The ∆a photometric system
Habilitation thesis
Ernst Paunzen
Department of Theoretical Physics and Astrophysics
Masaryk University
Kotlářská 2
CZ - 611 37 Brno
Brno, June 2020
Contents
1 Summary 4
2 The early history of the ∆a photometric system 5
3 The diagnostic tools of the ∆a photometric system 5
4 Other indices measuring the 5200Å region 7
5 The variability of the ∆a index 10
5.1 CP stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5.2 Be/shell stars - The case of Pleione . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.3 Variable star detection via ∆a photometry . . . . . . . . . . . . . . . . . . . . . . 15
5.3.1 Temporal analysis and results . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.3.2 Individual variables and Conclusions . . . . . . . . . . . . . . . . . . . . . 18
6 Chemically Peculiar stars of the upper main sequence 19
7 Other star groups interesting for the ∆a photometric system 21
7.1 Blue Stragglers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
7.2 Herbig Ae/Be stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
7.3 Be/shell stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
7.4 B[e] stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
7.5 Evolved and Population II stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
8 An inspection of the wavelength region from 4900 to 5700Å 26
8.1 The 5200Å flux depression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
8.2 Features of Stars across the HRD . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
8.3 Features of Quasars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
8.4 Features of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
9 Spectrophotometry of the 5200Å region for peculiar and normal type stars 40
9.1 Data and reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
9.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
9.3 Known peculiar objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
9.4 Apparent normal-type objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
9.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
10 A catalogue of ∆a measurements for Galactic field stars 50
10.1 Selection, preparation, and homogenization of the data . . . . . . . . . . . . . . . 51
11 The detection probability of the ∆a system for Population I stars 54
11.1 The normal type objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
11.2 Outliers not included in RM09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
11.3 CP1 stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
11.4 CP2 stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.5 CP3 stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.6 CP4 stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.7 λ Bootis stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.8 Supergiants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.9 Be/shell stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
1
11.10Newly confirmed CP stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
11.11Comparison with the Geneva ∆(V 1 − G) and Z indices . . . . . . . . . . . . . . 62
12 An empirical temperature calibration for the ∆a photometric system 63
12.1 The B-type stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
12.1.1 Sample of program stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
12.1.2 The estimation of the reddening . . . . . . . . . . . . . . . . . . . . . . . 66
12.1.3 The calibration of the effective temperature . . . . . . . . . . . . . . . . . 66
12.1.4 The calibration procedure for the ∆a photometric system . . . . . . . . . 68
12.2 The A-type and mid F-type stars . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
12.2.1 Sample of program stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
12.2.2 The estimation of the reddening . . . . . . . . . . . . . . . . . . . . . . . 72
12.2.3 The calibration of the effective temperature . . . . . . . . . . . . . . . . . 72
12.2.4 The result for the ∆a photometric system . . . . . . . . . . . . . . . . . . 73
13 Theoretical isochrones for the ∆a photometric system 74
13.1 Models, data selection, and isochrone fitting . . . . . . . . . . . . . . . . . . . . . 78
14 Synthetic ∆a photometry 79
14.1 The normality line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
14.1.1 The synthetic ∆a filter system . . . . . . . . . . . . . . . . . . . . . . . . 81
14.1.2 Calibration relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
14.1.3 Luminosity effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
14.1.4 Metallicity effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
14.2 The cool CP and λ Bootis stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
14.2.1 Model atmospheres for CP stars . . . . . . . . . . . . . . . . . . . . . . . 86
14.2.2 Selected sample of stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
14.3 Individual models: parameter determination with observed fluxes . . . . . . . . . 90
14.3.1 CP1 stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
14.3.2 CP2 stars with Teff 8500 K . . . . . . . . . . . . . . . . . . . . . . . . . 93
14.4 CP2 stars with 8500 K Teff 10000 K . . . . . . . . . . . . . . . . . . . . . . . 96
14.5 Comparison of the synthetic and observed ∆a photometry for ten CP stars . . . 99
14.5.1 λ Bootis stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
14.5.2 CP1 stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
14.5.3 CP2 stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
14.5.4 Spectroscopic observations of the 5200Å depression . . . . . . . . . . . . . 101
14.6 Observational constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
14.7 Microturbulence, abundances, and atomic data . . . . . . . . . . . . . . . . . . . 103
14.8 Stratification and magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
14.9 Stellar model atmospheres with magnetic line blanketing . . . . . . . . . . . . . . 105
14.9.1 The stellar model atmosphere code LLModels . . . . . . . . . . . . . . . . 105
14.9.2 The behaviour of ∆a, (∆V 1 − G), and Z in correlation with Teff and B . 106
14.9.3 Effects of the individual abundance patterns . . . . . . . . . . . . . . . . . 108
15 Heuristic observational correlations for CP stars 110
