0.10 1.20 ± 0.11
Flat fCDM 0.609 ± 0.073 0.104 0.34 ± 0.11 1.03 ± 0.10 1.28 ± 0.11
Non-flat fCDM 0.610 ± 0.073 0.108 0.34 ± 0.11 1.03 ± 0.10 1.28 ± 0.11
Flat ΛCDM—21 0.610 ± 0.100 0.364 0.50 ± 0.12 0.82 ± 0.09 1.20 ± 0.13
Note. We transform the luminosity-distance difference D Dlog L to the color excess EX−UV using Equation (12) with the best-fit slope of the LX–LUV relation (column
(2)) adopted from Khadka et al. (2023). Columns (3)–(6) (from the left to the right) list the EX−UV median and peak values, and the standard deviations to the positive
and the negative sides of the distributions, respectively. The quoted errors are the errors of the fit of the variable Gaussian function to the EX−UV histograms
14
For the variable Gaussian function, we use the form according to
Barlow (2004). The variable Gaussian function is introduced as =Gvar
( ( ) [ ( )])s- - +a x x x bexp 20
2 , where σ(x) = σ1 + σ2(x − x0), σ1 = (2σ+σ−)/
(σ+ − σ−), and σ2 = (σ+ − σ−)/(σ+ + σ−).
7
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
186 CHAPTER 7. PAPER 6: EFFECT OF EXTINCTION ON QUASAR DISTANCES
=-E 0.03X UV mag, which is comparable in magnitude to the
value inferred from the mean for the flat ΛCDM model.
The inferred peak values of EX−UV are positive for all
the cosmological models. The average value is
= -E 0.28 0.07X UV mag, and hence, is larger than the value
inferred from the medians. Overall, based on the average
median and the peak values, we estimate the X-ray/UV color
index of –~-E 0.03 0.28X UV mag for our sample.
The positive peak value of the EX−UV distributions for all the
cosmological models implies that the extinction is present in
the sample, and the effect is stronger in the X-ray band than in
the UV band. As we show by the comparison of distributions of
δ and ( ) [ ( )]g- - ¢F Flog log 2 1XUV in Appendix B, the
positive difference between τX − τUV results in the shift of their
sum to positive values due to the extinction term. In other
words, extinction causes the drop of the X-ray flux to the UV
flux density, i.e., -F Flog log XUV is positive, which is
correlated with the positive difference in optical depths,
τX − τUV. If we assume zero extinction in the UV domain,
we can convert –=-E 0.03 0.28X UV mag to the hydrogen
column density NH which is customarily used in X-ray studies.
Assuming just electron scattering, we derive the mean intrinsic
column density of NH = 4.2 × 1022
–3.9 × 1023
cm−2
, which is
moderate and in the Compton-thin regime. It can even be lower
if the effect is partially due to X-ray absorption. If UV
extinction is also present, then the corresponding NH would be
higher since we determine only the difference between the two
effects. However, it is not likely that the two effects just
compensate, so both X-ray and UV extinction effects are
noticeable but not dramatically strong in our sample.
Figure 3. R–L and LX–LUV relations in the flat ΛCDM model (Ωm0 = 0.3) in the left and the right panels, respectively, for the subsample of 21 sources. The top row
depicts the measurements alongside the best-fit relations, including the intrinsic scatter σ, while the bottom row shows the likelihood distributions for the slopes γ and
g¢, the intercepts β and b¢, as well as the intrinsic scatter σint for the corresponding relations.
Table 4
Marginalized One-dimensional Best-fit Parameters with 1σ Confidence Intervals for the 21 LX–LUV and R–L QSOs in the Flat ΛCDM Model
Model Data Ωm0 σint β, b¢ γ, g¢
Flat ΛCDM R–L QSOs L -
+
0.301 0.069
0.041
1.660 ± 0.120 0.360 ± 0.120
LX–LUV QSOs L -
+
0.244 0.054
0.031
25.541 ± 0.090 0.610 ± 0.100
8
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
187
Assuming that in our sample UV extinction is negligible, we
can use the mean X-ray extinction determined from our sample
to correct the measured values of the –Dlog L L L, X UV
. All actual
values should be larger by 0.032 if corrected for X-ray
extinction. When used for the flat ΛCDM cosmology, it
systematically pushes the best solution toward significantly
higher values of Ωm0, roughly by 0.14, as estimated from the
standard cosmology calculator for a median redshift of 0.99, as
in our sample. As we show in the derivations in Appendix A,
see Equations (A3) and (A7), the extinction affects -Dlog L R L,
by a factor of +0.2τUV, while the effect is more pronounced for
–Dlog L L L, X UV
, which is modified by +0.54τX − 0.33τUV.
Hence, for a negligible UV extinction, only the LX–LUV
luminosity distance is affected.
Our analysis result is just the difference between the
extinction effect in the X-ray and UV bands and we cannot
correct the sample without additional spectral studies.
6. Discussion
We have shown that the D Dlog L, and hence, the EX−UV
distributions are also significantly asymmetric and their peaks
are shifted to the positive side for all the cosmological models
considered. We attribute this to the extinction in the X-ray and
UV domains with the average value in the range of
–=-E 0.03 0.28X UV mag based on the average median and
peak values of the EX−UV distributions for all six cosmological
models.
This implies that the effect is not very strong but it is present,
and it can bias the cosmological results. Our sample of 58
sources contains all sources for which we have luminositydistance
measurements with both methods, and we did not
apply any preselection aimed at removing extinction based
on spectral studies of individual sources. By calculating the
αOX index (Khadka et al. 2023) and considering the ugriz
magnitudes from the SDSS catalog (see Appendix D), we can
conclude that our sample is, for the most part, not heavily
obscured and shares properties with the normal (blue) quasar
population.
Nevertheless, even though our sample is not heavily
obscured, we test the effect of extinction for our sample. By
applying X-ray and UV selection cuts, we arrive at a subsample
of 21 sources, for which the heavily absorbed sources were
removed. Furthermore, we connect EX−UV color index to the
more standard EB−V in the optical domain.
6.1. Subsample without Absorbed Sources
To test the extinction effect further, we attempt to remove
sources with larger extinction. In our original sample of 58
quasars (Khadka et al. 2023) no preselection was made since
the sample of X-ray-detected reverberation-mapped quasars is
already limited in size. In the new test, we apply the criteria of
Lusso et al. (2020), as described in Khadka et al. (2023), to
remove absorbed sources based on available hard X-ray photon
indices and far-UV slopes. According to Lusso et al. (2020),
the hard X-ray photon index should lie between 1.7 and 2.8,
which is satisfied for 41 sources, and the far-UV slope should
lie between −0.7 and 1.5, which is satisfied for 27 out of 31
sources for which GALEX EUV magnitudes are available.
Combining both criteria yields a subsample of 21 sources,
which supposedly does not contain heavily extincted quasars;
see Section 2 for the description of the subsample.
For these 21 sources, we construct R–L and LX–LUV relations
in the flat ΛCDM model (Ωm0 = 0.3), see Figure 3, whose
parameters are consistent with those for the corresponding
relations in the main sample of 58 sources, with a slightly
decreased intrinsic scatter of 0.28 and 0.23 dex for the R–L and
LX–LUV relations, respectively. The removal of absorbed
sources is also beneficial for increasing the correlation in both
relations. For the R–L relation, we obtain a Pearson correlation
coefficient of r = 0.63 (p = 2.38 × 10−3
), while for the whole
sample of 58 sources, it is r = 0.56 (p = 4.42 × 10−6
). For the
LX–LUV relation of the subsample of 21 sources, we get
r = 0.86 (p = 5.90 × 10−7
), while for the whole sample, we
have r = 0.78 (p = 6.54 × 10−13
).
We also performed the simultaneous fitting of the LX–LUV or
R–L relation parameters as well as cosmological parameters for
the flat ΛCDM model. For both relations, we list the parameters
in Table 4, including their 1σ confidence intervals. The R–L
and LX−LUV relation parameters for the 21 and 58 sources are
consistent within the uncertainties. The differences in γ and β
for the R–L relation are 0.62σ and 0.15σ, respectively. The
differences in g¢ and b¢ for the LX–LUV relation are 0.04σ and
0.88σ, respectively.
Luminosity distances for the 21 sources inferred using the
two relations are shown in Figure 4. We show the
unnormalized distributions of the luminosity-distance difference
in Figure 5 (left panel). We list the basic statistical
parameters of the unnormalized distribution in the last line of
Table 2. The removal of extincted sources does affect the
distribution by decreasing the mean value of the luminositydistance
difference. In addition, skewness becomes negative
since the positive tail of the distribution disappears. Fisher’s
kurtosis also gets smaller because the obscured sources in the
tails are removed. On the other hand, the median value
increases, which may be the effect of the small size of the
subsample. We also fit the D Dlog L and EX−UV distributions
using the normal Gaussian and the variable Gaussian functions,
see the left and the right panels in Figure 5, respectively, with
the variable Gaussian fitting the distributions better according
to the χ2
statistic. Actually, the distribution of EX−UV becomes
even more asymmetric with σ+ < σ−, see Table 3, and the peak
is positively shifted with EX−UV = 0.50 ± 0.12 mag, while the
median is at ∼0.4 mag. We thus see that the source preselection
Figure 4. Upper panel: luminosity distances for 21 sources (expressed in
104
Mpc) inferred using the R–L and LX–LUV relations in the flat ΛCDM
model. The blue solid line represents the prediction for the flat ΛCDM model
with Ωm0 = 0.3. Lower panel: fractional difference between the observed and
model-predicted luminosity distances for 21 sources. The colors follow the
upper panel convention. The black-dotted line indicates zero fractional
difference.
9
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
188 CHAPTER 7. PAPER 6: EFFECT OF EXTINCTION ON QUASAR DISTANCES
alleviates the problem of extinction by removing the outliers
and reducing the tails. The change in the distribution
characteristics between the samples of 58 and 21 sources
indicates that extinction plays a role in increasing the
distribution tails consisting of outliers and inducing a positive
skewness. However, even after the application of hard X-ray
and far-UV cuts, the positive shift of the distribution peak still
indicates a contribution from extinction.
The normalized distribution of luminosity-distance differences
shown in Figure 6 remains negatively skewed as in the
bigger sample of 58 sources analyzed in Khadka et al. (2023).
For the sample of 58 sources, the mean of the normalized
distribution is negative (−0.116), which indicates that
luminosity distances inferred from the LX–LUV relation are
smaller than those inferred from the R–L relation. This is
consistent with the overall preference of larger Ωm0 for the
LX–LUV relation constructed for 58 sources. The removal of
extincted sources and the final subsample of 21 sources exhibit
the normalized distribution with a positive mean value
(+0.075); hence, this indicates an opposite trend. However,
since the subsample of 21 sources is more than a factor of 2
smaller in size, the change in the sign of the mean value may be
the result of limited statistics and it does not reflect the trend in
the larger samples. However, as for the unnormalized
distribution, the absolute value of the mean decreases, which
implies that the removal of extincted sources is beneficial for
decreasing the luminosity-distance difference between the
LX–LUV and R–L relations.
6.2. Relation to the Extinction Curve and EB − V
Galactic extinction is generally corrected since the (B − V )
color excess is known for the whole range of Galactic
coordinates (see, e.g., Schlegel et al. 1998). Our sample of 58
sources is in a region in the sky that is far from the Galactic
plane, which has a Galactic extinction of EB − V ∼ 0.1 mag, see
Figure 1. However, there still may be uncertainty in the applied
Galactic extinction correction at the level of EB − V ∼ 0.001 mag.
For instance, for NGC 4151 the color index is EB − V ∼
0.024 mag according to Schlafly & Finkbeiner (2011), while it
was measured to be EB − V ∼ 0.027 mag according to Schlegel
et al. (1998); see the NASA/IPAC Extragalactic Database15
for
the extinction values and their scatter for the other sources.
The more uncertain extinction contribution is due to the
QSO optical, UV, and X-ray continuum emissions
being affected by intrinsic extinction. For the SDSS data
(4576 QSOs), Richards et al. (2003) constructed composite
Figure 5. Unnormalized distributions of –D = - -D D Dlog log logL L L L L R L, ,X UV and EX−UV for the sample of 21 (58) sources in the flat ΛCDM model in green
(gray). Left panel: distribution of the unnormalized luminosity-distance difference –D = - -D D Dlog log logL L L L L R L, ,X UV for the subsample of 21 sources. The solid
vertical green (gray) line denotes the distribution mean, the green-dashed vertical (gray) line represents the median, and the green-dotted vertical (gray) lines denote
the 16th and 84th percentiles. The best-fit Gaussian function is depicted by an orange-dashed line, while the best-fit variable Gaussian function is represented by a
blue-dotted line. Right panel: the distribution of EX−UV (in magnitude) in green (gray) for the sample of 21 (58) sources. The vertical lines as well as the blue-dotted
and the orange-dashed lines have the same meaning as in the left panel.
Figure 6. The distribution of –D = - -D D Dlog log logL L L L L R L, ,X UV normalized
by the square root of the sum of the luminosity-distance uncertainties. The
distributions are shown for the whole sample of 58 sources (gray) and the
subsample of 21 sources (green). The vertical lines denote the same statistical
properties as in Figure 5.
15
https://ned.ipac.caltech.edu/
10
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
189
spectra, which they categorized into six composite spectral
classes (Composites 1–6). Composite 1 corresponds to sources
with intrinsically blue (or optically flat) power-law continua,
while Composite 5 corresponds to reddened sources with
optically steep power-law continua. Most of the quasars belong
to rather bluer composite classes with a color excess of
EB − V < 0.04 mag, while only ∼10% are reddened.
Based on the composite spectra constructed by Richards
et al. (2003), Czerny et al. (2004) derived the extinction curve
of QSOs, which is generally similar to the Small Magellanic
Cloud extinction curve (Prevot et al. 1984), e.g., lacking the
absorption feature at 2200 Å except for the shortest UV
wavelengths. The QSO extinction curve can generally be
attributed to a circumnuclear dusty shell composed of
amorphous carbon grains that lack both silicate and graphite
grains based on the corresponding missing spectral features.
In the following, we use the simplified analytical extinction
curve in Czerny et al. (2004),
( [ ]) ( )/l m= - +l
-
A
E
1.36 13 log 1 m , 13
B V
and extrapolate it to the UV/X-ray range (2500 Å–2 keV).
Here Aλ is an extinction correction at wavelength λ, and EB − V
is the color excess measured between the B and V bands, which
are customarily used as the extinction measure in the optical/
UV band. Subsequently, from the inferred UV/X-ray color
excess of EX−UV =AX − AUV ∼ 0.03–0.28 mag (median and
peak values, see Table 3), we can use the relation
( )l l=- -E E13 logX B V XUV UV derived from Equation (13) to
obtain the color excess of EB − V ∼ 0.001–0.01 mag. This can
be interpreted to be predominantly the intrinsic color excess
expected for the majority of type I QSOs (Richards et al. 2003).
This extinction originates in the circumnuclear medium, e.g., in
an obscuring torus, a warped disk-like structure, or an
outflowing clumpy wind within ∼1 pc from the supermassive
black hole (Elvis et al. 2002; Gohil & Ballantyne 2017; Gaskell
& Harrington 2018; Gaskell et al. 2023), and the host galaxy
interstellar medium, also see Stolc et al. (2023) and Czerny
et al. (2023c) for discussions. Dust can also be present on the
scales of a few thousand gravitational radii, i.e., on subparsec
scales, within the BLR clouds (Pandey et al. 2023). Dusty
structures can be located close to a supermassive black hole on
subparsec scales, especially for lower-luminosity sources.
Considering the source at the low-luminosity end, see
Table 1, we have the UV luminosity of νUVLUV ∼ 1.2 ×
1043
erg s−1
, which implies the sublimation radius of
( ) ( )n~ - -r T L0.04 1500 K 10 erg s pcsub sub
2.8
UV UV
43 1 1 2 in the
optically thin limit (Barvainis 1987; Zajaček et al. 2014).
Actually, in the low-luminosity limit of the Galactic center,
compact dusty objects were detected on the scale of
∼1 milliparsec (Gillessen et al. 2012; Peißker et al. 2021),
hence understanding the 3D distribution and geometry of dust
in galactic nuclei as a function of their accretion rate is relevant
for estimating the intrinsic extinction in different wave bands.
Therefore, the discrepancy between luminosity distances
inferred using LX–LUV and R–L relations is expected for any
selection of QSOs. This is consistent with the finding that the
application of extinction cuts based on the hard X-ray index
and the far-UV slope (Lusso et al. 2020) only slightly mitigates
the extinction problem, as we showed in Section 6.1, by
eliminating the outliers forming the tails. However, other
qualitative properties of the EX−UV distribution, mainly the
peak shifted to positive values, persist even after applying the
extinction cuts.
We note that including many lower-luminosity QSOs in the
sample likely enhances the extinction effect. Weaver & Horne
(2022) in their study of 9242 QSOs, all located in SDSS Stripe
82, derived a median extinction EB − V of 0.1 for redshifts
around 2 and higher extinction values for lower and higher
redshifts (see their Figure A1).
Getting an estimate of the total reddening in AGN is crucial.
The typical method involves hydrogen line ratios along UV,
optical, and near-infrared wavelengths such as Lyα/Hβ,
Hα/Hβ, and Paβ/Hβ (Osterbrock & Ferland 2006; Panda 2022;
Gaskell et al. 2023). Other methods require simultaneous
measurements in a broad wavelength range (Shuder &
MacAlpine 1979; Choloniewski 1981; Cackett et al. 2007).
Unfortunately, none of these methods can be implemented for
our sample due to the lack of broadband measurements.
7. Conclusions
We find that the extinction (scattering and absorption) of
X-ray and UV photons from QSOs contributes to the
discrepancy between luminosity distances inferred using
LX–LUV and R–L relations.
For the nonzero luminosity-distance difference, i.e.,
–D = - -D D Dlog log logL L L L L R L, ,X UV
, the extinction term is
equal to ( ) ( ) [ ( )]t t gD = - - ¢D elog log 2 1L Xext UV , where
τX and τUV are optical depths in the X-ray and UV domains,
respectively, and g¢ is the slope of the LX–LUV relation. We
found that the distributions of D Dlog L are asymmetric and
positively shifted for all the six cosmological models
considered. We estimated an average X-ray/UV color index
of –=-E 0.03 0.28X UV mag in our sample, based on all six
distribution median and peak values. We have shown that this
amount of extinction is mild and overall typical for the majority
of type I QSOs since it is supposed to originate in the
circumnuclear and interstellar media of host galaxies (Czerny
et al. 2004). The dust-related systematic problem does not seem
to be completely removed by standard hard X-ray and far-UV
extinction cuts; hence, some caution is necessary when
interpreting the results (Khadka & Ratra 2021, 2022). Therefore,
using at least two complementary methods for larger
samples in the future is recommended.
Acknowledgments
This research was supported in part by Dr. Richard Jelsma (a
Bellarmine University donor), Research Foundation for the
SUNY, US DOE grant DE-SC0011840, by the Polish Funding
Agency National Science Center, project 2017/26/A/ST9/
00756 (Maestro 9), by GAČR EXPRO grant 21-13491X, by
Millenium Nucleus NCN19058 (TITANs), and by the Conselho
Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Fellowships (164753/2020-6 and 313497/2022-2). B.C. and M.
Z. acknowledge the Czech-Polish mobility program (MŠMT
8J20PL037 and PPN/BCZ/2019/1/00069). This project has
received funding from the European Research Council (ERC)
under the European Unionʼs Horizon 2020 research and
innovation program (grant agreement No. [951549]). Part of
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The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
190 CHAPTER 7. PAPER 6: EFFECT OF EXTINCTION ON QUASAR DISTANCES
the computation for this project was performed on the Beocat
Research Cluster at Kansas State University.