16 Investigating the λ Bootis spectroscopic binary hypothesis using ∆a photometry
116
16.1 Modelling the spectroscopic binary systems . . . . . . . . . . . . . . . . . . . . . 116
16.2 Results and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
2
17 The ∆a observations of Galactic open clusters 119
17.1 The characteristics of open clusters . . . . . . . . . . . . . . . . . . . . . . . . . . 120
17.2 Photoelectric ∆a observations of Galactic open clusters . . . . . . . . . . . . . . 121
17.2.1 Observations and reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 121
17.2.2 Feinstein 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
17.2.3 NGC 2168 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
17.2.4 NGC 2323 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
17.2.5 NGC 2437 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
17.3 CCD ∆a observations of Galactic open clusters . . . . . . . . . . . . . . . . . . . 126
17.4 The observation of Blue Stragglers in open clusters . . . . . . . . . . . . . . . . . 128
17.5 Statistics of the observed open clusters . . . . . . . . . . . . . . . . . . . . . . . . 128
18 The first ∆a observations of three Galactic globular clusters 133
18.1 Target selection, observations and reduction . . . . . . . . . . . . . . . . . . . . . 134
18.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
19 The ∆a observations within the Large Magellanic Cloud 141
19.1 Target fields and observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
19.2 Reduction and calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
19.3 The incidence of the apparent peculiar objects . . . . . . . . . . . . . . . . . . . . 145
19.4 The spectroscopic verification of one CP and Be star . . . . . . . . . . . . . . . . 147
19.4.1 Target selection, observations, and reductions . . . . . . . . . . . . . . . . 148
19.4.2 Results and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
19.5 The (non-)variability of magnetic CP candidates in the LMC . . . . . . . . . . . 150
19.5.1 I light variability of mCP stars . . . . . . . . . . . . . . . . . . . . . . . . 152
19.5.2 Periodograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
19.5.3 Discussion of periodograms . . . . . . . . . . . . . . . . . . . . . . . . . . 155
19.5.4 The mCP candidates suspected of periodic light variations . . . . . . . . . 156
19.5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
20 A case study of using Gunn g data to improve ∆a 159
21 The ALHAMBRA and COSMOS surveys 163
22 Conclusions and Outlook 165
23 References 166
3
1 Summary
This work describes the history, characteristics, observations, results and future prospects of the
∆a photometric system. Up to now, it successfully produced countless scientific output since its
development and first appearance on the astronomical scene initiated by Hans-Michael Maitzen
in 1976.
It was intended to study the typical and unique flux depression at 5200 Å found in mainly
magnetic chemically peculiar stars of the upper main sequence. Therefore the most important
measurement is through the g2 filter centred at this wavelength region. In addition, one needs
the information about the continuum flux of the same object. Originally, the g1 (centred at
5000Å) and Strömgren y (5500Å) was used to get the continuum flux. In principle, any other
filters such as Johnson BV RI can be used. However, the closer it is measured to the 5200Å
region and the narrower the used filters are, the results become more accurate. The a index
is then defined as the flux in g2 compared to the continuum one. Because there is a general
increase of opacity around 5200Å with decreasing temperature, one has to normalize a with
the index a0 of a non-peculiar star of the same temperature, to compare different peculiar (or
deviating) stars with each other (∆a index).
With this photometric system it is possible to measure any peculiarities, such as abnormal
absorption and emission lines, in the region of 5200Å. Soon, it was used to investigate metalweak,
Be/shell and supergiants in the Galactic field and open clusters.
At the end of the 1980ies, the highly developed photomultiplier technology, slowly but surely,
was replaced by the CCD technology. It took a few years until CCDs reached the same accuracy
as photomultipliers for the same exposure time and target brightness.
The first CCD ∆a observations which were performed 1995 with the same telescope, the 61
cm Bochum telescope at La Silla, by the same person, Hans-Michael Maitzen, who initiated in
1971 the observations of CS Vir in g1 and g2. The results of the first CCD observations, data for
25 Galactic field stars with known spectroscopic peculiarity types, were published in 1997. After
that, CCD observations of open clusters, the Large Magellanic Cloud and Globular clusters were
successfully secured.
This work goes one step further showing that the ∆a photometric system and the study
of its corresponding spectral region from 4900 to 5700Å is able to contribute significant new
insights at many fields of astrophysics. The list of objects which are potential targets is long:
cool-type Population I and Population II objects, supergiants, emission type objects, all type of
galaxies, and so on.
These research fields can be investigated by 1) new observations; 2) archival data not used
so far, for example cool-type objects in star cluster fields and 3) data from other surveys which
employ similar filters. For sure, all three approaches will be extensively utilized in the future.
4
2 The early history of the ∆a photometric system
The roots of the ∆a photometric system date back to the year 1969. The invention and development
of it is closely tied to ao. Univ.-Prof. i.R. tit. Univ.-Prof. Dr. Hans-Michael Maitzen
(HMM). The interested reader is referred to his article “Two decades of ∆a photometry” published
by Maitzen (1998) which includes a comprehensive overview of the history until then.
Here, a very short overview is given because it sheds more light on the original intentions
which are still state-of-the-art today.
In 1969, HMM got a position at the newly founded astronomical institute of the RuhrUniversity
of Bochum, Germany. Soon, the at that time, head of the institute, the late Prof.
Theodor Schmidt-Kaler invited him to perform photometric observations at the Bochum 61
cm telescope at ESO (La Silla). He started the observations in May 1969, only less than two
months after the official opening of the observatory on 23. March 1969. He monitored magnetic
stars (CP2) from the catalogue by Babcock (1958) as suggested to him by the late Prof. Karl
Rakos. This was to confirm the variability of these stars by means of Johnson UBV photometry.
The “key star” for the further historical development was CS Vir (HD 125248), a classical CP2
object. HMM found not only, as expected, a decrease of the variability amplitude from U to B,
but also the V light curve exhibited either half the period of U and B, or as we know today,
a double wave variation due to the variable continuum backwarming produced by strong line
absorption at shorted wavelengths.
These results were published by Maitzen & Rakos (1970). As next step, photometric observations
in the Strömgren system and spectroscopy of CS Vir was done. Because no filter covered
the wavelength interval where the transition from a single to a double wave variation occurred,
he decided to order two new interference filters (g1, λc = 5020 Å and g2, λc = 5240 Å, both with
FWHM = 130 Å). These filters are already very close to those used today (Sects. 9 and 14.1.1).
From their colour appearance to the human eye, Prof. Schmidt-Kaler suggested to name them
giftgrün (poisonous green, g1) and lindgrün (yellowish green, g2) which was rejected for practical
reasons. The first observations with these filter were conducted in 1971 in order to trace the
light variability of CS Vir but not in the way, the ∆a photometric system is used nowadays.
The most important result for the birth of the system was the detection of the characteristic flux
depression at 5200Å by Kodaira (1969) which can be measured via g2. This prompted HMM to
substantiate the feature by a more extended photometric campaign of different CP stars (not
only magnetic ones) and apparent normal type ones. Using the already available Strömgren y
filter, he defined the normality line, and the final ∆a parameter. The foundation paper then
appeared more than 40 years ago (Maitzen, 1976a).
3 The diagnostic tools of the ∆a photometric system
Here, an overview of the characteristics and diagnostic tools of the ∆a photometric system
is given. One has to refer to many consecutive Sections where these tools are applied and
discussed in more detail. Some of the information given here might be repeated there because
of the necessity to clarify some points within the context. However, it was tried to minimize
such duplicities.
Basically, the ∆a photometric system consists of one filter which measures the 5200Å region
(g2) and an additional information about the continuum flux of the same object. This can
be either achieved by measuring the flux at the adjacent spectral regions, for example with the
filters g1 (5000Å) and g3 = y (5500Å), but also by any other effective temperature (Teff) sensitive
colour, B − V , b − y, or B2 − V 1 to give some examples. The latter were indeed successfully
applied, for example, Maitzen et al. (1986) used b − y, whereas Maitzen (1993) also employed
B − V colours.
5
With these measurements, the index a can be calculated as
a = g2 −
g1 + y
2
(1)
a = g2 −
b + y
2
(2)
a = g2 −
B + V
2
(3)
In principle, the positioning of the continuum filters minimizes the influence of Teff on the
peculiarity index. The closer it is measured to the 5200Å region and the narrower the used filters
are, the results become more accurate. One has to avoid, for example, the hydrogen or helium
lines for the continuum measurement because they are very much sensitive to the projected
rotational velocity and the surface gravity.
In Sect. 10, Table 9 lists several different filters which were used in the past for different
purposes to obtain observations. There is a general increase of opacity around 5200Å with
decreasing temperature (Sect. 14.1). Therefore, one has to normalize a with the index a0 of
a non-peculiar star of the same temperature, to compare different peculiar (or deviating) stars
with each other. The photometric peculiarity ∆a index is therefore defined as
∆a = a − a0[(g1 − y); (b − y); (B − V ))]. (4)
The first diagnostic tool is the normality line which comprises of the location of the a0values
in respect to a Teff sensitive colour. Assuming that all stars exhibit the same interstellar
reddening, peculiar objects deviate from the normality line more than 3σ (Fig. 1).
From observations, it is known that the normality line is shifted by E(b − y) to the red
and by a small amount E(a) to higher a-values (Maitzen, 1993). It has to be emphasized that
correlations between the amount of reddening for different photometric systems exist (Sect.
12.1.2, Yuan et al., 2013), for example AV = 3.1E(B − V ) = 4.3E(b − y). These correlations can
be used to transform the reddening values between the different photometric systems. The ratio
of the shifts
f = E(a)/E(b − y) (5)
can be determined from the deviation of a reddened cluster normality line from the unreddened
relationship. On the other hand, assuming a mean f-value (≈ 0.05) and iterating the formula
a(corr) = a(obs) − fE(b − y) (6)
one can determine reddening values by the ∆a-photometry of clusters. The effect has only to
be taken into account for E(b − y) > 0.3 mag and a non uniform reddening distribution.