Appendix A
Derivation of DL,R−L, –DL L L, X UV
, and EX−UV Expressions in
the Presence of Extinction
A.1. Derivation of DL,R−L
Using the R–L relation in the form of
⎜ ⎟ ⎜ ⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
( )
t
b g= + h -
L
log
days
log
10 erg s
, A13000
1
where the monochromatic luminosity L3000 can be expressed in
the form of the UV flux density at 2500 Å as =L3000,int
( )p n p n=n
anD F D F4 4 2500 3000L L
2
3000, 3000
2
UV 3000, the R–Lbased
luminosity distance can be evaluated as
( )
[ ( ) ]
( )
g
t b
p h
= -
- + -
-D
F
log
1
2
log
1
2
log 4 15.036
1
2
log ,
A2
L R L,
UV
where we used αν ∼ −0.45 for the mean QSO continuum slope
(Vanden Berk et al. 2020). To extract the extinction term that
modifies -Dlog L R L, , we use the extinction law in the form of
= t-F F eUV UV, int
UV, where FUV, int is the intrinsic QSO UV
flux density. Equation (A2) can then be rewritten as
( ) [ ( ) ]
( )
g
t b p h
t
= - - - +
- +
-D
F
e
log
1
2
log
1
2
log 4 15.036
1
2
log
log
2
,
A3
L R L,
UV, int UV
where the nonzero UV optical depth clearly increases the R–L
luminosity distance with the term t t+ ~ +0.2
elog
2 UV UV.
A.2. Derivation of –DL L L, X UV
Analogously, from the LX–LUV power-law relation parameterized
as
⎜ ⎟ ⎜ ⎟
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
( )b g= ¢ + ¢ h- - ¢ - L
L
log
erg s Hz
log
10 erg s Hz
, A4X
1 1
UV
1 1
we can derive the LX–LUV-based luminosity distance –DL L L, X UV
that depends on X-ray and UV monochromatic flux densities at
2 keV and 2500 Å FX and FUV, respectively. The relation is as
follows:
( )
( )
( ) ( )
( )
–
b g h
g
p
g
g g
=
¢ - ¢ ¢
- ¢
-
+
¢
- ¢
-
¢
D
F F
log
2 1
log 4
2
log
2 1
log
2 1
. A5
L L L
X
,
UV
X UV
Using the extinction laws in the UV and the X-ray domains,
= t-F F eUV UV, int
UV and = t-F F eX X,int
X, respectively, we can
express Equation (A5) as
( )
( )
( )
( )
( )
( )
–
b g h
g
p
g t
g
t
g
=
¢ - ¢ ¢
- ¢
-
+
¢ -
¢
-
-
¢
D
F e
F e
log
2 1
log 4
2
log log
2 1
log log
2 1
. A6
L L L
X
,
UV, int UV
X,int
X UV
By separating intrinsic flux density terms from the extinction
terms, we obtain
( )
( )
( )
( ) ( )
( )
–
b g h
g
p
g
g
t
g
t g
g
=
¢ - ¢ ¢
- ¢
-
+
¢ -
¢
+
- ¢
-
¢
- ¢
D
F F
e e
log
2 1
log 4
2
log log
2 1
log
2 1
log
2 1
. A7
L L L
X
,
UV, int X,int
UV
X UV
Hence, for g¢ ~ 0.6 the extinction modifies –Dlog L L L, X UV
by
∼ + 0.54τX − 0.33τUV, i.e., the LX–LUV-based luminosity
distance depends more strongly on the UV optical depth
(it is decreased) than the R–L-based luminosity distance. In
addition, it is increased by the nonzero X-ray optical depth,
which is not present in the R–L-based luminosity-distance
relation. Also, it is essential to note that the extinction effect
for the LX–LUV relation depends on its slope g¢; hence,
this leads to a circularity problem in evaluating the extinction
terms.
A.3. Derivation of EX−UV
The color index between the X-ray and UV domains is
defined as EX−UV ≡AX − AUV = 1.086(τX − τUV). To obtain
EX−UV, we first calculate the difference between D =Dlog L
( )– –- =- -D D D Dlog log logL L L L R L L L L L R L, , , ,X XUV UV
using
Equations (A7) and (A3),
( )
( ) ( )
( )
( )
  
  
  
b g h
g
b t
g
h
g
t t
g
D
=
¢ - ¢ ¢
- ¢
+
-
+ +
-
¢
+
-
¢
d
=
A8
D
F F
e
log
2 1
log
2 2
7.518
log log
2 1
log
2 1
,
L
X
UV, int X,in
0 for intrinsic quasar emission
UV
extinction contribution
where the term ( ) [ ( )]d g+ - - ¢F Flog log 2 1UV, int X,int is
assumed to sum to zero for the intrinsic quasar emission, and
hence the luminosity-distance difference for any source is zero
without extinction. The nonzero difference is thus related to the
extinction term, from which the difference in the optical depth
is ( )t t g- = - ¢ D D e2 1 log logX LUV .
Finally, the color index EX−UV can be expressed just as
a function of the luminosity-distance difference and the slope
12
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
191
g¢ of the LX–LUV relation
( )( )
( ) ( )
g
g
= - ¢ D
- ¢ D
-E e D
D
2.172 log 1 log
5.001 1 log . A9
X L
L
UV
Appendix B
δ versus ( ) [ ( )]g- - ¢F Flog log 2 1XUV Distributions
To illustrate Equation (A8), i.e., dD = +Dlog L
( ) [ ( )]g- - ¢F Flog log 2 1XUV , we compare distributions of
δ, ( ) [ ( )]g- - ¢F Flog log 2 1XUV , and their sum D Dlog L in
Figure 7 for 58 sources and flat and non-flat ΛCDM models
(distributions are similar for the other cosmological models).
The mean value of δ is always negative, while the mean
value of ( ) [ ( )]g- - ¢F Flog log 2 1XUV is positive and of
a comparable magnitude. However, their sum, which is
equivalent to the difference in luminosity-distance logarithms,
is characterized by a distribution with positive skewness and a
nonzero mean in all cases (see Figure 7 and Table 2 for the
details). This behavior can qualitatively be attributed to the
extinction term in Equation (A8) proportional to τX − τUV, from
which the color index EX−UV can be quantified using
Equation (A9). If τX > τUV, then the extinction term is positive
and the distribution of D Dlog L is shifted to positive values. The
positive skewness is mainly given by the fact that for larger
-F Flog log XUV the optical depth difference tends to be
greater since τX > τUV for sources with a more absorbed X-ray
emission.
For the sample of 21 sources that pass the reddening criteria
of Lusso et al. (2020), the mean value of dD = +Dlog L
( ) [ ( )]g- - ¢F Flog log 2 1XUV decreases for the flat
ΛCDM model in comparison with the full sample of
58 sources (0.011 versus 0.017), see Figure 8. This implies
that the reddening cuts are beneficial for decreasing the offset;
however, the intrinsic extinction contribution seems to still be
present.
Figure 7. Comparison of distributions of the factor δ (blue histogram; see Equation (A8)), the factor ( ) [ ( )]g- - ¢F Flog log 2 1XUV (red histogram), and
( ) [ ( )]– d g- = + - - ¢-D D F Flog log log log 2 1L L L L R L X, , UVX UV (green histogram) for 58 sources for the flat and non-flat ΛCDM cosmological models in the left
and the right panels, respectively. The black solid vertical line denotes zero, while the colored dashed vertical lines (blue, green, and red) represent the means of the
corresponding distributions.
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192 CHAPTER 7. PAPER 6: EFFECT OF EXTINCTION ON QUASAR DISTANCES
Appendix C
EX−UV Distributions
Using Equation (12), i.e., º --E A AX XUV UV
( ) ( )g- ¢ á D ñD5.001 1 log L ext , we construct distributions of
the color index EX−UV from the luminosity-distance differences
for each source. We show histograms of EX−UV for six
cosmological models (flat and non-flat ΛCDM, XCDM, and
fCDM models from the top to the bottom rows) in Figure 9. All
of the 58 sources have EX−UV in the interval (−6,6) and the
histogram bin widths are determined based on Knuth’s rule. The
red solid vertical line represents the distribution mean, the
dashed vertical line denotes the median, and the red-dotted lines
represent the 16th and 84th percentiles. We also perform fits of
Gaussian and variable Gaussian functions to all the distributions,
which are shown by orange-dashed and blue-dotted lines,
respectively.
Figure 8. Comparison of distributions of the factor δ (blue histogram; see Equation (A8)), the factor ( ) [ ( )]g- - ¢F Flog log 2 1XUV (red histogram), and
( ) [ ( )]– d g- = + - - ¢-D D F Flog log log log 2 1L L L L R L X, , UVX UV (green histogram) for the subsample of 21 sources for the flat ΛCDM cosmological model. The
black solid vertical line denotes zero, while the colored dashed vertical lines (blue, green, and red) represent the means of the corresponding distributions.
14
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193
Figure 9. Distributions of the X-ray/UV color indices EX−UV for 58 sources for the flat and non-flat ΛCDM, XCDM, and fCDM cosmological models (from top to
bottom row). The X-ray/UV color index ( )g= - ¢ D-E D5.001 1 logX UV L is calculated based on the luminosity distances for each source and the LX–LUV relation
slope for each cosmological model. Solid red vertical lines represent EX−UV means, red-dashed vertical lines represent EX−UV medians, and red-dotted vertical lines
represent the corresponding 16th and 84th percentiles. The bin width is set based on the Knuth binning algorithm and the histogram y uncertainties for each bin are
s = Ny i i, , where Ni is the number of points in each bin. The best-fit Gaussian function is represented by an orange-dashed line, while the best-fit variable Gaussian
function is depicted by a blue-dotted line.
15
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194 CHAPTER 7. PAPER 6: EFFECT OF EXTINCTION ON QUASAR DISTANCES
Appendix D
Inference of the Reddening Using the SDSS Magnitudes
An alternative possibility to infer the reddening effect in our
sample involves using the ugriz magnitudes from the SDSS
database. To compare the behavior of our sample, we have
adopted the blue and red quasar samples defined by Glikman et al.
(2022). They considered red quasars as sources that have
EB−V > 0.25. We have obtained the u and z magnitudes from
the SDSS database, which are not reported by Glikman et al.
(2022). The SDSS magnitudes for the Mg II reverberation-mapped
sample were taken from Shen et al. (2019). In all cases,
the magnitudes were corrected for galactic extinction. Color–color
plots are shown in Figure 10, where it is possible to observe the
difference between the blue and the red samples. Most of the Mg II
reverberation-mapped sources are located at the left, bluer part of
the distribution, which indicates that they have EB−V < 0.25. This
result is consistent with the one found in Section 5. In Figure 10
we also identify the 21 sources that satisfy the selection criteria of
Lusso et al. (2020), see Section 2; these exhibit the same behavior
as the full 58 source sample. Some of our sources are located in
the red quasar zone or show peculiar behavior to the rest of the
sample. We have identified three sources (SDSS J141110.95
+524815.5, SDSS J142041.78+521701.6, and SDSSJ141645.58
+534446.8) that are in the red zone or show different behavior in
at least two color–color diagrams. The consistent location of
SDSS J141110.95+524815.5 and SDSS J142041.78+521701.6
in the red quasar zone suggests that they have a high extinction.
SDSS J141645.58+534446.8 shows extreme behavior, but it is
not necessarily located in the red quasar region. However, a visual
inspection of the spectrum shows a flat continuum in the optical
range, which suggests a high degree of reddening. One of these
sources (SDSS J142041.78+521701.6) belongs to the 21 source
sample. Thus, the criteria based on the hard X-ray index and farUV
slope criteria of Lusso et al. (2010) seem to be effective in
cleaning the sample.
Figure 11 shows the u − g and g − i distributions as a
function of redshift. Using the Calzetti et al. (2000) extinction
law, we obtained the expected change in relative color as a
function of redshift for EB − V = 0.04, 0.09, 0.15, and 0.2. We
assumed a continuum slope of α = −1.56 and α = −0.45
following the composite spectrum of Vanden Berk et al. (2001)
for u − g and g − i colors, respectively. The behavior is the
same as the one in Figure 10, red and blue quasar samples
occupy different zones in the diagrams, and most of the Mg II
reverberation-mapped sources overlap with the blue quasar
sample. The EB − V curves indicate that our sample has
EB − V < 0.2. EB −V = 0.09 is in the middle of the distribution,
which supports the results found in Section 5. In Figure 11 we
also show the limit for red sources at u − g = 0.8 according to
Richards et al. (2003), which coincides with the EB − V = 0.2
curve. Since most of the reverberation-mapped sample is to the
left of this curve, this suggests that our sample is more
consistent with a blue behavior. The EB − V curves confirm the
red color of the three sources identified above. These objects
should be excluded from future analyses.
Figure 10. Color–color diagrams for blue and red quasar (triangle symbols) samples defined by Glikman et al. (2022), and the Mg II reverberation-mapped sample
(green diamond symbols). Star symbols correspond to the 21 objects described in Section 2. Lowercase letters identify the redder objects of the Mg II reverberationmapped
sample: (a) SDSS J141110.95+524815.5 , (b) SDSS J142041.78+521701.6 , (c) SDSS J141645.58+534446.8.
16
The Astrophysical Journal, 961:229 (18pp), 2024 February 1 Zajaček et al.
195
ORCID iDs
Michal Zajaček https://orcid.org/0000-0001-6450-1187
Bożena Czerny https://orcid.org/0000-0001-5848-4333
Narayan Khadka https://orcid.org/0000-0001-5512-2716
Mary Loli Martínez-Aldama https://orcid.org/0000-0002-
7843-7689
Raj Prince https://orcid.org/0000-0002-1173-7310
Swayamtrupta Panda https://orcid.org/0000-0002-
5854-7426
Bharat Ratra https://orcid.org/0000-0002-7307-0726
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Chapter
8
Paper 7: UV FeII Emission Model
and BLR Time Delays
FeII emission has many line transitions, many of which contribute significantly to the UV and
the optical spectra of quasars, creating collectively a so-called FeII pseudocontinuum. The
UV FeII pseudocontinuum lies in the same wavelength range as the broad emission line of
MgII at 280 nm, hence the knowledge of the FeII contribution, or rather a UV FeII model,
can affect the inferred properties of the MgII line.
Previously, in Zajaˇcek et al. (2020), we determined the redshift of HE 0413-4031 based
on the UV FeII pseudocontinuum, which yielded the value of z = 1.3764. In this study, in
addition to the 11-year monitoring by the Southern African Large Telescope (SALT), we
included a near-IR spectrum obtained by the SOAR telescope. This gave an access to narrow
Hβ (486.1 nm) and [OIII] transitions (495.9 nm and 500.7 nm), which led to a much better
determination of the source redshift: z = 1.39117 ± 0.00017. The new and more precise
value of the redshift led to a different spectral decomposition into MgII and UV FeII spectral
contributions. The properties and the time delay of MgII (τMgII = 224+21
−23 days) were not
significantly influenced. However, the time delay of FeII (τFeII = 251+9
−7 days) is in agreement
with the FeII line full width at half maximum (4200 km s−1
), which is slightly smaller than
the MgII FWHM. These results are based on the new best-fitting FeII template and the same
virial black-hole mass for MgII and FeII lines. Hence, the UV FeII line emitting material is
more distant by 27 light days or ∼ 0.023 pc (4700 AU) than the MgII line emitting material
in HE 0413-4031. The new decomposition of the MgII+FeII complex also yields a much
smaller blueshift of the MgII line in the range between −270 km s−1
and −240 km s−1
, which
is consistent with the inferred line velocity shifts based on the composite spectra of quasars.
Furthermore, we also collect MgII time-delay measurements for as many as 194 sources,
and the best-fit MgII RBLR − L relation, log (τ/lt. day) = (0.32±0.04) log (L3000/1044
erg s−1
)+
(1.74 ± 0.04), remains significantly flatter than RBLR − L relations for the Hβ, UV and optical
FeII lines whose slopes are consistent with γ ∼ 0.5 within the uncertainties, and hence also
with the simple photoionization argument that assumes that the product of the ionization
parameter and the electron number density for the broad-line region clouds across all AGN
Uionne = Q(H)/(4πR2
BLRc) is approximately constant, and hence RBLR ∝ Q(H)1/2
∝ L1/2
since
the ionizing photon flux Q(H) =
+∞
νi
(Lν/hν)dν is proportional to the luminosity.
Credit: Zajaˇcek et al. (2024c), A&A 683, A140. Reproduced with permission ©ESO.
199
A&A, 683, A140 (2024)
https://doi.org/10.1051/0004-6361/202348172
c The Authors 2024
Astronomy
&
Astrophysics
UV FeII emission model of HE 0413−4031 and its relation to
broad-line time delays
Michal Zajaˇcek1 , Swayamtrupta Panda2 , Ashwani Pandey3 , Raj Prince3, Alberto Rodríguez-Ardila2,4,
Vikram Jaiswal3, Bo˙zena Czerny3 , Krzysztof Hryniewicz5, Maciej Urbanowicz6 , Piotr Trzcionkowski6,
Marzena ´Sniegowska7, Zuzanna Fałkowska8,3 , Mary Loli Martínez-Aldama9, and Norbert Werner1
1
Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotláˇrská 2, 611 37 Brno,
Czech Republic
e-mail: michal.zajacek31@gmail.com
2
Laboratório Nacional de Astrofísica, MCTI, Rua dos Estados Unidos, 154, 37504-364 Itajubá, MG, Brazil
3
Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
4
Instituto Nacional de Pesquisas Espaciais, Divisão de Astrofísica, Avenida dos Astronautas 1758, São José dos Campos,
12227-010 SP, Brazil
5
National Centre for Nuclear Research, ul. Pasteura 7, 02-093 Warsaw, Poland
6
Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warsaw, Poland
7
School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
8
Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland
9
Astronomy Department, Universidad de Concepción, Casilla 160-C, Concepción 4030000, Chile
Received 5 October 2023 / Accepted 20 December 2023
ABSTRACT
Context. FeII emission is a well-known contributor to the UV spectra of active galactic nuclei and the modeling of this part may affect
the results obtained for the MgII λ2800 emission, which is one of the lines used for black hole mass measurements and cosmological
applications.
Aims. We tested different FeII emission models when modeling the UV emission of the intermediate-redshift quasar HE 0413−4031
to see how the use of a specific template affects the MgII λ2800 line properties and the measurement of the MgII λ2800 and UV FeII
time delays with respect to the continuum.
Methods. We used the 11-year monitoring of the selected quasar HE 0413−4031 with the South African Large Telescope (SALT),
and we supplemented this monitoring with the near-IR spectrum taken with the SOAR telescope, which gave access to the Hβ λ4861
and [OIII] λλ4959, 5007 emission lines at the rest frame and allowed for a precise measurement of the redshift.
Results. A new redshift determination (z = 1.39117±0.00017) using [OIII] λλ4959, 5007 gave a very different value than the previous
determination based only on the UV FeII pseudocontinuum (z = 1.3764). It favors a different decomposition of the spectrum into
MgII and UV FeII emissions. The line characteristics and the time delay of the MgII emission (224+21
−23 days) are not significantly
affected. However, in comparison with the previous analysis, the rest-frame UV FeII time delay (251+9
−7 days) is consistent with the
inferred UV FeII line full width at half maximum (FWHM) of 4200 km s−1
that is only slightly smaller than the MgII line FWHM.
Hence the FeII-emitting material is more distant than the MgII-emitting gas in HE 0413−4031 by ∼0.023 pc (4700 AU). The inferred
velocity shift of both MgII and UV FeII lines with respect to the systemic redshift is now rather low, below 300 km s−1
. In addition,
we constructed an updated MgII radius-luminosity (R−L) relation from 194 sources, which is more than double the previous sample.
The MgII R−L relation is flatter than the UV FeII, optical FeII, and Hβ R−L relations. While the new decomposition of the spectrum
is satisfactory, we see a need to create better FeII templates using the newest version of the code CLOUDY.
Key words. accretion, accretion disks – techniques: photometric – techniques: spectroscopic – quasars: emission lines –
quasars: individual: HE 0413–4031
1. Introduction
The characteristic property of the bright active galactic nuclei
(AGN) is the occurrence of broad and strong emission lines in
the optical and UV bands (see Krolik 1999; Karas et al. 2021;
Czerny et al. 2023a,b, for reviews). Those emission lines are
clearly visible in the individual objects as well as in the quasar
composite spectra (e.g., Cristiani & Vio 1990; Francis et al.
1991; Vanden Berk et al. 2001). The strongest emission lines
usually listed in the quasar catalogs for individual objects
Based on observations made with the Southern African Large Telescope
(SALT).
CNPq Fellow.
are Hβ λ4861, MgII λ2800, CIII] λ1908, CIV λ1549, and
Lyα λ1215, depending on the object redshift and the coverage
in the corresponding rest frame. Many more lines are
listed in a single source or smaller sample studies (see,
e.g., Martínez-Aldama et al. 2018; Horne et al. 2021; Shen et al.
2023). Apart from the well-specified lines, there is a contribution
from the Balmer continuum supplementing the emission
of the accretion disk responsible for the continuum emission.
The last but very important contributor is the emission from the
FeII and FeIII ions (see e.g., Gaskell et al. 2022, for a short
review). Numerous transitions present in the optical and UV
data lead to the formation of the FeII pseudo-continuum. Particularly,
in the vicinity of the MgII line, there is a strong and
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200 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
overlapping contribution from FeII. The issue has been studied
for many years (e.g., Collin-Souffrin et al. 1979; Wills et al.
1980, 1985). The presence of FeII in bright AGN is universal; a
similar FeII/MgII line ratio is observed in AGN at all redshifts,
from nearby sources to z ∼ 5 objects (Dietrich et al. 2003).