More of a problem is the estimation of differential reddening within a star cluster (Bonatto
et al., 2012), for example. In principle, several methods can be applied (Sects. 12.1.2 and 12.2.2)
to overcome this problem:
• to deredden each individual object using the Strömgren uvbyβ photometric system and its
calibrations
• to use the Q-method for the Johnson UBV photometric system
An a versus (g1 − y)0 or (b − y)0 or (B − V )0 diagram should then be able to further strengthen
the membership of objects to the investigated star cluster since fore- and background deviate
significantly from the normality line. These deviations are in generally ten times higher than
those observed for the most prominent CP stars.
6
17
16
15
14
13
12
11
10
16
15
14
13
12
11
NGC 6451
-0.75 -0.60 -0.45 -0.30 -0.15 0.00 0.15
0.60
0.63
0.66
0.69
0.72
0.75
0.78
0.81
0.84
0.87
a
0
= 0.798 + 0.343 (g
1
- y)
(g
1
- y) [mag]
17
16
15
14
13
12
11
10
NGC 6192
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
0.80
a
0
= 0.786 + 0.251 (g
1
- y)
(g
1
- y) [mag]
NGC 6134
V[mag]
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
a
0
= 0.809 + 0.279 (g
1
- y)
a[mag]
(g
1
- y) [mag]
Figure 1: The two basis diagnostic tools of the ∆a photometric system for three open clusters:
the normality line a0 versus (g1 −y) and colour-magnitude MV versus (g1 −y) diagrams together
with isochrones.
The second diagnostic tool is a y versus (g1 −y) diagram. Instead of y, any other magnitude,
for example, V , R, I, and so on, can be taken. This is just a classical colour-magnitude diagram
(CMD) for the ∆a photometric system. With the knowledge of the reddening and the distance,
the absolute magnitude MV, and using the bolometric correction (B.C.) as well as the absolute
magnitude of the Sun, the luminosity log L/L⊙ can be calculated (Gómez et al., 1998).
In Sect. 13, a grid of isochrones with different initial chemical compositions for the ∆a system
is presented. There, it is shown that the accuracy of fitting isochrones to ∆a data without the
knowledge of the cluster parameters is between 5 and 15 %. This efficient tool has been already
widely used for star clusters and the LMC (Sects. 17 and 19).
Figure 1 shows MV versus (g1 −y) diagrams (upper panels) together with isochrones for three
open clusters. The capability to sort out non-members and to estimate the cluster parameters
are evident.
4 Other indices measuring the 5200Å region
One has to differentiate between indices which measure the flux in the 5200Å region directly
and those which measure the metallicity (line blanketing). The latter are capable to detect most
extreme CP stars because of their prominent overabundances. Those are, for example, the m1,
∆m1, and [m1] in the Strömgren system as well as m2 and δm2 in the Geneva 7-colour system
(Golay, 1974).
Another interesting approach was published by Masana et al. (1998). They defined a
reddening-depended peculiarity index ∆p as a linear combination of all Strömgren uvbyβ colours.
7
Figure 2: The filter transmission curves of the Geneva 7-colour (upper panel) and Vilnius (lower
panel) system taken from Bessell (2005).
They found a detection rate of up to 50% for early (hot) CP2 stars. However, this approach
was not systematically followed after the original paper has been published. It would be very
interesting to use the new photometric catalogue by Paunzen (2015) to update and upgrade this
method.
Besides the ∆a photometric system (Sect. 3), a few other indices are available which measure
the flux in the 5200Å region. These are described in more detail in the following.
The ∆a′ index by Adelman (1979): it basically works in the same way as the “classical ∆a
index”, but was especially designed for his spectrophotometric data. It is defined as
a′
= m5264 − [m4785 + 0.453 · (m5840 − m4785)]. (7)
The measurements at 4785 and 5840Å, which were both made at locations significantly bluer
than g1 and redder than y, represent a wavelength base for the continuum that is larger by a
factor of two than in ∆a photometry. The depression itself is represented by the 5264Å value.
Like the a index, the a′ index is slightly dependent on the colour of the star and therefore has
to be normalized by the index of non-peculiar stars with the same colour.
The ∆(V 1 − G) and Z indices of the Geneva 7-colour system: The Geneva 7-colour photometric
system (Fig. 2) is the most homogeneous one because unique filter sets together with
the same type of photomultipliers were used throughout its history (Golay, 1994). However,
unfortunately, no new observations are available for it because the original instrumentation is
not existing any more. The ∆(V 1 − G) index is the first measurement for peculiarity derived
from the Geneva 7-colour photometric system. The V 1 and G filters are centred at 5408 and
5814Å (bandwidths of about 200Å), respectively. Hauck (1974) was the first to propose this
index as peculiarity parameter. It is defined as
∆(V 1 − G) = (V 1 − G) − 0.289 · (B2 − G) + 0.302. (8)
On average, normal stars have ∆(V 1 − G) values of −5 mmag (Sect. 11.11). The zero point
of the ∆(V 1 − G) index represents the upper limit of the sequence of normal type objects and
8
not its mean value. This was done by using the upper envelope for normal type, luminosity class
V to III objects, based on a linear fit for the correlation of (V 1 − G) with (B2 − G) as given by
Hauck (1974) which introduces this negative shift. Consequently, a very strict significance limit
of +10 mmag for ∆(V 1 − G) was set by Hauck & North (1982) to avoid contamination of CP
objects.
Besides the ∆(V 1 − G) index, Z within the Geneva 7-colour photometric system is most
suitable for detecting CP stars. Originally, Cramer & Maeder (1979) defined a three-dimensional
grid [XY Z] for hot stars on the basis of the seven available filters (Fig. 2). The X parameter
is oriented along the main sequence (MS) of O- and B-type, whereas the Y is in the direction
of high luminosity stars. The Z parameters is normal to the [XY ] plane. It is defined (Cramer,
1999) as
Z = −0.4572 + 0.0255 · U − 0.1740 · B1 + 0.4696 · B2 − 1.1205 · V 1 + 0.7994 · G (9)
The Z index is virtually independent of temperature and gravity effects for stars hotter than
A0 or (b − y)0 < 0 mag. Furthermore, the only stars showing a significant deviation in the Z
direction, are the CP stars. Later on, Cramer & Maeder (1980) showed that Z is correlated
with the measured magnetic field of CP stars. This is line with the corresponding synthesized
photometry (Sect. 14.9.2). Cramer (1999) lists a limit of ±10 mmag for apparent peculiarity
(Sect. 11.11).
As the ∆a index (Sect. 5.1), ∆(V 1 − G) and Z also vary over the rotational period of CP2
stars (Muciek et al., 1984). However, the variations (±3 mmag) are less than those for the ∆a
index.
The different diagrams of the Vilnius system: The Vilnius system (Fig. 2) was developed
independently from the Geneva 7-colour system but for similar reasons, namely, to derive temperatures,
luminosities, and peculiarities in reddening and composition from photometry alone.
The colours are normalized by the condition U −P = P −X = X −Y = Y −Z = Z −V = V −S
for unreddened O-type stars. Therefore, all colours for normal stars are positive. Reddening
free indices are constructed as for the Geneva 7-colour and Strömgren systems. Interesting
enough, the Z filter was placed on the Mg i triplet as well as the MgH molecular band. It is
also sensitive to the luminosity classes of G- to M-type stars (Straižys et al., 1986). Straižys &
Žitkevičius (1977) proposed four diagrams to separate CP from normal type stars. They defined
the following index
QYZS = Y − Z − 0.538 · (Z − S) (10)
which is, in principle, independent of interstellar reddening. If a star exhibits QYZS <
−0.03 mag it can be considered as CP object. They found that 56% of CP stars (denoted as
Ap stars in their work) have such values with the classical hot Si stars show the largest and the
HgMn (CP3) the smallest deviations. It turned out that strongly reddened and cool type CP
stars can not be unambiguously detected. Also, this index fails to detected CP1 stars which is
similar to the situation within the ∆a photometric system (Sect. 11.3). However, CP1 stars can
be detected in the Vilnius system on the basis of CMDs including the U filter. Later on, North
et al. (1982) discussed the capabilities of a joint Vilnius and Geneva 7-colour (VILGEN) system
to detect CP stars. They improved the detection capability of ∆(V 1 − G) by using the Vilnius
Z filter (not to be confused with the Geneva Z index) instead of V 1. In addition, they defined
four peculiarity indices (PECx). Using these indices, 54% of magnetic Ap (CP2 and CP4) stars
were detected. Since then, no new corresponding investigation has been published employing
this extended system.
9
5 The variability of the ∆a index
If one looks very closely on the brightness of any arbitrary chosen star, one will find variability on
different time scales. The detection limit of the amplitude only depends on the instrumentation
and accuracy of the measurements. The Sun, as the closest star, shows variability with periods
from minutes (not visible by eye) to several years (sunspots). Variable stars are divided into
two categories: intrinsic variables, in which internal physical changes, such as pulsations or
eruptions, are the driving mechanism, and extrinsic variables, in which the light output fluctuates
due to planet transits, eclipses or stellar rotation (Percy, 2007). The further classification is
rather complex; originally it was based on a star’s light-curve characteristics, amplitude, and
periodicity (or the lack of it). Many astrophysical theories, for example pulsation, diffusion, and
evolutionary models, can be tested with variable stars (Handler, 2013).
It is also well known that the amplitude of almost all types of variability is depending on
the observed wavelength region. For example, CP stars exhibit larger amplitudes in the UV
than in the IR region (Krtička et al., 2012). Therefore, it was several times tested if and how
the variability of stars influences the 5200Å region and the ∆a index. The knowledge of this
behaviour is essential to estimate the percentage of missed positive (or negative) detections, for
example.
5.1 CP stars
Here, the published results of the analysis of the variability behaviour for 17 well established
CP stars is presented. Let us recall that the main characteristics of this group are (Sect. 6):
peculiar and often variable line strengths, quadrature of line variability with radial velocity
changes, photometric variability with the same periodicity and coincidence of extrema. Stibbs
(1950) introduced the Oblique Rotator concept of slowly rotating stars with non-coincidence of
the magnetic and rotational axes. This model reproduces the photometric variability by the
appearing and receding patches on the stellar surface similar to Sun spots.