However, the FeII contribution to the optical band
is not well correlated with FeII in the UV domain
(Kovaˇcevi´c-Dojˇcinovi´c & Popovi´c 2015, hereafter also denoted
as KDP15; Popovi´c et al. 2019). The optical FeII strongly correlates
with the source Eddington ratio, which underlies the
concept of the quasar optical main sequence (Boroson & Green
1992; Sulentic et al. 2000; Panda et al. 2018, 2019c). The existence
of the corresponding UV quasar plane based on MgII
line properties and the UV FeII is not so well established
(´Sniegowska et al. 2020). The UV and optical FeII emission
may be well correlated in a single object but it does not seem
to come from the same part of the broad line region (BLR;
Panda et al. 2019a; Zhao et al. 2020). In multi-object statistical
samples, there is an overall correlation between the quasar
luminosity and the UV FeII strength (Clowes et al. 2016). Several
works (Marziani et al. 2003; Shen & Ho 2014; Panda et al.
2019c; Zheng 2021; Panda & Marziani 2023) claim that the FeII
strength can actually be used as the Eddington ratio indicator.
The strong overlap between the UV FeII and MgII emissions
complicates the measurements of the MgII time delay
and makes the modeling of the emissivity and the dynamics
of UV FeII difficult. The FeII models in this spectral
range are either constructed from the data, with objects of
extremely narrow emission lines, such as I Zw 1, serving as
the best templates (Vestergaard & Wilkes 2001, hereafter also
denoted as VW01), or theoretically (Bruhweiler & Verner 2008;
Kovaˇcevi´c-Dojˇcinovi´c & Popovi´c 2015). The analysis is additionally
complicated by the fact that the FeII emission can be
considerably shifted with respect to the rest frame, which can
also make an identification of the individual transitions in the
data problematic.
The precision of the spectral decomposition close to the
MgII line has several important consequences. First, the measurements
of the kinematic width of the FeII and MgII components,
and the measurements of the corresponding delays should
shed light on the stratification of the BLR. The next issue is
the proper determination of the radius-luminosity (R–L) relation
for the MgII line which is essential for the black hole mass
measurements from a single spectrum in large statistical samples
(e.g., Wang et al. 2009; Kovaˇcevi´c-Dojˇcinovi´c et al. 2017;
Le et al. 2020). These R–L relations for both MgII and FeII can
also reveal stratification of the BLR. Proper determination of the
FeII is also important from the point of view of the statistical
studies of the AGN properties. The principal component analysis
(PCA) approach by Boroson & Green (1992) clearly showed
the dominant role of the two parameters: (i) the ratio of the FeII
equivalent width in the optical band to the equivalent width of Hβ
line, and (ii) the full width at half maximum (FWHM) of Hβ line.
These two parameters form the optical plane, but in a close analogy,
a UV plane can be introduced based on FeII emission in UV
and MgII line properties (Panda et al. 2019a; ´Sniegowska et al.
2020). Finally, the R–L relation can be successfully used in cosmological
studies to constrain the expansion rate of the Universe
(Khadka et al. 2021).
The spectral decomposition into FeII and MgII can be
improved by the wavelength-resolved time delay measurements.
Such studies of three intermediate-redshift quasars were performed
– for CTS C30-10 (Prince et al. 2022), and for HE
0413−4031 and HE 0435−431 (Prince et al. 2023), each monitored
for 11 years with the Southern African Large Telescope
(SALT). The results did not imply any outflow but indicated
different apparent stratification of the FeII and MgII emissions
in the three quasars. The study, when combined with the separate
FeII and MgII time delays available from the literature, also
enabled us to create the radius-luminosity relation for both spectral
features, which suggests more compact emission regions
with FeII-emitting clouds being located closer to MgII-emitting
material for a lower luminosity, while at higher monochromatic
luminosities, both regions are more distant and they radially converge.
However, our results were based on the assumption that
FeII is at the systemic redshift and this assumption certainly
could bias our choice of the FeII template.
The redshift determination for the source HE 0413−4031,
which is a bright, intermediate-redshift quasar studied in this
paper, was recently obtained based on the high-quality single
spectrum in the IR band in the observed frame (Panda et al.,
in prep.). The spectrum covered well the Hβ region with accompanying
narrow [OIII] λλ4959, 5007 lines. The position of the
[OIII] line allowed for a precise measurement of the source redshift
which was considerably different from the redshift used
originally by Zajaˇcek et al. (2020) for the MgII line reverberation
mapping and by Prince et al. (2023) for the wavelengthresolved
study. The previous value was determined based on
the UV FeII pseudocontinuum transitions seen in the observed
optical spectrum. Therefore, in this paper, we study several
FeII templates with the final aim of fitting better the spectra
and checking whether the substantial change in the FeII/MgII
decomposition affects the measurement of the MgII and UV
FeII time delays. This could have important implications for the
use of the quasar emission-line time delays for cosmology (see
e.g., Panda et al. 2019b; Czerny et al. 2021, 2023a; Khadka et al.
2021; Zajaˇcek et al. 2021, 2023b; Cao et al. 2022, 2024, for
applications).
The paper is organized as follows. We briefly describe the
photometric and spectroscopic data in Sect. 2 and present a
revised redshift for the source HE 0413−4031. In Sect. 3 we outline
the spectral decomposition of our SALT spectra. We present
the results (Sect. 4) from the spectral decomposition and the
time delay analyses from the spectrophotometric data and highlight
the significant effect on the measured parameters due to the
change in the redshift for this source. We discuss the implication
of the new time delays for the MgII and UV FeII emission lines
and show the location of HE 0413−4031 in the updated MgII and
FeII R–L relations in Sect. 5. The new R–L relation for MgII is
based on the largest sample used for this purpose. We also show
a new preliminary FeII spectral model using the updated version
of the CLOUDY photoionization code, which exhibits several differences
with respect to the older model. Furthermore, within
the same section, we discuss the location of this source in the
UV quasar main sequence. Finally, we summarize our findings
in Sect. 6.
2. Observational data
We use almost the same data for the quasar HE 0413−4031, first
identified in the Hamburg-ESO survey by Wisotzki et al. (2000),
as was done by Prince et al. (2023). We supplement it with
one new spectroscopic long-slit measurement from the Southern
African Large Telescope (SALT), obtained in January 2023,
so the whole spectroscopic monitoring covers the period from
January 2013 till January 2023. The basic raw data reduction
is done by the standard SALT pipeline for the Robert Stobbie
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201
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
Spectrograph (RSS; Burgh et al. 2003; Kobulnicky et al. 2003;
Smith et al. 2006; see also Crawford et al. 2010).
We supplement the spectroscopic data with photometric data
from several telescopes, as described in Prince et al. (2023). This
data is needed for the absolute calibration of the spectra. The
basic quasar properties were estimated previously (Zajaˇcek et al.
2020). The black hole mass based on the reverberation mapping
and the spectral energy distribution fitting is in the range
log (M• [M ]) = 9.0−9.7 (Zajaˇcek et al. 2020). The SMBH
accretes close to the Eddington limit, λEdd = 0.38−2.18, which
was estimated using the inferred range of SMBH masses and
different values of the bolometric correction (see Zajaˇcek et al.
2020, for details). The quasar is bright, with the V magnitude
typically about 16.5 as reported by Véron-Cetty & Véron
(2010).
The redshift was estimated as z = 1.3764 assuming that
the UV FeII emission in this source is at the quasar rest
frame (Zajaˇcek et al. 2020). Then the best fitting FeII template
was d12-m20-20-5.dat (hereafter d12), one of the theoretical
templates of Bruhweiler & Verner (2008), corresponding
to the cloud number density of 1012
cm−3
, the turbulent
velocity of 20 km s−1
, and the hydrogen ionizing photon flux
of 1020.5
cm−2
s−1
. However, a recent high-quality observation
of this source in the near-IR (NIR) using the TripleSpec4 longslit
spectrograph (Schlawin et al. 2014) on the 4.1 m SOAR (see
Fig. 1 and Table 1) brought the new determination of the redshift
of 1.39117 ± 0.00017 (Panda et al., in prep.). Briefly, we use a
custom script that calculates the barycenter of the data points
around a selected wavelength range and informs the wavelength
with respect to the peak position of the [OIII]λ5007 emission
line. We extract the wavelengths for the doublet [OIII]λλ4959,
5007 lines separately and find that the resulting redshifts are
identical up to the 4th decimal place. Henceforth, we consider
the value of the redshift derived from the [OIII]λ5007 line as
quoted above. The error on the redshift is estimated from the
RMS of the skylines in the spectrum in the 6th order of the crossdispersed
spectrum, that is where the Hβ region including the
[OIII]λλ4959, 5007 are observed.
The observations were made in cross-dispersed mode and
the spectral resolution (R) for this spectrum was ∼3500 across
the different dispersion orders. Observations were made nodding
in two positions along the slit. Right before the science target,
a telluric star (HIP18437), close in airmass to the former, was
observed to remove telluric features and to perform the flux calibration.
Cu-Hg-Ar arc frames were also observed at the same
position as the science target for wavelength calibration. The
rms for the calibrated spectrum was found to be 0.201 Å and
the wavelength scale has been realigned to the wavelength of
the skylines as recorded on the spectrum of the target. The spectral
reduction, extraction, and wavelength calibration procedures
were performed using spextool v4.1, an IDL-based software
developed and provided by the SpeX team (Cushing et al. 2004)
with some modifications specifically designed for the data format
and characteristics of TripleSpec4, written by Katelyn Allers
(priv. comm.). Telluric feature removal and flux calibration were
done using xtellcor (Vacca et al. 2003). The different orders
were merged into a single 1D spectrum from 1 to 2.4 microns
using the xmergeorders routine.
This new redshift value implies a rough velocity shift by
4400 km s−1
. It implies that either the FeII is outflowing with an
extreme velocity, higher than typically seen in the UV FeII component
(below 3000 km s−1
; Kovaˇcevi´c-Dojˇcinovi´c & Popovi´c
2015), or the FeII template used in our previous work is not
correct. For this reason, we try out different UV FeII templates
4700 4750 4800 4850 4900 4950 5000 5050
rest [Å]
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Flux[ergs1cm2Å1]
1e 16
H
O[III]5007
Fig. 1. Rest-frame spectrum for the HE 0413−4031 covering the spectral
range around the Hβ region obtained using the SOAR/TripleSpec4
NIR spectrograph. The redshift (z = 1.39117 ± 0.00017) was estimated
using the [O iii]λ5007 emission line. The zero-velocity positions of Hβ
and [O iii]λ5007 emission lines are marked using the dashed vertical
lines.
Table 1. SOAR IR fits with redshift z = 1.39117 ± 0.00017 implied by
fitting narrow lines.
Component FWHM σ EW
[km s−1
] [km s−1
] [Å]
Broad Hβ 5457±238 2820±21 55.1±0.7
Narrow Hβ 552.3±24.1 229.2±1.7 0.70±0.01
Narrow [OIII]4959 552.3±24.1 229.2±1.7 3.60±0.04
Narrow [OIII]5007 552.3±24.1 229.2±1.7 9.20±0.11
Notes. The full width at half maximum (FWHM), the line dispersion
(σ), and the line equivalent width (EW) are reported for the broad and
the narrow components of the Hβ, and the narrow components for the
[O iii]λ4959 and [O iii]λ5007, respectively.
to see if we can obtain a better fit and overall consistency than
previously.
3. Spectral decomposition method
The quasar HE 0413−4031 accretes at the high Eddington
ratio and it shares the characteristics of type A quasars
(Sulentic et al. 2000), analogs of Narrow Line Seyfert 1 class
(Osterbrock & Pogge 1985) for lower-mass sources, especially
its strong emission lines are well fitted with a single
Lorentzian profile. Although the FWHM of the broad Hβ line
is 5457 ± 238 km s−1
(see Table 1), which is above the canonical
FWHM division of 4000 km s−1
between type A and B
quasars (Sulentic et al. 2000), this division shifts toward a larger
FWHM for high-luminosity quasars as HE 0413−4031 (see
Marziani et al. 2018, for discussion).
Thus, following the previous studies on this source, we
assume a single kinematic component for the MgII line shape
(Zajaˇcek et al. 2020; Prince et al. 2023). However, we take into
account that MgII is a doublet, and this is included in our modeling,
assuming the same widths for the two components, fixed
separation. The value of the doublet ratio was optimized by
Zajaˇcek et al. (2020) using the mean spectrum. We use the same
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202 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
value of 1.9 in the current paper. The kinematic width, line position,
and normalization are free parameters of the model. The
underlying continuum is described as a power law with an arbitrary
normalization and a slope. We fit the data in a relatively
narrow range to avoid issues with broad-band normalization
of the SALT spectra. In Prince et al. (2023), we used the restframe
range of 2700–2900 Å which corresponds to 6416.50–
6891.79 Å in the observed frame. Next, we aim to compare fits
for the two values of the source redshift. Here we fit the data in
the same observed wavelength range, corresponding to fitting the
data in the range of 2683.09–2881.84 Å in the rest frame for the
new redshift of 1.39117 ± 0.00017. This is important since there
is imperfect subtraction of the sky lines at the longest wavelength
tail which might affect the data fitting and proper comparison of
the results.
For the FeII pseudocontinuum, we test several templates:
theoretical templates of Bruhweiler & Verner (2008), observational
VW01 templates, and mixed KDP15 templates. Templates
of Bruhweiler & Verner (2008) are just a collection of atomic
transitions, so they require two parameters: template broadening
and overall normalization. The VW01 template requires also two
parameters for additional broadening. KDP15 templates contain
six components with independent normalizations (five atomic
representative transition groups – Multiplets 60, 61, 62, 63 and
78, plus I Zw 1 component), so overall they require 7 parameters.
Optionally, we also consider the presence of the He II line
at 2733.28 Å in the quasar spectrum.
4. Results
In this section, we assess the best FeII model template for the
precisely determined redshift of HE 0413−4031, and subsequently,
we analyze the impact of the selected FeII templates
on the MgII and FeII emission full-width at half maximums
(FWHMs), equivalent widths (EWs), light-curve properties, and
time delays with respect to the continuum emission.
4.1. Spectral decomposition and the best FeII template
In the previous papers (Prince et al. 2023; Zajaˇcek et al. 2020),
we used the d12 template of Bruhweiler & Verner (2008). Thus,
after the redshift correction, we first fit the data with the same
template. However, all the fits with the d12 template for the new
redshift are worse. The ratio of the new χ2
value to the old one
is shown in Fig. 2. The previously used FeII template is thus not
compatible with the new redshift measurement.
The issue is a suitable representation of the apparent excess
which is now seen at ∼2730 Å, see the spectrum in Fig. 3 close
to 6540 Å in the observed frame. With the previous value of the
redshift, it was located at ∼2750 Å and it was fitted by one
of the strong FeII transitions seen in all Bruhweiler & Verner
(2008) templates. Thus, we supplemented the d12 FeII template
with the possibility of the contribution from the He II line
λ2733.28. This line was observed, for example, in the quasar
IRAS P09104+4109 by Tran et al. (2000). We assumed the arbitrary
position, the width, and the shift of this additional line.
However, this did not improve the fit considerably. We also
tested the VW01 template but the fit quality with the new redshift
was very low. This could be due to the sharp FeII peaks in
this template based on the observed spectrum of I Zw 1 with
exceptionally narrow broad emission lines. Thus, we applied
additional broadening to this template by convolving it with a
Gaussian profile. For a grid of models with the Gaussian width
Fig. 2. Ratio of the new to the old value of χ2
when two redshifts for
the FeII template d12 are used.
sampled from 1000 to 1400 km s−1
with the step 100 km s−1
,
we obtained a χ2
minimum at 1300 km s−1
. We give the value of
2600 km s−1
in Table 2 since this better represents the FWHM.
The new fit not only improved in comparison with the previous
case but it became much better than the fit of the old template
with an extra He II line.
Next, we used the set of UV FeII KDP15 templates. In the
previous paper, we did not favor this template (see Zajaˇcek et al.
2020, their Table C1) as it required a two-component shape of
the MgII line to give an improved fit with respect to the d12
template. However, we were using smaller values of the redshift
there. Now, with the new redshift from the IR data, we can
indeed fit the data significantly better with this template.
We compare various spectral fits in detail for Observation
14, which is one of the best from the SALT observing campaign
for the studied object (see Table 2). For the KDP15 template,
we studied the width range from 3800 km s−1
to 5000 km s−1
,
and the shift range from +1000 km s−1
to −4000 km s−1
. The
contour plot is shown in Fig. 4. The best fit was achieved for
a zero velocity shift of the FeII contribution and the broadening
factor of FWHM = 4200 km s−1
. The improvement in the
χ2
value is by more than 100, which is significant for the number
of new additional parameters of 5 (we now have 6 independent
normalization factors of the FeII multiplets instead of 1 free
parameter). However, since the number of degrees of freedom
in the fits with d12 template and KDP15 template are different,
we also determine the Bayesian Information Criterion (BIC)
for these fits, which in the case of χ2
fitting method reduces to
BIC = k log n + χ2
, where k is the number of free parameters in
the model and n is the number of data points (in our case, we
have 578 points). The strong decrease in the BIC parameter supports
the claim that the fit with the KDP15 template and the new
redshift is better. The fitted parameters are given in Table 2.
Visually, both fits, d12 and KDP15 with the shift of 0 km s−1
and the broadening of 4200 km s−1
(denoted as KDP15-0-4200),
provide a good fit to the data (see Fig. 3, upper panel). However,
the decomposition of the spectrum into the MgII component and
the FeII pseudo-continuum in both cases is rather different. We
plot the FeII component alone in Fig. 3 (middle panel) with the
same normalization. The FeII contribution to the spectrum is
much lower for the KDP15 template and its shape in the rest
frame is very different. We have made a test of fitting another
observation (Observation 7) using again a broad range of shifts
and widths for the KDP15 template. The best fit was found for
slightly different parameters: the best shift of −500 km s−1
, and
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203
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
Table 2. HE 0413−4031 fits of Observation 14 for different decompositions.
Model FWHM(MgII) EW(MgII) MgII shift FWHM(FeII) EW(FeII) χ2
k ∆ BIC
[km s−1
] [Å] [km s−1
] [Å]
z = 1.37648, d12 4601.6+105.8
−104.6 28.1+0.3
−0.3 1668+5
−24 2830 10.3+0.6
−0.6 1246.04 6 0
z = 1.37648, VW01 5187.5+129.4
−114.7 29.8+0.5
−0.5 1472+37
−37 – 4.9+0.6
−0.6 1940.00 6 693.96
z = 1.37648, VW01 5218.7+110.9
−121.6 30.0+0.6
−0.6 1476+49
−34 2400(∗)
5.2+0.7
−0.7 1932.50 6 686.46
d12 4906.3+50.3
−121.7 28.0+0.4
−0.4 −67+19
−24 2830 5.7 +0.5
−0.6 1787.35 6 541.31
d12 + He IIλ2733.28 5046.9+150.0
−119.7 28.9+0.3
−0.5 −108+20
−34 2830 3.8+0.7
−0.7 1485.76 9 258.80
VW01 5085.9+89.0
−115.1 33.7+0.5
−0.6 −212+12
−22 – 7.8+0.5
−0.5 1478.00 6 231.96
VW01 5031.3+115.5
−109.2 37.2+1.0
−1.2 −237+34
−9 2600 (∗)
13.8+4.0
−1.9 1189.35 6 –56.69
KDP15-0-4200 4503.1+58.0
−58.9 27.1+0.2
−0.3 −270 +15
−15 4200 4.0+0.43
−0.43 1130.50 11 –83.74
Notes. When the redshift is not mentioned, z = 1.39117 is adopted. Negative velocity implies blueshift and k is the number of free parameters in
the model. (∗)
Additional broadening on top of that originally in the template.
FWHM = 4800 km s−1
, although χ2
at this minimum is not much
lower than the χ2
value for the best shift and FWHM favored for
Observation 14.
The properties of the fitted FeII template are also rather
surprising since the normalization of the multiplet 62 (see
Appendix C in Zajaˇcek et al. 2020, for the descriptions of individual
UV FeII transitions), usually dominating at 2750 Å, converged
to zero in the fitting process. Instead, most of the FeII flux
at the blue wing of MgII (here and in the further text, the “blue
wing” of the UV FeII refers to the wavelength range 2683.09–
2800.00 Å in the source rest frame while the “red wing” refers
to the portion at 2800.00–2881.50 Å) is now provided by the
Multiplet 63 as well as by the I Zw 1 component contribution
(see Fig. 3, lower panel). It is also surprising to note that the
width of the FeII lines in the new fit is only slightly narrower
than the FWHM of the MgII line in this observation, which is
4503 km s−1
. However, this small FWHM difference is consistent
with the inferred MgII and FeII time delays, see Sect. 4.3.
To test the role of the FeII template shape, we fit Observation
14 using the VW01 template. It gave a good fit when an
optimized extra broadening was applied but not as good as the
KDP15 template. It resulted in a much stronger FeII contribution,
comparable to what we obtained for the old redshift and
the d12 template. This template also favored the new redshift, as
is seen from Table 2.
Since the KDP15-0-4200 template was the most satisfactory
for the new redshift, we used it to fit all observations. We allowed
all six normalization parameters of the template to vary but the
width and the shift were the same. We do not expect drastic variations
in the properties of the FeII emission during the campaign.