Table 1 lists the spectral types (Skiff, 2016), dereddened (b − y) colours (Sect. 10), averaged
quadratic effective magnetic field ⟨Be⟩ (Bychkov et al., 2009), the rotational period P, the
observed ∆a range, and the mean absolute ∆a value of the sample. It was chosen to list
here the ⟨Be⟩ values by Bychkov et al. (2009) because they compiled a homogeneous sample of
measurements. For the definition of ⟨Be⟩ and its correlation with the magnetic field modulus,
for example, the reader is referred to Bychkov et al. (2003). Briefly, the effective magnetic
field Be of a star is a complex average over the stellar disc of the projection of the local vector
of magnetic intensity on the line of sight, and can be measured as the splitting of circularly
polarized components of spectral lines.
Note that the g1, g2, g3/y filters, for example, used by Hensberge et al. (1981) are slightly
different than those used by Maitzen (1976a). Therefore, there is an offset between these systems
(see Section 7 in Hensberge et al., 1981). In Sect. 10, mean absolute ∆a values from different
sources are presented. These values can be, for some objects, higher than those derived by the
references mentioned in the following. However, the aim of this analysis is, if the individual
CP stars would have been detected independent of the knowledge about the observed phase of
variability. This is the most general case possible. Or in other words, is the expected minimum
∆a value over the phase still above the detection limit (Sect. 10). In the following, the results
of the individual stars, listed in Table 1, are discussed in more detail.
HD 3980: Nesvacil et al. (2012) performed a spectrum analysis in order to determine atmospheric
parameters for Doppler imaging. They detected also horizontal inhomogeneities (stratification)
in the stellar atmosphere. However, no obvious correlation between theoretical predictions
of diffusion in CP stars and the abundance patterns could be found. The rotational period
10
Table 1: The spectral types (Skiff, 2016), dereddened (b − y) colours (Sect. 10), averaged
quadratic effective magnetic field ⟨Be⟩ (Bychkov et al., 2009), the rotational period P (references
see text), the observed ∆a range (references see text), and the mean absolute ∆a value (Sect.
10). For some objects, the mean absolute ∆a value could be higher than the given range because
there is an offset between different applied filter systems (see Section 7 in Hensberge et al., 1981).
HD HIP Spec (b − y)0 ⟨Be⟩ P ∆arange ∆a
[mag] [G] [d] [mmag] [mmag]
3980 3277 Ap SrEuCr +0.079 780(25) 3.9516 +39 . . . +49 +38
5601 4488 Ap Si −0.056 1192(100) 1.11 +52 . . . +66 +49
19712 14736 A2p CrEu −0.060 2268(225) 2.1945 +44 . . . +62 +43
25267 18673 B9p Si −0.070 241(91) 1.21 +30 . . . +50 +36
30466 22402 B9p SiCr +0.025 1716(354) 2.7795 +42 . . . +57 +50
30849 22340 Ap SrCrEu +0.166 15.865 +12 . . . +37 +30
38823 27423 A5p Sr +0.151 1509(111) 8.635 +06 . . . +16 +19
50169 32965 Ap SrCrEu −0.035 1218(70) 1.729 +65 . . . +67 +78
52847 Ap CrEuSr +0.102 +53 . . . +58 +62
53116 34049 Ap SrEu −0.046 11.978 +38 . . . +63 +50
55540 Ap CrEu −0.068 +66 . . . +71 +70
56022 34899 Ap SiSr −0.022 202(117) 0.9184 +18 . . . +26 +16
72968 42146 A0p SrCr −0.039 445(181) 11.305 +12 . . . +21 +50
81009 45999 A2p SrCrEuSi +0.086 1431(204) 33.984 +29 . . . +37 +35
111133 62376 A0p SrEuCr −0.057 807(143) 16.31 +43 . . . +73 +56
116458 65522 Ap CrSrEu −0.036 1926(273) 126.18 +14 . . . +32 +54
126515 70553 A2Vp SrSiCr −0.038 1859(360) 129.95 +33 . . . +74 +52
of 3.9516 d was deduced by Maitzen et al. (1980). They also investigated the behaviour of the
∆a index over the rotational period (+39 . . . +49 mmag).
HD 5601: Besides the classification as CP star, not many investigations were devoted to
it. Joshi et al. (2009) unsuccessfully search for rapid oscillations (periods below 25 minutes)
whereas Hensberge et al. (1981) estimated a rotational period of close to one day. The ∆a index
varied for ±7 mmag on a very high absolute level.
HD 19712: The rotational periods published by Hensberge et al. (1981, 2.1945(2) d) and
Dubath et al. (2011, 2.0422 d) are slightly different. The latter is based on the Hipparcos
photometry (Høg et al., 2000). However, Hensberge et al. (1981) noticed that one of their
apparent constant comparison star, HD 20319, seems to be a low amplitude variable. Speckle
interferometry (Horch et al., 2006) revealed that HD 20319 is a close binary system with a
separation of about 1”. The variability of this object could be due to binarity. For HD 19712,
the variations of ∆a range from +44 to +62 mmag.