In Fig. 5, we compare the fit quality for all the observations
for the new redshift and the new templates (KDP15 and VW01)
to the previously used redshift and the old d12 template. We see
that some observations are now fitted better and some are not.
Statistically, the new redshift and the new template combination
works slightly better since the average ratio of the corresponding
χ2
is 0.99. Specifically, the newly selected template with the new
redshift gave the average value of the χ2
of 1793.77 while the fit
to all data with the old redshift and d12 template gave 1797.73.
Therefore, on average, we do not see a high improvement, particularly
when we keep in mind that the fit has, in principle, five
more free parameters related to the FeII template. However, the
fit is equally satisfactory as before and it uses the new redshift
coming from the IR data.
The new spectral decomposition does not strongly affect the
MgII line. The average value of the EW(MgII) is now 28.5±0.5Å
with a dispersion of 2.8 Å, while when we use the old redshift
and the old template, it is 30.7 ± 0.6Å with the dispersion of
3.2 Å. The small systematic shift is visible in Fig. 5, lower panel
and the level of variability dropped slightly. The pattern remains
roughly the same as in our old analysis, with the initial strong
rise, followed by a decrease up to JD 5000 and smaller variations
afterward. Only the roughly systematic shift down by ∼2 Å is
visible.
The new fit to MgII also shows an interesting improvement
after the change of the redshift. The position of the line during
the fitting is a free parameter and the average shift of MgII now
is only −234 km s−1
(blueshift), so the line is much closer to
the systemic redshift than in the previous fitting (1650 km s−1
,
redshift). The average width of the MgII line remains larger than
that of the FeII (4605 km s−1
vs. 4200 km s−1
). A small systematic
shift of the MgII line (from −212 to −270 km s−1
) is consistent
with the velocity shifts with respect to [OIII] λ5007 in the
composite spectra of the quasar population (Vanden Berk et al.
2001).
However, the properties of FeII drastically changed. The
new decomposition lowered the FeII EW level from the average
12.5±0.4 Å down to 3.2±0.1 Å in the studied wavelength band.
Thus, the fractional variability in EW(FeII) is now higher, 24%
while in the previous analysis, it was 17%. We did not subtract
the measurement error here, so the quoted value is not the excess
variance. In addition, the change does not look like a simple shift
pattern but shows considerable randomness in time.
The fitted FeII template in principle has six independent
components, corresponding to five Multiplets plus
one component named I Zw 1, added for completeness
(Kovaˇcevi´c-Dojˇcinovi´c & Popovi´c 2015). This extra component
did not find support in the theoretical analysis of the strongest
FeII transitions close to MgII but some strong features contributing
at ∼2715 Å and peaking at around ∼2840 Å were present
in the spectrum of the object I Zw 1, and such a component
seemed to be required to fit the spectra of other objects so it was
included in the KDP15 set as a sixth component named UVFeIIIZw1
lines. We later refer to this component as I Zw 1 component.
However, not all of the six components were actually
important for fitting the object studied in this paper. Actually,
during the fitting, some of these six components were best fitted
with a zero normalization, as in the case of Observation 14.
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204 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
KDP15-0-4200
VW01, new redshift
d12, old redshift
VW01, old redshift
KDP15-0-4200
VW01. new redshift
d12, old redshift
VW01, old redshift
Fig. 3. Modeling spectra with various FeII templates for the old and the
new redshift. Upper panel: Four fits of Observation 14 in the observed
frame: two models for the old redshift z = 1.37648, d12 and VW01 templates
with extra broadening, and two for the new redshift z = 1.39117,
the KDP15 template, shift = 0, FWHM = 4200 km s−1
, and the VW01
template with additional broadening. Dashed lines show the corresponding
continua. Middle panel: FeII contribution in the rest frame
for all the FeII templates used for the fits in the upper panel (see the
legend). Lower panel: Decomposition of the fitted FeII with the KDP15
template into individual multiplets: I Zw 1 (red dashed line), multiplet
60 (blue long dashed), multiplet 61 (green, dash-dot), multiplet 62 (yellow,
invisible in the scale), multiplet 63 (magenta, dotted), and multiplet
78 (cyan, almost invisible in the scale), with the black line corresponding
to the total FeII emission. The FeII flux density in all three panels is
expressed in erg s−1
cm−2
Å−1
.
Fig. 4. Contour plot for fitting the KDP15 template to Observation 14.
The upper panel shows the results for a broad parameter range, and the
lower panel shows the best fit, and 1σ, 2σ, 3σ, and 4σ errors.
The key element that never vanishes is the Multiplet 63. The
second component that is important in some of the spectra – but
not in all the spectra – is the empirical I Zw 1 component. The
largest variation was seen in Multiplet 60 which was occasionally
zero, but sometimes present with a relatively large amplitude.
This is related to the fact that this transition is usually
strong but it peaks around 2950 Å, and below 2900 Å we see
only its tail (see Kovaˇcevi´c-Dojˇcinovi´c & Popovi´c 2015, their
Fig. 4). A larger number of the degrees of freedom in the FeII
template increased the relative variations of the FeII intensity
as a function of time. It happened despite the fact of using the
same shift and width in all 32 data sets. We additionally tested
the effect of the change of the shift and the FWHM of the FeII
on the final FeII strength. As we mentioned above, for Observation
7, the best shift was −500 km s−1
, and the best FWHM was
4800 km s−1
, which slightly differs from the values adopted here
and based on Observation 14. In this nonstandard fit, the EW of
FeII was indeed higher, 6.9 Å instead of 3.9 Å for a standard fit
illustrated in Fig. 5. However, this value is still below the value
obtained with the old redshift (13.8 Å).
To illustrate better the FeII properties in the current fits, we
created the average FeII profile by combining FeII contributions
from all the observations. In Fig. 6, we show the mean unnormalized
FeII as fitted by the model, together with Multiplet 63
(black line). This component peaks at ∼2742 Å. The weakness of
A140, page 6 of 18
205
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
Fig. 5. Comparison of the fit quality using the new UV FeII templates
and the previous one. Upper panel: χ2
ratio between the new redshift fits
for the KDP15 template with no shift, 4200 km s−1
broadening (black
line), and for the VW01 template (magenta line) with additional broadening
and the fit with the d12 template and the old redshift. Middle
panel: EW(FeII). Lower panel: EW(MgII) in these fits (blue, old redshift
and template; red, KDP15; and green, VW01). Observation 14 is
highlighted with an open circle.
Fig. 6. Mean FeII emission averaged over all 32 observations (red) as
fitted by all six components. The black line represents the contribution
from the multiplet 63 and the remaining part is almost entirely due to
the I Zw 1 component (see KDP15), for FWHM of 4200 km s−1
, and no
shift with respect to the systemic redshift. FeII flux density is in units of
erg s−1
cm−2
Å−1
.
Multiplet 62 is rather surprising since this should be the strongest
of the transitions.
4.2. MgII and FeII light curves
To perform time-delay measurements, we created MgII and FeII
light curves as we did in Prince et al. (2023) by normalizing each
spectrum with the help of photometry and subtracting the underlying
power-law component as well as MgII and FeII contributions,
accordingly. In comparison to Prince et al. (2023), in this
work, we have an additional SALT spectrum taken on January
26, 2023 (MJD 59970) extending the total duration from January
0.8
0.9
1.0
1.1
1.2
1.3
Flux[arbitraryunits]
continuum
ASAS-SN
4.5
5.0
5.5
6.0 total MgII
6500 7000 7500 8000 8500 9000 9500 10000
Time[MJD]
1.5
2.0
2.5
total FeII
F[erg/cm2/s/A]
Fig. 7. All photometric light curves including archival data from the
ASAS-SN. The middle and lower panels show the total MgII and FeII
emission light curves in units of 10−16
erg cm−2
s−1
derived using the
new redshift, z = 1.39117, respectively. The FeII pseudocontinuum was
modeled using the VW01 template.
2013 to January 2023. The SALT spectrum is reduced following
a similar procedure as described in Prince et al. (2023). The total
length of the continuum light curve is 3799.30 days with a mean
cadence of 37.25 days. The BLR line-emission light curves have
a total length of 3655.98 days, with a mean sampling of 117.93
days.
The normalized MgII and FeII light curves, together with the
continuum light curve are shown in Fig. 7. For the continuum V
band data, the photometric information is collected from various
telescopes, namely the 1.5 m telescope at OGLE observatory,
40 cm Bochum Monitoring Telescope (BMT), and SALT
measurement with the SALTICAM (all are shown in orange
color). In addition, we also include the archival V-band data from
ASAS-SN (in purple) to extend the baseline of the continuum
emission.
4.3. MgII and FeII time delays
Using the continuum, MgII, and FeII light curves, we performed
time-delay analyses to find out if robust time delays can be
detected for the new UV FeII templates. In particular, in comparison
with the previous time-delay analyses of HE 0413−4031,
here we focus on the role of the FeII emission model (template)
in affecting the line-emission correlation with the continuum,
and thus the time-delay determination.
We used different time-delay methodologies, namely interpolated
cross-correlation function (ICCF; Peterson et al. 1998),
discrete correlation function (DCF; Edelson & Krolik 1988),
z-transferred DCF (zDCF; Alexander 1997), χ2
method
(Czerny et al. 2013), JAVELIN (Zu et al. 2011, 2013, 2016),
von Neumann, and Bartels estimators (Chelouche et al. 2017)
to infer the best time delay. For completeness, we show the
plots and the inferred time-delay estimates for all the methods
in Appendix A. For comparison, two comparably good
FeII templates were considered to infer the MgII and the FeII
emission time delays: the KDP15 template and the VW01
template. The uncertainties were typically inferred using the
time-delay peak distributions constructed from several hundred
light curves generated using the bootstrap method (see e.g.,
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206 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
Table 3. Summary of MgII emission time delays inferred using different
methodologies.
Method KDP15 VW01
ICCF – highest r 541 (r = 0.87) 606 (r = 0.73)
ICCF – peak 552+79
−70 605+30
−219
ICCF – centroid 491+50
−47 517+95
−90
DCF 565+34
−34 586+29
−29
zDCF 597+35
−75 638+49
−93
χ2
619+26
−116 623+27
−62
Javelin 493+4
−15 493+3
−17
Von Neumann 495+12
−113 405+42
−27
Bartels 495+19
−113 405+45
−34
τ – observer’s frame 538+51
−56 534+89
−94
τ – rest frame 225+21
−23 223+37
−39
Final MgII time delay 224+21
−23
Notes. For individual methods, time delays are expressed in days in the
observer’s frame, while the last two rows represent the mean time delays
expressed in days in the rest frame of the source.
Zajaˇcek et al. 2019, 2020; Prince et al. 2023, where we already
applied all the methods used in this paper).
The time delay results for MgII emission are summarized
in Table 3, where the values are expressed in the observer’s
frame unless stated otherwise. The time delays are generally
between ∼500 and ∼600 days, except for the Bartels method
and the VW01 template, which indicates the best time delay at
∼405 days. The time-delay calculations for the MgII line with
the new redshift give very similar results to what was obtained
in Prince et al. (2023) as well as in Zajaˇcek et al. (2020) using
the old redshift. This is related to the fact the decomposition in
both cases (the older and the new redshift) yielded very similar
values of the equivalent width of MgII (see lower panel of
Fig. 5).
The MgII light curve is very strongly correlated with the
continuum light curve, which implies that the observed continuum
is the driving photoionizing emission. In particular, the case
of the best-fit FeII template KDP15 exhibits the peak correlation
coefficient of r ∼ 0.87. For the VW01 template, the correlation
coefficient only slightly drops to r ∼ 0.73. This trend
is also reflected for other time-delay methods, for which the
cases with the VW01 template exhibit lower correlation coefficients
(zDCF) or the minima are located at larger values of
the corresponding measures (χ2
, von Neumann, and Bartels estimators,
see Appendix A). This can be interpreted as the result
of the VW01 FeII emission model, which is older and more
approximate than the KDP15 model, which lowers the overall
correlation of MgII with the continuum. Despite that the determined
best MgII time delays are consistent within the uncertainties
among the different time-delay methods and the two templates,
see Table 3. By averaging the time delays among different
methods and the two templates, we arrive at the final value
of τMgII = 224+21
−23 days in the rest frame of the source. This value
is within 2σ uncertainty consistent with the values reported in
Prince et al. (2023) and Zajaˇcek et al. (2020), whose mean values
are ∼26% and ∼35% larger than the one found here for the
new redshift and KDP15/VW01 templates.
However, the FeII intensity is much different in these two
cases. The FeII emission in the new KDP15 decomposition
based on the new redshift is now by a factor of 3 fainter. We performed
time-delay computations but we did not obtain a satisfactory
solution for the time delay. The situation is best illustrated
in the case of the ICCF plot (see Fig. 8, left panel, dashed lines).
The maximum value of the correlation coefficient r is close to
0.8 for both KDP15 and VW01 templates which clearly shows
that the FeII light curve and the continuum are very well correlated.
However, the function peaks close to the zero time delay,
see the summary of peak and centroid values for both templates
in Table 4 (first three rows). This strongly suggests that the FeII
light curve is strongly contaminated by the continuum itself and
the decomposition of the spectrum into FeII and continuum is
probably not satisfactory.
In the next attempt to search for a FeII time delay, we just
consider the blue wing of the FeII emission in the wavelength
range 2683.09–2800.00 Å, which is dominated by FeII multiplet
63. The blue wing of the FeII emission is more pronounced
within the KDP15 model, see Figs. 3 and 6, and thus less contaminated
by the continuum. This does not result in a qualitative
change of the ICCF and the peak correlation coefficient is again
close to zero, see Fig. 8 and Table 4.
Finally, we assess that the large peak close to zero days is due
to the continuum long-term trend present in both light curves.
For the FeII emission light curve, the trend is present due to significant
contamination by continuum. Therefore, to isolate the
FeII variability and response, we subtract the long-term (hereafter
LT) trend from both light curves using the fitted third-order
polynomial in the form ftrend = f1(t−t0)3
+ f2(t−t0)2
+ f3(t−t0)+ f4,
where f1, f2, f3, and f4 are the fitted parameters. We show
the continuum and the UV FeII emission light curves after the
LT trend subtraction in Fig. 9 for the case of the KDP15 template
(the FeII emission corresponds to the more prominent blue
wing), wherein the top panels we display the original light curves
and in the bottom panels we show the corresponding light curves
after the LT term subtraction and with the addition of the mean
flux densities of the original light curves. This proves efficient in
enhancing the correlated and delayed FeII emission (see Fig. 8,
solid lines), which is revealed by the asymmetric ICCF that is
increasing for positive time delays. When we consider negative
and positive time delays in the ranges (−800, 0) days and
(0,+800) days, the calculated mean values of correlation coefficients
for the templates KDP15, KDP15–blue wing, and VW01
are listed in Table 5, where we see that after the LT trend subtraction
(templates denoted by the star), the ICCF gets asymmetric
with the mean correlation coefficients for time delays above
zero days being greater and positive. For the large time-delay
interval of (−1500, 1500) days, the peak and centroid values
become larger and mostly positive with respect to the cases without
the LT trend subtraction, see Table 4. However, this is at the
cost of generally lower correlation with the peak values of only
r ∼ 0.3−0.4. The well-defined correlation peak at ∼600 days (in
the observer’s frame) for the KDP15 FeII template–blue wing is
considered as the best candidate time-delay peak. Thus, when we
narrow down the search interval to (450, 750) days for KDP15,
KDP15–blue wing, and VW01 templates, all three cases share
consistent peak and centroid ICCF values close to ∼600 days,
see Table 4 (last three rows). This is also confirmed visually in
Fig. 9 (bottom left panel), where we superpose the rescaled FeII
light curve shifted by −600 days. Although these time-delay values
correspond to rather low correlation coefficients, we treat
the time delay of τFeII = 251+9
−7 days (average of the peak and
the centroid values for the KDP15-blue wing case expressed in
the rest frame) as a plausible candidate value of the true FeII
emission time delay.
A140, page 8 of 18
207
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
1500 1000 500 0 500 1000 1500
time delay [days]
1.00
0.75
0.50
0.25
0.00
0.25
0.50
0.75
1.00
r
ICCF: FeII (-1500, 1500)
KDP15
KDP15: blue wing
VW01
KDP15*
KDP15: blue wing*
VW01*
450 500 550 600 650 700 750
time delay [days]
0.10
0.05
0.00
0.05
0.10
0.15
0.20
0.25
r
ICCF: FeII (450, 750)
KDP15* KDP15: blue wing* VW01*
Fig. 8. ICCF for the FeII emission using different FeII templates (KDP15 and VW01). Left panel: The ICCF for the FeII templates KDP15,
KDP15–blue wing, and VW01 without the long-term subtraction (dashed lines). By subtracting the long-term trend from the continuum and lineemission
light curves, the ICCF becomes asymmetric with respect to zero (solid lines) and the time-delay peak between 450 and 750 days can be
identified, especially for the blue-wing part of the KDP15 template. Right panel: The ICCF for all the three considered cases (KDP15, KDP15–blue
wing, VW01) in the interval between 450 and 750 days in the observer’s frame. For the best-fitting KDP15 template, the cross-correlation peak is
at ∼600 days. See Table 4 for the summary of the peak and the centroid values (last three rows).
Table 4. Summary of FeII emission time-delay constraints (expressed in days in the observer’s frame) using the ICCF.
Method KDP15 KDP15 – blue VW01
ICCF – highest r (−1500,+1500) 50 (r = 0.86) −71 (r = 0.80) −237 (r = 0.75)
ICCF – peak (−1500,+1500) 34+62
−132 22+187
−542 −237+270
−122
ICCF – centroid (−1500,+1500) −38+93
−109 −69+165
−269 −85+92
−215
ICCF ( )
– highest r (−1500, +1500) 134 (r = 0.38) 600 (r = 0.27) −1034 (r = 0.36)
ICCF ( )
– peak (−1500, +1500) 134+162
−234 128+472
−1194 −31+569
−1016
ICCF ( )
– centroid (−1500, +1500) 127+183
−219 114+483
−1184 −50+580
−990
ICCF ( )
– highest r (450, 750) 594 (r = 0.13) 600 (r = 0.27) 539 (r = 0.21)
ICCF ( )
– peak (450, 750) 595+96
−66 600+31
−10 574+67
−43
ICCF ( )
– centroid (450, 750) 592+102
−55 602+28
−30 570+76
−39
Final FeII time delay (rest frame) 251+9
−7
Notes. The results denoted with the star (ICCF( )
) represent the cases with the long-term trend subtraction (using the third-order polynomial fit)
from both light curves. The time interval in the parentheses denotes the search interval for the best time delay.
In Appendix A.7, we also verify that after the subtraction of
the LT trend from the MgII light curve, it is possible to recover the
time delay reported previously. Using the ICCF, we can recover
a time-delay peak between ∼400−600 days (in the observer’s
frame), albeit at a significantly lower correlation coefficient of
∼0.4−0.5. When the centroid and the peak values are averaged
among the two templates, the mean rest-frame time delay 213+62
−35
days is in agreement with the previously reported time delay without
any LT trend subtraction. Hence, in summary, the LT trend
subtraction can help recover a time delay between the two light
curves, especially for line light curves contaminated by the underlying
continuum emission, such as for the FeII emission in this
paper,althoughitisatacostofloweringthecorrelationcoefficient
and increasing the uncertainty in the time-delay determination.
5. Discussion
We analyzed the spectroscopic data collected in the years
2013–2023 with the telescope SALT for the intermediateredshift
quasar HE 0413−4031, concentrating on the MgII spectral
region. These data include one more spectrum than the
data analyzed by Prince et al. (2023) but most importantly, in
the meantime, we determined the precise redshift to the quasar
from the IR observation at the observed frame with the telescope
SOAR which is based on the narrow optical [OIII] λλ4959, 5007
lines considered as the most reliable indicators of the quasar
rest frame. New redshift determination essentially changed the
decomposition of the quasar UV spectrum into MgII, FeII, and
the underlying continuum. We checked how it affected the time
delay measurements.
We showed that the MgII time delay was not affected by
the change of the redshift and decomposition. The new decomposition
with the UV FeII KDP15 template implies no shift
with respect to the systemic redshift while the previous redshift/decomposition
indicated the velocity shift between the FeII
and MgII. Nevertheless, the time delay remained the same,
from 500 to 600 days in the observed frame, independent of
the decomposition, redshift, and the time delay measurement
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208 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
Table 5. Comparison of correlation coefficients for different FeII
templates for time delays below and above zero days (up to 800
days).
Template (−800, 0) (0, 800)
KDP15 0.74 0.68
KDP15–blue-wing 0.71 0.68
VW01 0.63 0.53
KDP15(∗)
–0.01 0.16
KDP15(∗)
–blue-wing –0.04 0.11
VW01(∗)
–0.08 0.10
Notes. After the long-term trend subtraction from both continuum and
FeII light curves, the ICCF becomes clearly asymmetric, and for time
delays larger than zero days, the mean correlation coefficient is greater
and positive. The templates denoted by (∗)
represent the light curves with
the long-term trend subtraction (last three rows).
method. Thus the maximum systematic error is on the order of
10%. We thus stress that the MgII line time delay can be used
reliably for probing the properties of the BLR and for cosmology,
and the results are not sensitive to the actual method.
However, the line properties of the FeII emission are very
sensitive to the redshift and the best-fitting FeII model. Previously,
in Prince et al. (2023) we performed the time-delay
analysis of the total FeII emission as well as wavelengthresolved
reverberation mapping of the MgII+FeII complex.
The recovered MgII and FeII time delays based on different
methods, 314.4 and 330.6 days, respectively, are in tension
with the MgII and FeII FWHMs, FWHM(MgII) =
4380 km s−1
and FWHM(FeII) = 2820 km s−1
, respectively.
Assuming that the MgII and FeII material is fully virialized
with the same virial factor, the FeII time delay should be significantly
larger than the one reported by Prince et al. (2023),
τFeII = 314.4(4380/2820)2
days ∼ 758 days. In the current
analysis, with the new redshift and the new KDP15 template,
the inferred MgII and FeII time delays and the corresponding
FWHMs appear to be fully in agreement since
the FeII rest-frame time delay expected from the virialized
motion, τFeII = τMgII(FWHM(MgII)/FWHM(FeII))2
∼
224(4503.1/4200)2
days ∼ 257 days, is consistent with the FeII
time delay inferred from reverberation, τFeII = 251+9
−7 days.
This implies that FeII emitting material is more distant than
MgII line-emitting material by ∼27 light days or 0.023 pc
(∼4700 AU).
The quasar HE 0413−4031 does not seem to exhibit a
separate very broad Gaussian component forming the wings
of the MgII line as it is typical for lower Eddington
sources (quasar type B population; Sulentic et al. 2000;
Kovaˇcevi´c-Dojˇcinovi´c & Popovi´c 2015), so the line is well modeled
by a single Lorentzian shape which helps to disentangle better
FeII and MgII emission. This makes the decomposition into
MgII and FeII relatively easier than in lower Eddington sources.
This property remained true for all our experiments with the two
redshifts and various FeII templates. HE 0413−4031 is therefore
a good candidate for further FeII studies, complementing
the nearby object I Zw 1.
An even more advanced technique is to use the wavelengthresolved
time delays which allow us to trace separately the
wings of the lines from the core as well as the kinematics of
the BLR medium when multiple lines contribute to a given
wavelength range. Such studies were done for more than 35
AGNs by various authors (Bentz et al. 2010; Denney et al. 2010;
Grier et al. 2012; Du et al. 2018; De Rosa et al. 2018; Xiao et al.
2018; Zhang et al. 2019; Hu et al. 2020; U et al. 2022) for lowredshift
sources. When we analyzed the SALT data for the quasar
HE 0413−4031 by subtracting the underlying continuum but
without separating the MgII and FeII, we concluded that the FeII
emission originates in a region slightly more distant than MgII
(Prince et al. 2023). So the issue of the FeII emission region
geometry is much more complex due to the pseudo-continuum
character of this component than MgII which gives firm and reliable
results.
The UV FeII emission template is also relevant for estimating
the FeII pseudocontinuum and MgII emission contribution
to the AGN UV emission in near-UV photometric bands. This
is especially relevant for the future monitoring of nearby AGN
using one-band (e.g., the ULTRASAT mission; Shvartzvald et al.
2023) or two-band UV photometry (e.g., the QUVIK mission;
Werner et al. 2022, 2023; Krtiˇcka et al. 2023), with the attempt
to perform UV continuum reverberation mapping of accretion
disks (Zajaˇcek et al. 2023a). The reprocessing of the harder radiation
by the BLR clouds dilutes the disk temporal response,
which affects the continuum time delay measurements in a distinct
way (Netzer 2022). The correct understanding of the UV
FeII multiplet emission and its geometric distribution will help
to account for and understand the reprocessing contribution by
the BLR gas.
5.1. HE0413 and UV MgII and FeII R−L relations
Given the new redshift and best-fit FeII template, which
resulted in slightly modified MgII and FeII time delays,
we construct an updated UV MgII radius-luminosity relation
or R−L relation. We build upon its previous versions
presented in Czerny et al. (2019), Zajaˇcek et al. (2020, 2021),
Martínez-Aldama et al. (2020), and Prince et al. (2023), where
we included a progressively larger number of MgII RM quasars
(see also Homayouni et al. 2020; Yu et al. 2023).
Here we combine the sample of RM quasars with significant
(>2σ) detections from the SDSS RM program (163 sources;
Shen et al. 2016, 2023; Homayouni et al. 2020), OzDES RM
program (25 sources; Yu et al. 2023), and 6 sources from
other RM campaigns (Metzroth et al. 2006; Lira et al. 2018;
Czerny et al. 2019; Prince et al. 2022, 2023). Altogether we collected
194 measurements, which is one of the largest samples
of RM MgII AGN up to today. The sample exhibits a significant
positive correlation between the rest-frame time delays and
monochromatic luminosities at 3000 Å with the Pearson correlation
coefficient of 0.54 (p = 2.22 × 10−16
) and the Spearman
rank-order correlation coefficient of 0.50 (p = 8.56 ×
10−14
). Next we fit the power-law relation log (τ [days]) = β +
γ log (L3000/1044
erg s−1
) to the data. Using the Markov chain
Monte Carlo (MCMC) approach implemented in the python
package emcee, we infer the best-fit MgII R−L relation,
log
τ
day
= (1.74+0.04
−0.04) + (0.32+0.04
−0.04) log
L3000
1044 erg s−1
. (1)
We show the MgII R−L relation including the best-fit relation
given by Eq. (2) in Fig. 10, see the top left panel. In the bottom
left panel of Fig. 10, we display one-dimensional likelihood
distributions and two-dimensional likelihood contours of
the searched parameters. We can especially notice a distinct
degeneracy (negative correlation) between the intercept and the
slope. However, despite this degeneracy, the inferred slope is
much flatter than 0.5, which is expected from arguments based
A140, page 10 of 18
209
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
6000 7000 8000 9000 10000
time [MJD]
2.4
2.6
2.8
3.0
3.2
3.4
3.6
fluxdensity[arbitraryunits]
3rd-order polynomial
continuum
6000 7000 8000 9000 10000
time [MJD]
2
3
4
5
6
7
8
9
fluxdensity[1017ergs1cm2Å1]
3rd-order polynomial
FeII, KDP15-blue
6000 7000 8000 9000 10000
time [MJD]
2.6
2.8
3.0
3.2
3.4
fluxdensity[arbitraryunits]
rescaled FeII light curve shifted by -600 days
continuum (LT subtracted)
6500 7000 7500 8000 8500 9000 9500 10000
time [MJD]
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
fluxdensity[1017ergs1cm2Å1]
FeII, KDP15-blue (LT subtracted)
Fig. 9. Time-delay analysis using the long-term (hereafter LT) trend subtraction from continuum and FeII emission light curves. Upper panels:
Continuum (left) and FeII emission light curve (right), which was inferred using the KDP15 template considering the more prominent blue
wing, with the corresponding 3rd-order polynomial fits. Lower panels: Continuum and FeII emission light curves in the left and the right panels,
respectively, after the LT trend was subtracted from both of them. The final light curves were reconstructed by adding the mean flux density value
of the corresponding original light curves. In the left panel for the continuum light curve, we also show the rescaled FeII light curve shifted by
−600 days, which corresponds to the ICCF maximum for this case.
on the ionization parameter (Davidson & Netzer 1979; see also
the discussion in Bentz et al. 2013) or from the dust-based BLR
model (Czerny & Hryniewicz 2011). The inferred intrinsic scatter
is substantial, σint = 0.30+0.02
−0.02, however, it is moderate
given a relatively large number of time-delay measurements and
comparable to the scatter found previously for a significantly
smaller number of sources (Prince et al. 2023; Homayouni et al.
2020).
We also revisit the UV FeII R−L relation, which was first
presented in Prince et al. (2022) for 2 measurements only and
in Prince et al. (2023) for 4 measurements, given the updated
time delay for HE0413−4031 presented in Sect. 4.3. The two
best-fit relations (RL1 and RL2) and their corresponding parameters
found using the same MCMC approach as for the MgII
are shown in Fig. 10 (top and bottom right panels). The two
relations stem from the two plausible values for the UV FeII
time delay for the quasar CTS C30.10 as found by Prince et al.
(2022). This difference is, however, small and the two relations
are identical within the uncertainties. The smaller RMS
scatter is exhibited by the first UV FeII R−L relation (RL1 in
Fig. 10) where we take into account the smaller UV FeII time
delay of CTS C30.10 (τFeII = 180.3+26.6
−30.0 days). The best-fit
relation is,
log
τ
day
= (1.18+0.21
−0.20) + (0.49+0.10
−0.09) log
L3000
1044 erg s−1
, (2)
with the intrinsic scatter of σint = 0.22+0.26
−0.12. For this relation,
we show the one-dimensional likelihood distributions and twodimensional
likelihood contours in Fig. 10 (bottom right panel).
Although the number of UV FeII time-delay measurements is
limited, we see in Fig. 10 that there is a tendency for UV FeII R−L
relation to be positioned below the MgII R−L relation because of
the smaller intercept. However, it appears to be steeper than the
MgII R−L relation, with the slope γ ∼ 0.5 consistent with the
standard photoionization theory of the BLR clouds. This results
in larger differences between MgII and UV FeII time delays for
lower luminosity sources, for which τMgII > τFeII, while at higher
luminosities, both relations converge and intersect, which results
in τMgII τFeII. This also appears to be the case of HE 0413−4031
which is effectively at the high luminosity end of both MgII and
UV FeII R−L relations. This trend also seems to be in contrast
with the R−L relations in the optical domain, where both Hβ
(Bentz et al. 2013) and optical FeII R−L (Prince et al. 2023) relations
are nearly identical with each other within the uncertainties
when expressed for 3000 Å, see Fig. 10. Their slopes are also
A140, page 11 of 18
210 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0
log (L3000[erg s−1
])
−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
log(τ[days])
SDSS RM (163)
OzDES (25)
HE0413
UV MgII R − L relation
best-fit RL: log τ = (0.32+0.04
−0.04) log L44 + 1.74+0.04
−0.04, σ = 0.30+0.02
−0.02
Bentz+13: log τ = (0.533+0.035
−0.033) log L44 + (1.391+0.040
−0.039)
MgII measurements (194)
43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0
log (L3000[erg s−1
])
−2
−1
0
1
2
3
log(τ[days])
NGC5548 (UV FeII)
NGC5548 (MgII)
CTS C30.10
HE0435
HE0413
UV FeII R − L relation & comparison
best-fit RL1: log τ = (0.49+0.10
−0.09) log L44 + 1.18+0.21
−0.20, σ = 0.22+0.26
−0.12
best-fit RL2: log τ = (0.50+0.14
−0.14) log L44 + 1.21+0.29
−0.28, σ = 0.33+0.29
−0.14
MgII RL: log τ = (0.32 ± 0.04) log L44 + (1.74 ± 0.04)
optical FeII RL: log τ = (0.46 ± 0.07) log L44 + (1.44 ± 0.09)
Bentz+13: log τ = (0.533+0.035
−0.033) log L44 + (1.391+0.040
−0.039)
UV FeII measurements
γMgII = 0.32+0.04
−0.04
1.60
1.68
1.76
1.84
βMgII
βMgII = 1.74+0.04
−0.04
0.16
0.24
0.32
0.40
γMgII
0.24
0.27
0.30
0.33
0.36
σint
1.60
1.68
1.76
1.84
βMgII
0.24
0.27
0.30
0.33
0.36
σint
σint = 0.30+0.02
−0.02
γFeII,1 = 0.48+0.10
−0.10
0.6
1.2
1.8
2.4
βFeII,1
βFeII,1 = 1.18+0.21
−0.19
0.4
0.8
1.2
γFeII,1
0.2
0.4
0.6
0.8
σint
0.6
1.2
1.8
2.4
βFeII,1
0.2
0.4
0.6
0.8
σint
σint = 0.21+0.27
−0.11
Fig. 10. Position of HE 0413−4031 in the UV MgII and FeII R−L relations. Upper panels: MgII R−L relation (left panel) constructed from
194 measurements (163 SDSS RM, 25 OzDES, and six other sources including HE 0413−4031). The best-fitted relation is in the legend. For
comparison, we also include the Hβ relation (Bentz et al. 2013) recalculated for 3000 Å (dashed orange line). In the right panel, we show the UV
FeII R−L relation based on four RM measurements for NGC 5548, CTS C30.10, HE 0435−4312, and HE 0413−4031 (two comparable relations
are plotted by solid black and dashed blue lines since there were two plausible FeII time delays for CTS C30.10). The UV FeII relation is steeper
and lower than the flatter and higher MgII R−L relation, which results in the convergence and their intersection towards higher luminosity sources.
In the right panel, we also show for comparison the optical FeII relation inferred by Prince et al. (2023) from multiple measurements as well as the
Hβ R−L relation by Bentz et al. (2013) that are depicted by dashed red and green lines, respectively. Lower panels: One-dimensional confidence
histograms and two-dimensional confidence contours for the searched parameters (slope γ, intercept β, and the intrinsic scatter σint) of the UV
MgII R−L relation (left panel) and of the UV FeII R−L relation (right panel). For the UV FeII R−L relation, we show the case with a smaller
scatter, and hence the smaller FeII time delay of CTS C30.10.
in agreement with the simple photoionization arguments unlike
MgII R−L relation, which is significantly flatter.
5.2. Simple tests of CLOUDY models of the FeII emission
The three FeII templates we use are almost comparable in the
fit quality for Observation 14 (see Fig. 3) but their shapes are
considerably different. To have some insight into the physical
nature of each template, we use the recent version C22.01
of the code CLOUDY to model the reprocessed continuum (see
also Pandey et al. 2023). As in Bruhweiler & Verner (2008), we
parameterize the CLOUDY solution with the incident flux, log φ,
the local density of the cloud, log nH, and the turbulent velocity,
vturb. The results are discussed below.
The template d12 used in Prince et al. (2023) was obtained
with the CLOUDY several years ago, and in the meantime,
the atomic content of the code improved significantly. We
thus compared the available template d12 with the output of
the CLOUDY (version 22.01) using the same input parameters:
log (φ[cm−2
s−1
]) = 20.5, log (nH[cm−3
]) = 12, and the turbulent
velocity of 20 km s−1
. The column density was assumed
to be 1024
cm−2
. The incident SED was very similar, that
is a standard AGN SED in our computation, and the SED
from Korista et al. (1997) in Bruhweiler & Verner (2008). We
smeared the results with the Gaussian profile corresponding to
the FWHM of 4200 km s−1
as used in the current paper. The
upper panel of Fig. 11 shows the FeII emission over the broadband
range (2000–7000 Å). In the middle panel, we show just
the enlarged UV part, relevant to the current work. It shows that,
compared to the Bruhweiler & Verner (2008) template, there is a
marginal shift in the peak of FeII pattern towards a shorter wavelength
in the case of the new CLOUDY output; more importantly,
though, the bluer portion of the FeII pattern is more asymmetric.
Thus, this template is more consistent with the new redshift
A140, page 12 of 18
211
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
2000 3000 4000 5000 6000 7000
Wavelength (Å)
0.0
0.2
0.4
0.6
0.8
1.0
FFeII(a.u.)
Cloudy version 22.01
Bruhweiler & Verner (2008)
2650 2700 2750 2800 2850 2900
Wavelength (Å)
0.0
0.2
0.4
0.6
0.8
1.0
FFeII(a.u.)
Cloudy version 22.01
Bruhweiler & Verner (2008)
KDP15 template
2650 2700 2750 2800 2850 2900
Wavelength (Å)
0.0
0.2
0.4
0.6
0.8
1.0
FFeII(a.u.)
Cloudy version 22.01
Bruhweiler & Verner (2008)
Fig. 11. Comparison of Bruhweiler & Verner (2008) template with the
CLOUDY C22.01 output for log (φ[cm−2
s−1
]) = 20.5, log nH[cm−3
] = 12,
the turbulent velocity of 20 km s−1
, and the column density of 1024
cm−2
. Upper panel: For a wavelength range of 2000–7000 Å with a
Gaussian broadening assuming FWHM ∼4200 km s−1
. Middle panel:
The zoomed-in version of the upper panel in the wavelength range 2650–
2900 Å. Here wealso addthe broadened KDP15templatefor comparison
(green solid line). Lower panel: The nonbroadened version of the middle
panel. Here, the templates are renormalized for a better comparison.
when we look at the position of the blue wing of the VW01
and KDP15 templates (see also Fig. 3). Comparing the red-wing
peak positions, we see that the red peak of the VW01 template
(or d12) is shifted towards the red part and that of KDP15
is shifted slightly towards blue or lower wavelengths. In terms
of the intensity, VW01 template is overpredicting the red wing
while the d12 and KDP15 templates show a fainter red-wing (see
Fig. 3, middle panel). In addition, the maximum of the KDP15
template is close to 2740 Å , hence at a slightly smaller wavelength
in comparison to the new CLOUDY template. However, the
blue peaks of both the old d12 template and the KDP15 template
are rather symmetric, while the new CLOUDY template exhibits a
prominent blueward asymmetry.
That rather implies that new templates should be constructed
for a broader range of parameters and compared to the data
which is beyond the scope of the current paper. The KDP15 template
has 6 parameters but the setup does not have the required
flexibility since finally only two of them were used efficiently,
with the other four going frequently to zeros (see Sect. 3 and
Fig. 6 for the discussion). Their transitions peak at (maybe) too
long wavelengths (2740 Å– transition 63 and 2747 Å– transition
62) in the blue wing part to represent well the pattern. The
actual number of FeII transitions is very high, as we illustrate
in the lower panel of Fig. 11. The strongest transition is close
to ∼2750 Å in both cases. However, in the new computations,
some of the transitions at shorter wavelengths, close to 2730 Å ,
become stronger, pushing the smeared pattern toward the blue
part.
We also checked the CLOUDY output for the ionization
parameter log (φ [cm−2
s−1
]) = 20, local hydrogen density
log (n [cm−3
]) = 12, and the turbulent velocity 20 km−1
to see
if there are any transitions close to the two peaks visible in the
empirical I Zw 1 component: 2715.20 Å and 2839.88 Å. Indeed,
we see a strong FeII transition at 2715.60 Å (transition 2
G0
9/2 →
2
G7/2
1
), with the intensity 4.0 × 105
erg s−1
cm−2
, and the transition
at 2839.80 Å (transition 6
D9/2 → 6
p0
7/2), with the intensity
of 1.2 × 106
erg s−1
cm−2
. The ratio of the second to the first one
is about 3.08, as in the case of the two peaks in the I Zw 1 component
in the KDP15 template (2.80).
In summary, the computations with the use of the latest
CLOUDY version give a different shape of the FeII emission than
the old d12 template. The shift between the two is seen in the
middle panel of Fig. 11 where we plot the broadened version of
the templates, but none perfectly represents the peak obtained
with the KDP15 template. That shows that there is room for
an improvement of the standard one-dimensional FeII templates
(not based on several multiplets as in KDP15) as well, but the
broad search of the parameter space is beyond the scope of the
current paper. It should also be noted that such shifts in the templates
can partially be responsible for the large systemic shifts
reported in the literature. For example, Rusakov et al. (2023)
reports a shift of 4100 km s−1
of the broad Hβ line with respect
to the narrow component although the MgII shift is moderate,
only by −1200 km s−1
, and they propose a shock wave due to
the recent supernova as an explanation. But the effect might also
be due to the applied FeII template, this time in the optical band.
5.3. Quasar location in the UV plane
The quasar optical plane is a very convenient way to
study the statistical properties of quasars (Sulentic et al. 2000;
Shen & Ho 2014; Sulentic & Marziani 2015; Fraix-Burnet et al.
2017; Marziani et al. 2018; Panda et al. 2018, 2019c). It is
based on a two-dimensional plot using the FWHM(Hβ) and
the parameter RFe = EW(FeIIopt)/EW(Hβ). Here optical FeII
1
The exact transition was identified using the NIST Spectral
Database: https://physics.nist.gov/PhysRefData/ASD/
lines_form.html
A140, page 13 of 18
212 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
0
2000
4000
6000
8000
10000
12000
14000
0 5 10 15 20 25 30 35
FWHM(MgII)[kms-1]
RFeUV
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
logEW(MgII)[Å]
Fig. 12. Quasar UV plane with sources from ´Sniegowska et al. (2020).