HD 25267: Glagolevskij & Nazarenko (2015) presented a detailed analysis of the magnetic
field geometry for this star with its period slightly longer than one day. The rather large
variability of the ∆a index (Hensberge et al., 1981) can be possibly explained by the strong
dipole shift across the axis when the magnetic poles are located close to each other (Glagolevskij
& Nazarenko, 2015).
HD 30466: It is a double wave photometric variable CP2 star (P = 2.7795 d) with an averaged
quadratic effective magnetic field of about 1.5 kG (Bychkov et al., 2009). The measured ∆a
values over the rotational period are between +42 and +57 mmag (Maitzen, 1976b) which are
well above detection limit.
11
HD 30849: This star was often used as a “standard object” which does not show any rapid
oscillation (Balmforth et al., 2001). It is one of the coolest CP star investigated for variations
in the ∆a index. The rotational period of about 15.865 d (Hensberge et al., 1982) is well
established. The lower measured ∆a of +12 mmag (Hensberge et al., 1981, 1982) is close to the
defined detection limit.
HD 38823: Hensberge et al. (1981) found a rotational period of 8.635 d for this cool CP star
with a rather strong averaged quadratic effective magnetic field (1.5 kG, Bychkov et al., 2009).
The maximum observed ∆a index of +19 mmag (Sect. 10) is not very high, probably because of
its rather low Teff and the decreasing sensitivity of ∆a in this regime (Sect. 14.9.2). In certain
phases of the rotational cycle, HD 38823 would have been not detected photometrically.
HD 50169: There is variability of a very long time scale (at least 1200 d) and one which should
be connected to the rotational period (1.729 d) present (Heck et al., 1987). However, none of
these periods is firmly settled. Adelman et al. (1998), on the other hand, found no variations
in their own Strömgren uvby as well as Hipparcos photometry. Therefore, the characteristics of
the variability still remains unsolved. But due the well established CP classification (Adelman,
1981) and the measured magnetic field, one should expect stellar spots and rotational induced
variability. This conclusion is support be the very large ∆a value of +78 mmag (Sect. 10).
HD 52847: Up to now, no evidence for variability of this star was found (Maitzen, 1976a;
Hensberge et al., 1981). The measured range of ∆a values was interpreted as intrinsic scatter.
Maitzen (1976a) deduced ∆a = +63(4) mmag from 16 measurements whereas Hensberge et al.
(1981) presented only three measurements. Freyhammer et al. (2008) confirmed the CP nature of
HD 52847 and also found a strong mean magnetic field modulus of 4.4 kG. Based on photometric
data from the All Sky Automatic Survey (ASAS, Pojmanski, 2002) they established an upper
limit for the amplitude of variability of 4.3 mmag.
HD 53116: Hensberge et al. (1981, 1982) found a rotational period of 11.978 d with evidence
for an antiphase relation of variations for Strömgren v with uby (Vogt & Faúndez, 1979). The
presence of a strong magnetic field was only concluded on the basis of photometric data (North
& Kroll, 1989). The significant variations not only in ∆a, but also within Strömgren uvby
strongly supports that a strong magnetic field is present causing large surface spots.
HD 55540: Freyhammer et al. (2008) detected a strong mean magnetic field modulus of
12.7 kG for this object. There are no other investigations of this star available in the literature
which shows that many members of this group are still hardly investigated. Maitzen (1976a)
list ∆a = +70(5) mmag and found no signs of variability. Hensberge et al. (1981) reported
significant differences (40 mmag) in Strömgren ub on a long time base. No other investigations
in this respect are available in the literature.
HD 56022: This is a CP2 star with a rather weak averaged quadratic effective magnetic field
and a well established period of 0.9184 d. Hempelmann & Schöneich (1988) presented a detailed
analysis of its light curve in the UV region including the spot characteristics using data from
the TD-1 (Humphries et al., 1976) and ANS (Wesselius et al., 1982) satellite experiments. HD
56022 is one of the rare CP2 stars for which the “null wavelength” λ0, defined where for λ < λ0
a light curve is in counterphase to a curve λ > λ0, is between 2500 and 3300 Å (NUV region).
Hensberge et al. (1981) found no significant variations in Strömgren vby but for u. This is in line
with the results by Hempelmann & Schöneich (1988) who found the largest amplitudes in the
Far-UV with a decrease to the Near-UV. The absolute ∆a value (+16 mmag) and its variations
are very small and can be explained by the above mentioned characteristics.
HD 72968: Maitzen et al. (1978) presented extensively photometric data for this double
wave variable CP2 star with a period of 11.305 d. The listed observations (see Table 1 therein)
were used to calculate ∆a over the period, resulting in a range between +12 and +21 mmag.
This low values can be explained by the rather weak averaged quadratic effective magnetic field
(500 G, Bychkov et al., 2009) of this star. According to the detection limit deduced in Sect. 11,
12
it would be recognised as CP star candidate only in certain phases.