The location of the quasar HE 0413−4031 is marked with a triangle.
is usually measured close to Hβ, in the spectral range of
4434–4684 Å (Boroson & Green 1992; Marziani et al. 2018;
Panda et al. 2018). The study of the quasar main sequence allows
us to understand the diversity of Type-1 AGNs and how their
spectral properties are tied to the fundamental black hole parameters,
such as their mass and accretion rate (Marziani et al. 2018;
Panda et al. 2018, 2019c,a; Panda 2021) and the physical conditions
of the broad line-emitting region (Panda et al. 2018, 2019c;
´Sniegowska et al. 2021; Panda 2022; Mengistue et al. 2023).
When the near-UV spectra are studied, a similar concept of
the UV plane can be introduced (´Sniegowska et al. 2020). A large
sample of objects was located on this plane using the QSFIT
package (Calderone et al. 2017) for data analysis. This package
is based on the VW01 FeII template. For the quasar studies in this
paper, we also have the results of fitting the VW01 template for
Observation 14. The difference between the QSFIT and our fitting
is in the wavelength range which covers 1250–3090 Å while
we fit only the range 2683.09448–2881.49854. To make the values
of EW comparable, we integrated the VW01 template in the
two ranges and determined the scaling parameter 6.39345. We
adopted the second solution for this template from Table 2 since
the broadened version works better. After rescaling, the parameters
of UV FeII are the following: EW(FeII) = 88.23 Å, and
RFe = 2.37.
The location of the quasar HE 0413−4031 in the UV plane
together with the sample from ´Sniegowska et al. (2020) is shown
in Fig. 12 with a triangle colored with EW(MgII) as the rest of the
sample. The UV FeII emission seems rather weak in the studied
object. In the whole sample of ´Sniegowska et al. (2020), there are
only 14 quasars with RFe < 2.0, and two with RFe < 1.5. The
number of sources with RFe < 2.37 is 47 (out of 2962 total). The
smallest value in this sample is 1.28 ± 0.15, for the object SDSS
100352.65+212851.5 with the FWHM(MgII) = 5760 km s−1
.
6. Conclusions
Our detailed study of the bright, intermediate-redshift quasar HE
0413−4031 based on 10-year monitoring with SALT combined
with a single IR exposure with the telescope SOAR showed that
– determination of the redshift from a narrow emission line
is important for the spectral decomposition of the entire
IR/optical/UV band. The precise redshift determination of
z = 1.39117 ± 0.00017 is significantly larger with respect to
the previous value (z = 1.3764),
– the decomposition of the MgII+FeII complex based on the
precise redshift results only in the small blueshifted offset of
the MgII line in the range between −240 and −270 km s−1
,
which is consistent with the quasar composite spectra of the
UV region,
– the velocity of the MgII line with respect to the systemic
redshift is therefore significantly affected by the new redshift
and the corresponding template since previously the velocity
shift was in excess of 1000 km s−1
,
– some properties of the strong UV line, in particular MgII,
such as its FWHM, EW, and the time delay with respect to
the continuum are determined robustly, even without precise
redshift determination, so applications of MgII line for cosmology
are justified,
– the MgII emission based on the best-fitting KDP15 template
with FWHM(MgII) = 4503.1 km s−1
is significantly correlated
with the continuum. The final MgII time delay in the
rest frame of the source, which is based on 7 different timedelay
methods, is τMgII = 224+21
−23 days,
– determination of the FeII properties, including its time delay
with respect to the continuum, is very sensitive to the proper
redshift determination and the use of the proper FeII template.
The FeII emission is also strongly correlated with the
continuum (the peak correlation coefficient is r = 0.86), but
the peak time delay is consistent with zero, which suggests
that the FeII light curve is strongly contaminated with the
continuum long-term trend,
– after subtracting the long-term trend from both continuum
and FeII light curves, we detect the candidate FeII time delay
at τ = 251+9
−7 days in the rest frame, albeit the correlation
coefficient is relatively low (r = 0.27),
– the rest-frame time delay of UV FeII is consistent with
the MgII/FeII FWHMs inferred using the FeII best-fit template
KDP15. Assuming that the MgII/FeII-line emitting
material is fully virialized, the FeII time delay should be
τFeII = τMgII(FWHMMgII/FWHMFeII)2
∼ 257 days, which
is consistent with the reverberation result. Hence, for HE
0413−4031, the UV FeII material is more distant than the
MgII line-emitting material by ∼27 light days,
– we update the MgII radius-luminosity relation with new
measurements, which results in 194 sources, that is more
than twice as much as used previously. The MgII R−L relation
is significantly flatter than the UV FeII, optical FeII, and
Hβ R−L relations,
– we suggest to build new FeII emission templates based
on the newest version of the photoionization code CLOUDY
since there are new FeII transitions included that indicate
extension of the emission towards shorter wavelengths with
respect to the older FeII templates currently in usage.
Acknowledgements. We thank the anonymous referee for constructive comments,
which helped to improve the manuscript. All spectroscopic observations
reported in this paper were obtained with the Southern African Large Telescope
(SALT). The project is based on observations made with the SALT under
programs 2012-2-POL-003, 2013-1-POL-RSA-002, 2013-2-POL-RSA-001,
2014-1-POL-RSA-001, 2014-2-SCI-004, 2015-1-SCI-006, 2015-2-SCI-017,
2016-1-SCI-011, 2016-2-SCI-024, 2017-1-SCI-009, 2017-2-SCI-033, 2018-1MLT-004
(PI: B. Czerny). Polish participation in SALT is funded by grant
No. MEiN nr 2021/WK/01. Based in part on observations obtained at the
Southern Astrophysical Research (SOAR) telescope, which is a joint project
of the Ministério da Ciência, Tecnologia e Inovações (MCTI/LNA) do Brasil,
the US National Science Foundation’s NOIRLab, the University of North
Carolina at Chapel Hill (UNC), and Michigan State University (MSU). The
project was partially supported by the Polish Funding Agency National Science
Centre, project 2017/26/A/ST9/00756 (MAESTRO 9). BC and MZ acknowledge
the OPUS-LAP/GAˇCR-LA bilateral project (2021/43/I/ST9/01352/OPUS
22 and GF23-04053L). This project has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation program (grant agreement No. [951549]). SP acknowledges the
financial support from the Conselho Nacional de Desenvolvimento Científico
A140, page 14 of 18
213
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
e Tecnológico (CNPq) Fellowships (164753/2020-6 and 313497/2022-2). MS
acknowledges support from the Polish Funding Agency National Science Centre,
project 2021/41/N/ST9/02280 (PRELUDIUM 20), the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
program (grant agreement 950533), and the Israel Science Foundation,
(grant 1849/19). M.L.M.-A. acknowledges financial support from Millenium
Nucleus NCN19-058 (TITANs). NW acknowledges the financial support
from the GAˇCR EXPRO grant no GX21-13491X. We are grateful to
Marianne Vestergaard for allowing us to use their FeII template.
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214 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
Appendix A: MgII time-delay determinations
A.1. Interpolated cross-correlation function
1500 1000 500 0 500 1000 1500
time delay [days]
0.4
0.2
0.0
0.2
0.4
0.6
0.8
r
ICCF: MgII
KDP15
VW01
Fig. A.1. ICCF for the MgII emission using the KDP15 and the VW01
templates depicted by blue and green lines, respectively. The dotted vertical
lines show the time-delay peaks at 541 and 606 days (highest crosscorrelation
coefficient).
200 300 400 500 600 700 800
time delay [days]
0.4
0.5
0.6
0.7
0.8
0.9
1.0
r
DCF: MgII
KDP15
VW01
Fig. A.2. DCF for the MgII emission using the KDP15 and the VW01
templates depicted by blue and green lines, respectively. The dotted vertical
line shows the time-delay peak at 580 days (highest correlation
coefficient).
We calculate the Interpolated cross-correlation function (ICCF)
using the basic definition of the cross-correlation coefficient
between two light-curve points separated by the time delay
τk = k∆t,
CCF(τk) =
(1/N) N−k
i=1 (xi − x)(yi+k − y)
[(1/N) N
i (xi − x)2]1/2[(1/N) N
i (yi − y)2]1/2
,
(A.1)
where ∆t = ti+1 − ti is the regular time step, and x and y
denote light curve means. Both continuum and line-emission
light curves are interpolated with the time step of ∆t = 1 day
1500 1000 500 0 500 1000 1500
time delay [days]
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
zDCF
zDCF: MgII
KDP15
VW01
Fig. A.3. zDCF for the MgII emission using the KDP15 and the VW01
templates depicted by blue and green lines, respectively, with the corresponding
error bars. The dashed vertical lines show the time-delay
peaks at 597 days (KDP15) and 638 days (VW01) while the dotted lines
mark the corresponding 1σ uncertainties.
1500 1000 500 0 500 1000 1500
time delay [days]
100
200
300
400
500
2
2: MgII
KDP15
VW01
Fig. A.4. χ2
as a function of a time delay (in the observer’s frame) for
the MgII emission using the KDP15 and the VW01 templates depicted
by blue and green lines, respectively. The dashed vertical lines depict
the time-delay peaks at 619 days (KDP15) and 616 days (VW01).
(symmetric interpolation). In Figure A.1, we show the ICCF for
the MgII line emission inferred using the KDP15 template and
the VW01 template.
A.2. Discrete correlation function (DCF)
We employ the discrete correlation function (DCF) that
is suited for irregular and unevenly sampled light curves
(Edelson & Krolik 1988). We utilize the python implementation
of the DCF by Robertson et al. (2015). For both KDP15 and
VW01 FeII templates, we show the DCF results in Figure A.2.
A.3. z-transferred DCF (zDCF)
The z-transferred DCF replaces equidistant time bins with
equipopulation time bins. The minimum number of overlapping
A140, page 16 of 18
215
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
Fig. A.5. Heat map with contours for the posterior distributions of the scaling factor vs. the time delay (in the observer’s frame) as determined by
the JAVELIN method for the MgII emission light curve. We performed the analysis using the KDP15 FeII template (left panel) and the VW01 FeII
template (right panel). The dashed vertical line depicts the time-delay peak at 492.5 days, which is the same for both FeII templates. The color
scale depicts the Gaussian kernel density of MCMC realizations (altogether 40 000) in the scaling factor–time delay plane with the grid of 400 ×
400 bins.
1500 1000 500 0 500 1000 1500
time delay [days]
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
VonNeumannestimator
Von Neumann: MgII
KDP15
VW01
Fig. A.6. Von Neumann estimator as a function of a time delay (in
the observer’s frame) for the MgII emission using the KDP15 and the
VW01 templates depicted by blue and green lines, respectively. The
dashed vertical lines depict the time delays corresponding to the estimator
minima at 504 days (KDP15) and 380 days (VW01), respectively.
light-curve pairs is 12. The method was developed by
Alexander (1997), who also implemented it within a fortran
code. The zDCF is suitable for sparse and irregular light
curves. In Figure A.3, we show zDCF as a function
of the observed time delay for both KDP15 and VW01
FeII templates that are depicted by blue and green lines,
respectively.
A.4. χ2
method
We also apply the χ2
method frequently used in lensing studies.
Czerny et al. (2013) showed that this method performs better
than the ICCF for red-noise AGN variability. In Figure A.4, we
show χ2
as a function of the time delay of the MgII line emission
with respect to the photoionizing continuum. The solid blue line
1500 1000 500 0 500 1000 1500
time delay [days]
400
600
800
1000
1200
1400
Bartelsestimator
Bartels: MgII
KDP15
VW01
Fig. A.7. Bartels estimator as a function of a time delay (in the
observer’s frame) for the MgII emission using the KDP15 and the
VW01 templates depicted by blue and the green lines, respectively. The
dashed vertical lines depict the time delays corresponding to the estimator
minima at 382 days (KDP15) and 410 days (VW01), respectively.
stands for the KDP15 FeII template, while the solid green line
represents the VW01 template.
A.5. JAVELIN
Another method to estimate the time delay in galactic nuclei is
to model the continuum emission as a stochastic process, for
example by using a damped random walk (Kelly et al. 2009;
Kozłowski et al. 2010; MacLeod et al. 2010; Kozłowski 2016),
and to assume that the line emission is a time-delayed, scaled,
and smoothed version of the continuum emission. Based on this
approach the JAVELIN package (Just Another Vehicle for Estimating
Lags In Nuclei) was developed and tested (Zu et al. 2011,
2013, 2016). We applied JAVELIN to infer independently the
time delay of the MgII emission with respect to the continuum.
A140, page 17 of 18
216 CHAPTER 8. PAPER 7: UV FEII EMISSION MODEL AND BLR TIME DELAYS
Zajaˇcek, M., et al.: A&A, 683, A140 (2024)
0 200 400 600 800 1000
time delay [days]
0.0
0.2
0.4
0.6
0.8
r
ICCF: MgII - LT subtracted
KDP15
KDP15: LT subtracted
VW01
VW01: LT subtracted
Fig. A.8. ICCF as a function of the time delay in the observer’s frame
for the MgII light curve with the LT trend subtraction. Solid lines correspond
to the original light curves (blue for the KDP15 template and
green for the VW01 template). Dashed lines correspond to the continuum
and the MgII light curves with the LT trend subtracted using the
third-order polynomial to represent the LT trend (a blue dashed line
stands for the KDP15 template, while the green dashed line corresponds
to the VW01 template). Although a significant drop in the correlation
coefficient is noticeable, the main time-delay peak around ∼400 − 600
days can be recovered.
In Figure A.5, we plot the heatmaps of the scaling factor vs. time
delay. In the left panel, we present the case with the KDP15 FeII
template, while in the right panel, we show the case with the
VW01 FeII template.
A.6. Measures of regularity and randomness
Recently, the estimators of time-series regularity or randomness
were proposed as a way to estimate the true time delay between
the two light curves (Chelouche et al. 2017).
In Figure A.6, we present the von Neumann estimator as a
function of the time delay in the observer’s frame of reference.
As was done previously for the other methods, two FeII templates
are compared: KDP15 (blue line) and VW01 (green line).
Furthermore, we also calculate the Bartels estimator, which is
Table A.1. Summary of MgII emission time delays inferred using the
ICCF for the light curves with the LT trend subtracted. Time delays
are expressed in days in the observer’s frame, while the last two rows
represent the mean time delays expressed in days in the rest frame of
the source.
Method KDP15 VW01
ICCF* - highest r 372 (r = 0.47) 539 (r = 0.38)
ICCF* - peak 410+345
−50 605+242
−238
ICCF* - centroid 446+317
−103 571+275
−203
τ – observer’s frame 428+234
−57 588+183
−156
τ – rest frame 179+98
−24 246+77
−65
Final MgII time delay 213+62
−35
similar to the von Neumann estimator but rather operates on
the ranked combined light curve. In Figure A.7, we show the
Bartels estimator values as a function of the time delay for
both templates. Overall, the minima values and their uncertainties
as inferred from the best time-delay distributions are
quite similar to the values determined using the von Neumann
estimator.
A.7. Subtraction of long-term trend
In a similar way as for the UV FeII line (see Subsection 4.3),
we verify that for the MgII light curve the long-term (LT) trend
subtraction does not obliterate the main time-delay peak.
We fit the third-order polynomial to both continuum and
MgII light curves. Subsequently, we subtract the best-fit trend
from both light curves. Then we apply the ICCF, for which we
find the time delays corresponding to the peak r value, the centroid,
and the peak distributions. Both KDP15 and VW01 templates
are considered. The results are summarized in Table A.1.
It is possible to recover the time delay at ∼400 − 600 days
in the observer’s frame, although with a significantly lower correlation
of r ∼ 0.38 − 0.47. For the KDP15 template, the peak
and centroid time delays are smaller than the previously determined
values, though within the uncertainties they are consistent
with the time delays reported without any subtraction. When we
average the peak and the centroid values for both templates, the
rest-frame time delay is 213+62
−35 days, which is in agreement with
the previously reported value.
A140, page 18 of 18
217
Chapter
9
Discussion and Conclusions
“The history of astronomy is a
history of receding horizons."
— Edwin Powell Hubble
(1889-1953)
The common theme of the seven papers presented in this Habilitation Thesis (see Chapters
2 through 8) is the astrophysics of galactic nuclei. Five papers that are included in
Chapters 2, 3, 5, 7, and 8 deal with the nuclei of other galaxies, while two papers (Paper 3 in
Chapter 4 and Paper 5 in Chapter 7) focus on the Galactic center, i.e. the nucleus of our own
Milky Way galaxy.
Although the topics of the papers may seem quite heterogeneous and just loosely related, it
is just an illusion since the activity of a galactic nucleus appears to be crucial for understanding
the evolution of not only our own Galaxy but galaxies in general. In analogy to stars, galaxies
undergo an evolution with different phases since their formation, which took place just during
the first 200 - 400 million years after the Big Bang (corresponding to the redshift range
z ∼ 20 − 11). This evolution involved accumulation of gas, from which stars formed, as well
as simultaneously different feedback processes operated – supernovae and the activity of the
central SMBH. The energy and the momentum feedback from supernovae and the SMBH
led to the expulsion and heating of the cold gas, which would otherwise be available for
star formation and the accretion onto the SMBH. In this way, the central SMBHs can play a
central role in shaping galaxies by regulating star-formation across the whole galaxy as well
as its own activity.
Studying the galaxy evolution is even more complicated when one considers that the
expansion of the Universe should be properly included. It is represented by the Hubble
parameter that depends on the redshift (scaling parameter and thus cosmic time) as well as
the cosmological parameters, H(z, p). The expansion of the Universe and structure formation
during its evolution implies that the mergers of galaxies of different sizes can occur and are
indeed observed across the cosmic history. When two galaxies merge, star formation and
the accretion onto the SMBH tend be enhanced due to the refuelling of gas reservoir. To
get the grasp of the main ingredients of galaxy evolution, we illustrate the sources of cold
219
220 CHAPTER 9. DISCUSSION AND CONCLUSIONS
Figure 9.1: Illustration of the main processes affecting the galaxy evolution across the
cosmic history. The basic ingredient is the reservoir of cold gas, from which stars can form
and which also feeds the central SMBH(s). This reservoir can be supplied by the intergalactic
accretion and mergers (top). In contrast, it is depleted by negative feedback processes, such
as the active galactic nucleus and supernova explosions of massive stars (bottom). The figure
is adopted from Karas et al. (2021). Courtesy of Michal Zajaˇcek.
gas (intergalactic accretion and mergers) and the feedback processes (SMBHs and stars) in
Fig. 9.1.
By studying the Galactic center and low- to intermediate-redshift galaxies, we can study
in detail star-formation and accretion processes that are common for the galaxy evolution
throughout the cosmic history. In particular, the compact nuclear star cluster (NSC) at the
center of the Milky Way is a unique laboratory for studying the mutual dynamical interaction
among stars, compact remnants, infalling gas, and the activity of the SMBH (Schödel et al.
2014b). Specifically, in Paper 3 (Chapter 4), we proposed a new feedback process of how
the active nuclear jet can affect the evolved, late-type stars that are expected to dominate the
composition of the nuclear star cluster. An estimated mass removal caused by the red-giant
collision with the nuclear jet can both make old stars appear younger and the colliding star
can also affect the velocity field and the composition of the jet flow. We suggest that the red
giant-jet collisions can partially address the missing bright red giants in the inner nuclear
star cluster of the Milky Way. It complements other processes that operate closer to the
SMBH (tidal disruption of red-giant envelopes) and further away (collisions of red giants
with the dense, star-forming clumps within a large-scale gaseous disc), see also Fig. 9.2 for
the illustration and Zajaˇcek et al. (2020) for more details. In the dense environment of the
nuclear star cluster, star-star and star-compact remnant collisions can also contribute to the
overall dearth of evolved stars within the inner half parsec, as was first detected by Sellgren
221
jet
tidal domain
jet-ablation domain
0.04 pc 0.5 pc
star-disc interaction domain 
(gravitationally unstable disc with Q<1)
0.1 mpc
red giant-black hole
 
collisions 
red giant-main sequence star collisions
Figure 9.2: Illustration of the processes that likely contributed to the depletion of latetype
stars (red giants/supergiants, asymptotic giant-branch stars) in the inner 0.5 pc
of the Galactic center. It seems that the depletion of red giants is linked to the enhanced
accretion activity of Sgr A* a few million years ago, which could have been accompanied
by an active nuclear jet. In the vicinity of the SMBH, tidal forces perturb large envelopes of
red giants, while at larger distances, a gravitationally unstable disc hosts denser cores, with
which orbiting red giants can collide and lose mass through increased ram pressure. At the
intermediate scales (≳ 0.1 mpc and ≲ 0.04 pc), red giant collisions with the jet can ablate
their outer layers. Throughout the dense nuclear star cluster, red giant–main-sequence star
and red giant – compact remnant collisions take place occasionaly and hence can contribute
to the depletion of red giants.
et al. (1990) via the decrease in the CO bandhead absorption strength.
Moreover, by studying the orbits and the light curves of orbiting stars around the SMBH,
one can in principle constrain their nature by the level of brightening due to the Doppler effect
(see Paper 5 in Chapter 6). Objects with colder atmospheres, e.g. dust-enshrouded stars or
brown dwarfs, as well as non-thermal spectra, e.g. pulsars, generally exhibit an enhanced
Doppler (de)boosting with respect to main-sequence stars by a factor of four to ten. With high
enough near- and mid-infrared photometric sensitivity in the near future, this effect could
help constrain the low-mass end of the Galactic center stellar population, and thus its initial
mass function in the vicinity of the SMBH. One exciting possibility is the discovery of a
brown-dwarf population in the Galactic center, which would constrain the star-formation
process not only in the center of the Milky Way but also in other galactic nuclei.
Potential cycles of AGN feedback associated with the activity of the SMBH can be
revealed by studying optical-radio properties of a sample of radio galaxies. In particular, in
Paper 1 (Chapter 2) we studied the distribution of a radio spectral index (4.85 GHz-10.45
GHz) in the narrow-line optical diagnostic diagrams. Seyfert galaxies tend to have high
ionization potential and a large radio loudness and they also have rather steep spectral indices
222 CHAPTER 9. DISCUSSION AND CONCLUSIONS
(α < −0.7), which can be associated with older radio structures (radio lobes). On the other
hand, low-ionization nuclear emission-line region (LINER) galaxies are characterized by
a rather low radio loudness, but they have flatter to inverted radio spectral indices. This
indicates that a substantial fraction of LINER galaxies are undergoing a renewed nuclear
activity with compact, optically thick radio cores and jets. Hence, in some sense, the standard
optical diagnostic diagram (Baldwin-Phillips-Terlevich/BPT diagram) seems to trace galaxyevolutionary
cycles in the nearby Universe, i.e. in the recent cosmic history. However, the
described cycles of nuclear (accretion disc-jet) activity are expected to have occurred since
the formation of the first SMBH seeds. Linking this back to the studies of the Galactic center
nuclear star cluster (Papers 3 and 5), a question arises if and how a dense collection of stars
with their stellar winds, sometimes really powerful (Wolf-Rayet stars and supernovae), can
influence the cycles of the nuclear activity and the associated radiative and radio-mechanical
feedback. In Zajaˇcek et al. (2022), we studied the change in the size of the stagnation radius,
which is the length-scale from the SMBH where the radial flow velocity goes through zero,
i.e. it divides the inflow from the outflow region. The basic effect is that for a missing NSC
or a core-like number-density distribution the stagnation radius is larger than for a cusp-like
distribution of the NSC, see Fig. 9.3. This can influence the amount of the gas inflow towards
the SMBH and hence the nuclear feedback, though a more detailed numerical model analysis
in combination with optical/X-ray data is necessary to draw more robust conclusions.
To understand the distribution and the kinematics of the ionized gas in the vicinity of an
active galactic nucleus, which is the source of characteristic broad lines in the UV/optical
portion of a typical AGN spectrum (e.g., MgII and FeII), we performed the reverberation
mapping of two intermediate-redshift quasars: HE 0413-4031 (Paper 2 in Chapter 3) and
HE 0435-4312 (Paper 4 in Chapter 5). For both of the studied quasars, the rest-frame time
delay of the MgII broad-line emission is about 200-300 days. Because of their high UV
luminosities (L3000 ∼ 1046
−1047
erg s−1
), both quasars have been essential for constraining the
MgII broad-line region radius-luminosity relation (RBLR − L relation or correlation). Hence, in
analogy to Hβ RBLR − L relation, which has been constructed from reverberation mapping of
nearby, low-redshift quasars (see e.g. Bentz et al. 2013; Martínez-Aldama et al. 2019), MgII
RBLR − L relation can be used to determine SMBH masses for higher, intermediate-redshift
AGN just from one obtained spectrum. This way the growth of SMBHs close to the peak
of the SMBH/star formation activity can be better understood. At the moment, the MgII
RBLR − L is well constrained using the reverberation mapping of nearly 200 sources, see
Fig. 9.4. However, it has a substantial scatter around the best-fit relation. The slope of the
best-fit MgII RBLR − L relation is also significantly flatter than the Hβ RBLR − L relation
as well as the optical and UV FeII relations (γ ∼ 0.3 vs. 0.5), and hence it also deviates
from the simple photoionization arguments inferred using the definition of the ionization
parameter. Both the reason behind a considerable scatter and the MgII RBLR − L relation
flatness will need to be addressed using advanced photoionization and dynamical models of
the MgII line-emitting material, including a proper treatment of radiation pressure acting on
the gaseous-dusty material at the BLR length-scales in addition to the dominant gravitational
field of the SMBH.
A difficulty with the spectral decomposition of the quasar continuum emission and the
MgII broad-line emission is that the MgII line emission overlaps spectrally with the UV
FeII pseudocontinuum. For the MgII line flux determination, a precise FeII model is desired.
In Paper 7 (Chapter 8), utilizing the precise redshift determination for HE 0413-4031, we
analyze how different FeII templates affect MgII and FeII properties and their correspond-
223
Figure 9.3: Potential relation between the Nuclear Star Cluster (NSC) surface brightness
(number-density distribution) and the nuclear feedback. Panel (a) on the left shows a
large-scale AGN feedback (on the scale of megaparsecs), in particular radio-mechanical
feedback in the circumgalactic medium, which heats up the gas and prevents if from cooling
and forming stars. Since the nuclear feedback on large scales has the origin at the very center
of galaxies, within the Bondi radius of the SMBH, the way how wind-blowing stars are
distributed around the SMBH may affect the size of the inflow/outflow regions (see Panels
b and c on the right). Specifically, for a cusp-like distribution (panel c) we expect a smaller
stagnation radius than for a core-like distribution of the NSC.
ing time delays with respect to the driving photoionizing continuum. The precise redshift
determination based on the narrow [OIII] lines (1.39117 ± 0.00017) leads to a different
spectral decomposition than the previous one based on the approximate redshift inferred
from the FeII pseudocontinuum. In particular, the systematic blueshift of the MgII line is
only 300 km s−1
and the FeII FWHM of 4200 km s−1
is consistent with its slightly larger time
delay with respect to the MgII line (251 days vs. 224 days in the rest frame). Based on this
specific analysis, we recognize that a more precise model of the FeII pseudocontinuum, which
consists of plenty FeII transitions, is required to yield a satisfactory MgII/FeII decomposition.
Older FeII templates currently in use are empirical, theoretical or the combination of both
approaches but generally based on just specific sources and incomplete line transitions.
However, despite different FeII templates, the MgII line properties and its time delay
in HE 0413-4031 were not affected significantly by the spectral decomposition. The MgII
broad-line emission can therefore be reliably used for the SMBH mass determination as
well as applied to standardize quasars and use them as alternative cosmological probes (see
e.g. Czerny et al. 2023, and references therein). In comparison with standard cosmological
probes, such as type Ia supernovae, AGN with their broad redshift range from z ≈ 0 to
z ∼ 7 and potentially more bridge local, cosmic-ladder measurements in the late Universe
with the distant cosmic microwave background (CMB) in the early Universe. In this way,
224 CHAPTER 9. DISCUSSION AND CONCLUSIONS
42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0
log (L3000[erg s−1
])
−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
log(τ[days])
SDSS RM (163)
OzDES (25)
HE0413
HE0435
UV MgII R − L relation
best-fit RL: log τ = (0.32+0.04
−0.04) log L44 + 1.74+0.04
−0.04, σ = 0.30+0.02
−0.02
Bentz+13: log τ = (0.533+0.035
−0.033) log L44 + (1.391+0.040
−0.039)
MgII measurements (194)
43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0
log (L3000[erg s−1
])
−2
−1
0
1
2
3
log(τ[days])
NGC5548 (UV FeII)
NGC5548 (MgII)
CTS C30.10
HE0435
HE0413
MgII & FeII R − L relations: comparison
best-fit RL1: log τ = (0.49+0.10
−0.09) log L44 + 1.18+0.21
−0.20, σ = 0.22+0.26
−0.12
best-fit RL2: log τ = (0.50+0.14
−0.14) log L44 + 1.21+0.29
−0.28, σ = 0.33+0.29
−0.14
MgII RL: log τ = (0.32 ± 0.04) log L44 + (1.74 ± 0.04)
optical FeII RL: log τ = (0.46 ± 0.07) log L44 + (1.44 ± 0.09)
Bentz+13: log τ = (0.533+0.035
−0.033) log L44 + (1.391+0.040
−0.039)
UV FeII measurements
Figure 9.4: UV MgII and FeII radius-luminosity relations. Left panel: MgII radiusluminosity
relation for 194 quasars, including 163 SDSS RM sources, 25 OzDES sources,
and 6 sources from other programs. In particular, we highlight two measurements of the
MgII time delay for HE 0413-4031 (Paper 2) and HE 0435-4312 (Paper 4) denoted by red
stars, which are among few high-luminosity sources that are crucial for constraining the
MgII RBLR − L relation. Right panel: MgII and FeII RBLR − L relations in the UV domain
and their comparison with optical Hβ and FeII relations. Optical Hβ and FeII relations are
shifted towards larger time delays (radii) in comparison with the UV FeII RBLR − L relation.
MgII RBLR − L relation is clearly flatter than the other relations, which leads to the large
separation of the MgII line-emitting material at smaller luminosities and a comparable time
delay (radius) at high luminosities.
Figure 9.5: Turning quasars into standardizable candles. Using non-linear power-law
relations, such as the broad-line region RBLR −L relation and the X-ray/UV luminosity relation
LX − LUV, one can test whether quasars can be standardized and used as cosmological probes.
The illustration depicts the UV emission of an accretion disc (blue) and a relatively fainter
X-ray emission of the hot corona (yellow, above the disc). Since the LX − LUV relation is
non-linear, the luminosity distance can be determined to a given quasar. Copyright: NASA /
CXC / M. Weiss
225
cosmological constraints based on quasars can help solve current cosmological tensions,
such as the Hubble tension (see e.g. Abdalla et al. 2022). Currently, two non-linear powerlaw
relations can be used to standardize quasars: (i) correlation between UV and X-ray
luminosities or the LX − LUV relation (Risaliti & Lusso 2019) and (ii) broad-line region radiusluminosity
relation or RBLR − L relation (Khadka et al. 2021). The quasar standardization
procedure using relations (i) and (ii) thus nicely connects, in principle, AGN “microphysics”
with the large-scale structure of the Universe, see Fig. 9.5 for illustration. The question
arises if the two standardization relations are mutually consistent, i.e. if they yield consistent
cosmological constraints for the same sample of sources. In Khadka et al. (2023), we identified
the sample of 58 sources (59 measurements) that have a significant X-ray emission and were
also reverberation-mapped, hence both relations can be applied to them. For these sources, the
LX − LUV relation prefers a larger value of the current relative matter density parameter Ωm0
in comparison with the value inferred using the RBLR − L relation as well as the value derived
using standard cosmological probes. In Paper 6 (Chapter 7) we analyze the distributions of
the differences of luminosity distances (∆ log DL ≡ log DL,LX−LUV
− log DL,R−L) in different
cosmological models. We find that the distributions are generally asymmetric and the peak
is shifted to positive values, which implies that one method is more affected by a certain
systematic effect. We find that the differential extinction of UV and X-ray photons always
contributes to the non-zero luminosity-distance difference and that the X-ray/UV luminosity
relation is more affected by extinction than the RBLR − L relation. This opens a way for the
further application of the broad-line region RBLR − L relation in cosmological studies.
In conclusion, based on Papers 1-7 presented in this Habilitation Thesis (and references
therein), the existence of SMBH(s) is currently firmly established. The main evidence is
the following. First, we can detect its gravitational influence via the motion of S stars and
other objects (e.g. “G” objects) in the Galactic center. Second, in other galactic nuclei, their
gravitational influence is revealed via broad emission lines, which is the manifestation of
the fast motion of an ionized, clumpy material around SMBHs. SMBHs also clearly affect
the evolution of their host galaxies, which is hinted by several correlations between their
masses and large-scale properties of their hosts (velocity dispersion, bulge mass). One of the
main driving mechanisms behind these correlations is the AGN feedback, whose strength and
nature (radiative or radio-mechanical) traced by the ionization potential and the radio loudness
varies across different optical spectral classes of galaxies. This shows that the SMBH activity
can generally be variable and recurrent in the nearby Universe (low to intermediate redshifts).
The imprints of the AGN feedback can be traced on the large scales of galaxy groups and
clusters (e.g. it prevents the warm/hot intergalactic medium from cooling; X-ray cavities), but
the epochs of an enhanced nuclear activity could have plausibly left fingerprints at the small
scale as well. In particular, there may be distinct traces revealed via the properties of nuclear
star clusters due to repetitive star-disc and star-jet collisions.
Since antiquity, the center of the Universe has been shifting – once it was the Earth, then
the Sun, and later the Galactic center. Now we know that there is no particular center of
the Universe, which is also known as the Copernican principle. However, for our Universe
“island”, the Milky Way, to which we are gravitationally bound, the supermassive black hole
Sgr A* is the true center, both dynamical and geometric, which has also been influencing the
Milky Way on larger scales via its variable activity during the past billions of years. Therefore,
in any modern orrery demonstration (see Fig. 9.6), the supermassive black hole should be
present at its center to mark its significance, not only for the Milky Way, but also for other
galaxies, and thus the Universe as a whole.
226 CHAPTER 9. DISCUSSION AND CONCLUSIONS
Figure 9.6: Orrery with the black hole at its center. Author: Olena Shmahalo (for Quanta
magazine).
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Curriculum Vitae
Name and surname, including degrees: RNDr. Michal Zajaˇcek, Dr. rer. nat.
Date and place of birth: December 31st 1988, Malacky, Slovakia
Citizenship: Slovak
Permanent residence: L. Novomeského 4, 901 01 Malacky, Slovakia
Current position, unit, institution: astrophysics researcher, Department of Theoretical
Physics and Astrophysics, Faculty of Science, Masaryk University
Education:
• September 17, 2014 - October 12, 2017: University of Cologne / Max Planck Institute
for Radioastronomy (Cologne / Bonn, Germany) - Dr. rer. nat. in Experimental Physics,
graduated as very good with the grade 1.00; Thesis title: Interaction between interstellar
medium and black hole environment (Supervisor: Prof. Dr. Andreas Eckart)
• December 15, 2014: Charles University in Prague (Prague, Czechia) - Rigorosum
examination – RNDr. degree; Thesis title: Neutron stars near a galactic centre
• 2012–2014: Charles University in Prague (Prague, Czechia) - Master of Science in
Astronomy & Astrophysics, graduated with honours; Thesis title: Neutron stars near a
galactic centre (Supervisor: Prof. Dr. Vladimír Karas)
• 2009–2012: Charles University in Prague (Prague, Czechia) - Bachelor of Science in
General Physics, graduated with honours; Thesis title: The Late Heavy Bombardment
at various places of the Solar System (Supervisor. Prof. Dr. Miroslav Brož)
Work experience:
• July 2021 - present: Masaryk University, Faculty of Science, Department of Theoretical
Physics and Astrophysics (Brno, Czechia); position: postdoctoral researcher & lecturer,
principal investigator of the Czech Science Foundation Junior Star grant “Stars in
galactic nuclei: interrelation with massive black holes”
• January 2019 - June 2021: Center for Theoretical Physics, Polish Academy of Sciences
(Warsaw, Poland); position: postdoctoral researcher (PI: Prof. Bozena Czerny)
243
244 CURRICULUM VITAE
• October 2017 - January 2019: Max Planck Institute for Radioastronomy (Bonn, Germany);
position: junior postdoctoral researcher (PIs: Dr. Silke Britzen, Prof. J. Anton
Zensus)
Significant Research Results
Significant research outcomes of the associate professor candidate are listed in this section. In
the first subsection, first-author papers published in international, peer-reviewed journals are
included while in the following subsection we list manuscripts co-authored by the candidate
that were published in Nature and Science journals or papers published in a Letter format.
First-author refereed publications
• ZAJAˇCEK, M.*(corresponding author)*, B. CZERNY, N. KHADKA, M. L. MARTINEZALDAMA,
R. PRINCE, S. PANDA and B. RATRA. Effect of Extinction on Quasar Luminosity
Distances Determined from UV and X-Ray Flux Measurements. Astrophysical
Journal. 2024, 961(2, Article 229). ISSN 1538-4357. Available at: doi:10.3847/1538-
4357/ad11dc; citation: Zajaˇcek et al. (2024b)
• ZAJAˇCEK, M.*(corresponding author)*, B. CZERNY, V. K. JAISWAL, M. ŠTOLC,
V. KARAS, A. PANDEY, D. R. PASHAM, M. ´SNIEGOWSKA, V. WITZANY, P.
SUKOVA, F. MUNZ, N. WERNER, J. ˇRÍPA, J. MERC, M. LABAJ, P. KURFÜRST
and J. KRTI ˇCKA. Science with a Small Two-Band UV-Photometry Mission III: Active
Galactic Nuclei and Nuclear Transients. Space Science Reviews. 2024, 220(3, Article
29). ISSN 1572-9672. Available at: doi:10.1007/s11214-024-01062-5; citation:
Zajaˇcek et al. (2024a)
• ZAJAˇCEK, M.*(corresponding author)*, S. PANDA, A. PANDEY, R. PRINCE, A.
RODRIGUEZ-ARDILA, V. JAISWAL, B. CZERNY, K. HRYNIEWICZ, M. URBANOWICZ,
P. TRZCIONKOWSKI, M. ´SNIEGOWSKA, Z. FALKOWSKA, M. L.
MARTINEZ-ALDAMA and N. WERNER. UV FeII emission model of HE 0413-4031
and its relation to broad-line time delays. Astronomy & Astrophysics. 2024, 683(A140,
Article A140). ISSN 1432-0746. Available at: doi:10.1051/0004-6361/202348172;
citation: Zajaˇcek et al. (2024c)
• ZAJAˇCEK, M.*(corresponding author)*. Enhanced Doppler Beaming for Dustenshrouded
Objects and Pulsars in the Galactic Center. Astrophysical Journal. 2021,
915(2, Article 111). ISSN 1538-4357. Available at: doi:10.3847/1538-4357/ac043a;
citation: Zajaˇcek (2021)
245
246 SIGNIFICANT RESEARCH RESULTS
• ZAJAˇCEK, M.*(corresponding author)*, B. CZERNY, M. L. MARTINEZ-ALDAMA,
M. RALOWSKI, A. OLEJAK, R. PRZYLUSKI, S. PANDA, K. HRYNIEWICZ, M.
´SNIEGOWSKA, M.-H. NADDAF, R. PRINCE, W. PYCH, G. PIETRZYNSKI, C. Sobrino
FIGAREDO, M. HAAS, J. ´SREDZINSKA, M. KRUPA, A. KURCZ, A. UDALSKI,
V. KARAS, M. SARNA, H. L. WORTERS, R. R. SEFAKO and A. GENADE.
Time Delay of Mg ii Emission Response for the Luminous Quasar HE 0435-4312:
toward Application of the High-accretor Radius–Luminosity Relation in Cosmology.
Astrophysical Journal. 2021, 912(1, Article 10). ISSN 1538-4357. Available at:
doi:10.3847/1538-4357/abe9b2; citation: Zajaˇcek et al. (2021)
• ZAJAˇCEK, M.*(corresponding author)*, A. ARAUDO, V. KARAS, B. CZERNY and
A. ECKART. Depletion of Bright Red Giants in the Galactic Center during Its Active
Phases. Astrophysical Journal. 2020, 903(2, Article 140). ISSN 1538-4357. Available
at: doi:10.3847/1538-4357/abbd94; citation: Zajaˇcek et al. (2020)
• ZAJAˇCEK, M.*(corresponding author)*, B. CZERNY, M. L. MARTINEZ-ALDAMA,
M. RALOWSKI, A. OLEJAK, S. PANDA, K. HRYNIEWICZ, M. ´SNIEGOWSKA,
M.-H. NADDAF, W. PYCH, G. PIETRZYNSKI, C. Sobrino FIGAREDO, M. HAAS, J.
´SREDZINSKA, M. KRUPA, A. KURCZ, A. UDALSKI, M. GORSKI and M. SARNA.
Time-delay Measurement of Mg II Broad-line Response for the Highly Accreting
Quasar HE 0413-4031: Implications for the Mg II-based Radius-Luminosity Relation.
Astrophysical Journal. 2020, 896(2, Article 146). ISSN 1538-4357. Available at:
doi:10.3847/1538-4357/ab94ae; citation: Zajaˇcek et al. (2020)
• ZAJAˇCEK, M.*(corresponding author)*, G. BUSCH, M. VALENCIA-S, A. ECKART,
S. BRITZEN, L. FUHRMANN, J. SCHNEELOCH, N. FAZELI, K. C. HARRINGTON
and J. A. ZENSUS. Radio spectral index distribution of SDSS-FIRST sources across
optical diagnostic diagrams. Astronomy & Astrophysics. 2019, 630(A83, Article A83).
ISSN 1432-0746. Available at: doi:10.1051/0004-6361/201833388; citation: Zajaˇcek
et al. (2019a)
• ZAJAˇCEK, M.*(corresponding author)*, B. CZERNY, M. L. MARTINEZ-ALDAMA
and V. KARAS. Reverberation mapping of distant quasars: Time lag determination
using different methods. Astronomische Nachrichten. 2019, 340(7), 577–585. ISSN
1521-3994. Available at: doi:10.1002/asna.201913659; citation: Zajaˇcek et al. (2019b)
• ZAJAˇCEK, M.*(corresponding author)* and A. TURSUNOV. The Electric Charge Of
Black Holes: Is It Really Always Negligible?. Observatory. 2019, 139(1273), 231–236.
ISSN 0029-7704; citation: Zajacek & Tursunov (2019)
• ZAJAˇCEK, M.*(corresponding author)* and A. A. TURSUNOV. A stellar fly-by
close to the Galactic center: Can we detect stars on highly relativistic orbits?. Astronomische
Nachrichten. 2018, 339(5), 324–330. ISSN 1521-3994. Available at:
doi:10.1002/asna.201813499; citation: Zajaˇcek & Tursunov (2018)
• ZAJAˇCEK, M.*(corresponding author)*, A. TURSUNOV, A. ECKART and S. BRITZEN.
On the charge of the Galactic centre black hole. Monthly Notices of the Royal
Astronomical Society. 2018, 480(4), 4408–4423. ISSN 1365-2966. Available at:
doi:10.1093/mnras/sty2182; citation: Zajaˇcek et al. (2018)
247
• ZAJAˇCEK, M.*(corresponding author)*. Cologne-Prague-Kiel Meetings 2013-2017:
From Accretion To Star Formation In Galactic Nuclei. Observatory. 2017, 137(1261),
267–272. ISSN 0029-7704; citation: Zajacek (2017)
• ZAJAˇCEK, M.*(corresponding author)*, S. BRITZEN, A. ECKART, B. SHAHZAMANIAN,
G. BUSCH, V. KARAS, M. PARSA, F. PEISSKER, M. DOV ˇCIAK, M.
SUBROWEIT, F. DINNBIER and J. A. ZENSUS. Nature of the Galactic centre NIRexcess
sources: I. What can we learn from the continuum observations of the DSO/G2
source?. Astronomy & Astrophysics. 2017, 602(A121, Article A121). ISSN 1432-0746.
Available at: doi:10.1051/0004-6361/201730532; citation: Zajaˇcek et al. (2017)
• ZAJAˇCEK, M.*(corresponding author)*, A. ECKART, V. KARAS, D. KUNNERIATH,
B. SHAHZAMANIAN, N. SABHA, K. MUZIC and M. VALENCIA-S. Effect of an
isotropic outflow from the Galactic Centre on the bow-shock evolution along the orbit.
Monthly Notices of the Royal Astronomical Society. 2016, 455(2), 1257–1274. ISSN
1365-2966. Available at: doi:10.1093/mnras/stv2357; citation: Zajaˇcek et al. (2016)
• ZAJAˇCEK, M.*(corresponding author)*, V. KARAS and D. KUNNERIATH. Galactic
Center Minispiral: Interaction Modes Of Neutron Stars. Acta Polytechnica. 2015, 55(3),
203–214. ISSN 1805-2363. Available at: doi:10.14311/Ap.2015.55.0203; citation:
Zajacek et al. (2015)
• ZAJAˇCEK, Michal*(corresponding author)*, V. KARAS and A. ECKART. Dustenshrouded
star near supermassive black hole: predictions for high-eccentricity passages
near low-luminosity galactic nuclei. Astronomy & Astrophysics. 2014, 565(A17,
Article A17). ISSN 1432-0746. Available at: doi:10.1051/0004-6361/201322713;
citation: Zajaˇcek et al. (2014)
Publications in Nature, Science, and Letter format
• PEISSKER, F., M. ZAJAˇCEK, L. LABADIE, E. BORDIER, A. ECKART, M. MELAMED
and V. KARAS. A binary system in the S cluster close to the supermassive black hole
Sagittarius A*. Nature Communications. 2024, 15(10608). ISSN 2041-1723. Available
at: doi: 10.1038/s41467-024-54748-3; citation: Peissker et al. (2024)
• PASHAM, D. R., F. TOMBESI, P. SUKOVÁ, M. ZAJAˇCEK, S. RAKSHIT, E.
COUGHLIN, P. KOSEC, V. KARAS, M. MASTERSON, A. MUMMERY, T. W. S.
HOLOIEN, M. GUOLO, J. HINKLE, B. RIPPERDA, V. WITZANY, B. SHAPPEE,
E. KARA, A. HORESH, S. VAN VELZEN, I. SFARADI, D. KAPLAN, N. BURGER,
T. MURPHY, R. REMILLARD, J. F. STEINER, T. WEVERS, R. ARCODIA, J. BUCHNER,
A. MERLONI, A. MALYALI, A. FABIAN, M. FAUSNAUGH, T. DAYLAN,
D. ALTAMIRANO, A. PAYNE and E. C. FERRARA. A case for a binary black hole
system revealed via quasi-periodic outflows. Science Advances. 2024, 10(13, Article
eadj8898). ISSN 2375-2548. Available at: doi:10.1126/sciadv.adj8898; citation:
Pasham et al. (2024c)
• PASHAM, D. R., E. R. COUGHLIN, M. ZAJAˇCEK, I. LINIAL, P. SUKOVÁ, C. J.
NIXON, A. JANIUK, M. ´SNIEGOWSKA, V. WITZANY, V. KARAS, M. KRUMPE, D.
ALTAMIRANO, T. WEVERS and R. ARCODIA. Alive but Barely Kicking: News from
248 SIGNIFICANT RESEARCH RESULTS
3+ yr of Swift and XMM-Newton X-Ray Monitoring of Quasiperiodic Eruptions from
eRO-QPE1. Astrophysical Journal Letters. 2024, 963(2, Article L47). ISSN 2041-8213.
Available at: doi:10.3847/2041-8213/ad2a5c; citation: Pasham et al. (2024b)
• PASHAM, D. R., M. ZAJAˇCEK, C. J. NIXON, E. R. COUGHLIN, M. ´SNIEGOWSKA,
A. JANIUK, B. CZERNY, T. WEVERS, M. GUOLO, Y. AJAY and M. LOEWENSTEIN.
Lense–Thirring precession after a supermassive black hole disrupts a star. Nature.
2024. 630(8016), 325–328. ISSN 1476-4687. Available at: doi:10.1038/s41586-
024-07433-w; citation: Pasham et al. (2024d)
• GUOLO, M., D. R. PASHAM, M. ZAJAˇCEK, E. R. COUGHLIN, S. GEZARI,
P. SUKOVÁ, T. WEVERS, V. WITZANY, F. TOMBESI, S. VAN VELZEN, K. D.
ALEXANDER, Y. YAO, R. ARCODIA, V. KARAS, J. C. A. MILLER-JONES, R.
REMILLARD, K. GENDREAU and E. C. FERRARA. X-ray eruptions every 22 days
from the nucleus of a nearby galaxy. Nature Astronomy. 2024, 8(3). ISSN 2397-3366.
Available at: doi:10.1038/s41550-023-02178-4; citation: Guolo et al. (2024)
Acknowledgements
“If I have seen further it is by
standing on the shoulders of
Giants."
— Isaac Newton
(1642/1643-1726/1727), in a letter
to Robert Hooke,
February 5th, 1675
Since this is my fourth thesis already, I confirm that all of my previous acknowledgements
are still fully valid :) At this point I would like to express my sincere acknowledgements to
the people who have enabled me to do research, motivated me, and from whom I have learned
a lot for the subsequent research work. To start with my Bachelor Thesis, I am grateful to Prof.
Dr. Miroslav Brož, who supervised me during my bachelor studies at the Charles University
in Prague. From Prof. Brož, and also Prof. David Vokrouhlický, Prof. Ladislav Šubr, and
other researchers and lecturers at the Astronomical Institute of the Charles University, I got
very important basics of the analysis techniques in celestial mechanics, which I have been
using in various problems. Later I continued with my master thesis focused on the Galactic
center. At this stage my master-thesis supervisor Prof. Dr. Vladimír Karas played a big role.
He suggested the topic “Neutron stars near a galactic center”, which sounded as very exotic
to me but at the same time thrilling. I invested a lot of time into trying to find a way to detect
the “hidden” population of neutron stars close to the Galactic center. I think we succeeded
partially and the results got published to a certain extent, though we should still finalize it
now after 10 years! In general, I learned a lot about the center of the Milky Way during this
period. Especially the twist towards the mysterious G2 “cloud", which is likely not a pure
cloud anymore, has been highly influential and probably affected my whole career afterwards.
I really enjoyed my PhD studies at the University of Cologne/Max Planck Institute for
Radioastronomy, especially many discussions with my supervisor Prof. Dr. Andreas Eckart
and a lot of advice from him. Andreas has always been very kind, patient, and supportive,
which is quite rare in current busy times. I would also like to express big thanks to the whole
Cologne and Bonn groups, in particular our aegroup, especially to Dr. Florian Peissker, with
whom we intensively collaborate till now on many problems and puzzling objects in the
249
250 ACKNOWLEDGEMENTS
Galactic Center region. In addition, we discussed a lot with Mónica Valencia-Schneider,
Gerold Busch, Nastaran Fazeli, Matthias Subroweit, and many others.
In the following stage of my career, I continued as a junior postdoctoral fellow at the
Max Planck Institute for Radioastronomy in Bonn. I was supported by a large collaborative
research grant SFB 956. During this time I really appreciated the collaboration with Dr. Silke
Britzen and colleagues concerning the investigation of jet kinematics and precession in blazars
and other radio galaxies. One of our favourite sources has been OJ287, the “Rosetta stone” of
blazars, which exhibits an exemplary jet precession/nutation pattern, and we actually managed
to prove it. This collaboration continues till now and has been bringing very interesting results,
also concerning the connection between the jet precession and SED changes and a potential
origin of high-energy neutrinos in blazars.
I would also like to highlight the contribution of Dr. Arman Tursunov from the Silesian
University in Opava (now a Humboldt fellow at MPIfR), who has not only been an exemplary
collaborator but also one of my best friends among friends-scientists. The work on the blackhole
charge and the related spin-offs has gained a lot of world-wide visibility and impact,
which I didn’t expect at the time when we started to discuss the problem of the black-hole
charge “over some Kölsch beer” back in Bad Honnef close to Bonn.
Later, during the years 2019-2021, I spent my second postdoc in Warsaw, at the Center for
Theoretical Physics of the Polish Academic of Sciences, in the group of Prof. Bo˙zena Czerny.
Bo˙zena is probably one of the most clever and “universal”, or as one would call it in music –
multi-instrumental, astrophysicists I have ever met. During this time I partially switched form
the extremely underluminous Galactic center to (mostly, but not only) intermediate-redshift
quasars, some of which accrete close to the Eddington limit. This experience complemented
my previous expertise and I started to understand more connections among systems accreting
at different rates. Some of these aspects I tried to stress in this thesis. I have also enjoyed
many discussions and collaborative projects with the whole Warsaw group – to name the most
influential people – Swayam Panda, Marzenka Šniegowska, Mary Loli Martinez Aldama,
Mohammad Naddaf, Raj Prince, Vikram Kumar Jaiswal, Ashwani Pandey, Amit Kumar, and
many other people at the CFT PAN and CAMK. I also have to stress that now, in retrospect, I
really appreciate that we remained well focused and organized during the COVID pandemic
lock-downs and we managed to discuss and solve many problems via numerous zooms.
After my Warsaw stay, in 2021 I got a position at the Masaryk Universe in Brno, the
Czech Republic, in the High-energy Astrophysics group led by Prof. Norbert Werner. I would
really like to express my gratitude to Norbert, the leader of the High-Energy Astrophysics
group, and Prof. Rikard von Unge, the director of the Department of Theoretical Physics
and Astrophysics, for this opportunity to continue with my research in Brno, which is only
∼ 100 km from my home-town Malacky. I especially thank Norbi for his support, many
discussions about interesting projects on the Earth and in space, and also interviews about
other, sometimes even personal matters. The workplace that I found in Brno is generally very
positively oriented and constructive. I also got an opportunity to supervise students and to
contribute to the course on the Structure and the Evolution of the Universe. I would like to
thank all the current and past members of the HEA group for a stimulating environment and a
lot of scientific and other fun. These people are mainly the following ones (the order is quite
random): Petr Kurfürst, Jean-Paul Breuer, Tomáš Plšek, Matej Kosiba, Dan Hu, Orsi Kovács,
Jakub ˇRípa, Filip Münz, Filip Hroch, Henry Best, Izzy Garland, Congyao Zhang, Matúš Labaj,
Martin Mondek, Martin Koláˇr, Monika Pikhartová, Lýdia Štofanová, Marianna Dafˇcíková,
Jolie L’Heureux, Ania Wójtowicz, Kristýna Voroboková, Kristína Kallová, Klaudia Protušová,
251
Ramona Valková, Lea Szakszonová, Romana Grossová, Samuel Kováˇcik, Artem Gorodilov,
Wladimiro Leone, Edoardo Borciani, Jakub Vyskoˇcil, and many students (I apologize if I
forgot someone, I tried not to :)). I also thank Terka Jeˇrábková, my new/old colleague and
friend, for a lot of stimulating discussions and advice during the past 10 years since our
studies in Prague. In addition, I am proud of Lýdia Štofanová, another new/old colleague,
who was also my first student that I mentored, for the successful defence of her PhD thesis
and a continuing career in astrophysics and space-related activities. I hope that I learned
from my mistakes that I did during the counselling of Lýdia’s thesis and I apologize to her
and Vladimir (Karas) if it caused trouble and extra work since I was mostly out of Prague in
Cologne at that time.
I would also like to thank for a lot of support and advice to Prof. Zdenˇek Mikulášek, Prof.
Rikard von Unge, Prof. Miloš Zejda, Prof. Jiˇrí Krtiˇcka, Dr. Honza Janík, Vašek Glos, Mrs.
Santarová, and all the other colleagues at the Department of Theoretical Physics. I have to
admit that I enjoy our common morning coffees on Friday before the institute seminar – and
for this reason I am willing to always sacrifice some money to buy typical Czech pastries and
cakes – it is always fun to discuss with people with a different expertise and views.
I would also like to express my gratitude for many stimulating discussions and input to
my close scientific collaborators during the last 5 years (some of whom were not explicitly
mentioned earlier), these are mainly Florian Peissker, Silke Britzen, Petra Suková, Vojta
Witzany, Arman Tursunov, DJ Pasham, Muryel Guolo, Francesco Tombesi, Eric Coughlin, Ali
Kurmus, Louis Deslauriers, Bharat Ratra, Narayan Khadka, Shulei Cao, Bart Ripperda, Sean
Ressler, Shubham Kejriwal, Alvin Chua, Ana Laura Müller, Anabella Araudo, Jirka Horák,
Ladislav Šubr, Myank Singhal, Maria Melamed, Emma Bordier, Marcel Štolc, Sebastiano
von Fellenberg, Christian Fendt, and many, many others.
During the years after my PhD studies, I have appreciated the support of several research
grants that largely enabled to do research presented in this thesis. During my stay at the
MPIfR in Bonn and at the University of Cologne (2017-2019), I was supported by SFB 956
(“Conditions and Impact of Star Formation – Astrophysics, Instrumentation and Laboratory
Research”). Subsequently, during my postdoctoral fellowship at the Center for Theoretical
Physics, Polish Academy of Sciences in Warsaw (2019-2021) I received the support from the
National Science Center, Poland, grant No. 2017/26/A/ST9/00756 (Maestro 9). During my
current research stay at the Masaryk University in Brno, I have been supported by several
research grants, specifically the Czech Science Foundation EXPRO grant no. GX21-13491X
(“Exploring the Hot Universe and Understanding Comic Feedback”), MUNI Award in Science
and Humanities 3 (Space-Based High-Energy Astrophysics, MUNI/I/0003/2020), the Czech
Science Foundation Lead Agency grant no. GF23-04053L (Czech-Polish bilateral grant
“Weather effects in using disk continuum time delays in active galactic nuclei to measure the
expansion rate of the Universe”), and the Czech Science Foundation Junior Star grant no.
GM24-10599M (“Stars in galactic nuclei: interrelation with massive black holes”).
I would also like to highlight the work of the Slovak Association for Youth, Science, and
Technology (AMAVET), who helped me to present my project about the measurement of
the Solar “constant” at the nationwide Science and Technology Fair in 2008. Meeting many
talented and motivated peers certainly boosted my motivation further. Subsequently, I became
involved in the science popularization projects of AMAVET. I was also a member of the
Local Organization Committee of the MILSET Expo Sciences International in Bratislava in
2011 as well as in 2013 in Abu Dhabi. Every year I do my best to serve as a judge at the
Science and Technology fair in Bratislava, which always boosts my motivation to continue
252 ACKNOWLEDGEMENTS
doing science while talking to many young motivated people. On an international level, I also
served as an adult-in-charge at the Intel International Science and Engineering Fair (ISEF) in
Phoenix,Arizona in 2019 and at the Genius Olympiad 2023 and 2024 in Rochester, New York.
At the Genius Olympiad, I also served as a judge of the selected projects twice.
Concerning the preparation of this Habilitation Thesis and the whole procedure, I owe
many thinks to Mgr. Michaela Švestková and Mgr. Jana Procházková for all of their guidance
and for checking details in my documents. In addition, I really appreciate the help of Mgr.
Jana Nguyen Baluchová and Mgr. Marie Novosadová Šípková with collecting all of my
published papers in the right format and listing their corresponding citations. Without their
help, the whole preparation process would be much slower. I would also like to thank Prof.
Bo˙zena Czerny for reading and checking the parts of this thesis, mainly the Introduction. I am
also grateful to Vladimír Karas for his comments and recommendations during the writing
process.
Last but the most important, I would like to thank my closest family, especially my parents,
Viera and Marián, my sister Barbora, and her children Nina, Sebastian, and Kristian, for a
lot of support, love, and encouragement, without which this work would not be possible. I
would like to thank all the other (non-astronomy) family members and friends in Slovakia,
the Czech Republic, and elsewhere for all the support, inquiring questions, comments, and
encouragement that helped me to push forward all the scientific, popularization as well as
non-scientific efforts in my life :)
Photogallery
This small photogallery illustrates my research and educational activities both at home and
abroad. Figure 1 captures a moment after my successful PhD Thesis defence in Cologne, Germany.
Figures 2, 4, 5 were taken during my participation at talks, seminars, and conferences in
the Czech Republic, while Figures 3, 6, 7 capture such events abroad. Figure 8 represents a pie
chart from the NASA Astrophysics Data System showing my overall co-author connections
at the end of 2024.
Figure 1: A moment after the PhD defence on October 12, 2017 at the University of
Cologne. Photography author: V. Karas
253
Figure 2: Enjoying a canteen lunch with Prof. Jiˇrí Biˇcák (1942-2024) at the Faculty of
Mathematics and Physics of the Charles University in Prague. The photo was taken after
my talk about the James Webb Space Telescope (“James Webb Space Telescope and Intricate
Physics of Star Formation in the Galactic Center and Beyond”) presented at the Department
of Theoretical Physics colloquium on February 22nd, 2022.
Figure 3: A conference group photo at the Eighth Giant Magellan Telescope Community
Science Meeting focused on Black holes at all scales. The photo was taken at the beginning
of September 2022 in the Village of Oak Creek, Sedona, Arizona.
254 ACKNOWLEDGEMENTS
Figure 4: Lecturers of the Autumn school of astronomy, physics and mathematics at
the Cheb High School. The photo was taken at the end of the school on Friday, November
11, 2022. The lecturers in the photography are (from the left to the right): Prof. Zdenˇek
Mikulášek, Prof. Petr Chvosta, Mgr. Jaroslava Dirlbecková, Mgr. Jan Dirlbeck, Dr. Jiˇrí
Grygar, and me.
Figure 5: A conference group photo taken at the Cologne-Prague-Brno meeting, June
1st-3rd, 2022, at the Brno Observatory and Planetarium.
255
Figure 6: A photo with the members of the Center for Computational Relativity and
Gravitation led by Prof. Manuella Campanelli at the Rochester Institute of Technology.
Prof. Campanelli is the third person from the right. I gave a presentation at the RIT on the
Lense-Thirring precession of the accretion disc-jet system in galactic nuclei on June 14th,
2024.
Figure 7: Among Czecho-slovak young participants at the 73rd Lindau Nobel Laureate
Meeting, June 30th - July 5th 2024, Lindau, Germany. In the photo, there is
David Wineland (Nobel prize in physics, 2012; fourth from the right) and Countess Bettina
Bernadotte af Wisborg, the president of the Council of the Lindau Nobel Laureatte Meeting
(fourth from the left).
256 ACKNOWLEDGEMENTS
Figure 8: A pie chart of the author network as of December 2024 according to NASA
Astrophysics Data System.