HD 81009: This is a very close visual binary system with a separation of the components
(∆V = 1.2 mag) between 0.1 and 0.2” (Tokovinin et al., 2015). The properties of this very
interesting system was investigated in more detail by Wade et al. (2000). They found that
HD 81009 is a highly eccentric (ϵ = 0.718), long-period (Porb = 29.3 yr) binary system composed
of two MS A-type stars. The hotter primary component was identified as the slowly rotating
(Prot = 33.984 d) magnetic CP2 star. The longitudinal magnetic field strength varies between 6.8
and 9.8 kG. The photometric variations presented by Hensberge et al. (1981) have the highest
amplitude in Strömgren v. No significant light variations were detected in Strömgren y and ∆a.
HD 111133: Again, a CP2 star with a moderate strong averaged quadratic effective magnetic
field of about 1 kG (Bychkov et al., 2009) and a rotational period of 16.31 d (Buchholz & Maitzen,
1979). The latter investigated this object in the region between 4800 and 5600Å using a spectrum
scanner. They observed ∆a ten times over the complete phase. The values ranged between +43
and +73 mmag which makes this star to one with the largest measured ∆a values.
HD 116458: This is a spectroscopic binary system containing at least one CP star with an
orbital period of 126.18 d (Ren & Fu, 2013). There was also a 2 kG strong averaged quadratic
effective magnetic field detected (Bychkov et al., 2009). It is a very unusual and peculiar object
showing strong variations of Co, Hg, Mn, and Si (Dworetsky et al., 1980). The original mean
∆a measurement was +54 mmag (Maitzen, 1976a). Measurements at two different phases by
Maitzen & Wood (1977) resulted in a relative ∆a value variation between 14 and 32 mmag,
respectively.
HD 126515: Glagolevskij (2005) modelled the magnetic field variations (P = 129.95 d) assuming
a strongly decentred magnetic dipole in order to achieve the best agreement between
the calculated and observed phase relations. He found that the field structure is determined by
a barlike dipole with a considerable distance between the monopoles. Hensberge et al. (1986)
presented a detailed investigation of the ∆a variability in correlation with the different magnetic
field components. Their most important conclusion was that magnetic intensification effects do
not control the ∆a strength.
Conclusions: Table 2 compares the observed magnitude ranges, defined as the difference
between the lowest and highest value over the rotational period, for ∆a, Strömgren uvby, and
Johnson V , respectively. In general, it can be concluded that absolute differences for ∆a are
much smaller than those for the other filters. This can be easily understood by the definition of
∆a as measuring the flux at 5200Å and at the adjacent spectral regions (Sect. 3). Therefore, it
is the difference of the amplitudes of the light variations at 5200Å and the mean of the adjacent
regions. The effect of rotation is therefore minimized.
The total sample of investigated stars includes 17 CP2 objects (Table 1). This means that
one star equals to 5.9% of the total sample. Since CP2 stars are normally slowly rotating in
comparison to their apparent normal type counterparts (North, 1984), the rotational periods (1
to 130 d) of the sample represent the whole group very well. Also the magnetic field strengths
seem to cover the range of the majority of CP2 stars (Bychkov et al., 2009). If one assumes the
detection limit of +15 mmag which can be even easily achieved for much fainter Galactic open
cluster members (Sect. 17.2.1), four stars (HD 30849, HD 38823, HD 72968, and HD 116458)
would have been missed at certain phases of their rotational periods. The lower limits for these
objects are +12, +6, +12, and +14 mmag, respectively, which is very close, but still below, the
detection limit. One also have to emphasize that most targets with already very high absolute
∆a values were chosen in order to study the possible effects of rotation.
The mean variation for all 17 stars is ±8(5) mmag with a median value of ±7 mmag, respectively.
Taking these values and looking at the absolute values in Table 1, one can assume that
the probability of a non-detection of an individual Galactic CP star due to a single observation
at the minimum phase is about 10%. This probability can be significantly lowered by conduc-
13
Table 2: The observed magnitude ranges, defined as the difference between the lowest and
highest value over the rotational period, for ∆a, Strömgren uvby, and Johnson V , if available.
For HD 111133 and HD 126515, no additional data to the ∆a ones are available.
HD ∆a u v b y V
[mmag] [mmag] [mmag] [mmag] [mmag] [mmag]
3980 10 39 85 56 21
5601 14 54 43 22
19712 18 44 34 30 19 41
25267 20 76 60 29 24 51
30466 15 61 55 31 28
30849 25 51 92 20
38823 10 70 130 24
50169 2 5 6 5 7 4
52847 5 11 11 24 6 8
53116 25 107 69 58 103 56
55540 5 45 9 4 10 17
56022 8 19
72968 9 34 25 33 35
81009 8 17 56 18 7
116458 18 86 67 63 54
tion individual observations during several nights and taking averaging values. The situation
in the LMC on the basis of the available photometry is different (Sect. 19.5). There it was
concluded that the rotationally modulated variability of the studied mCP candidates in the V
and I bands is very weak (if present at all). It is very likely that the true amplitudes are much
lower than 10 mmag, which is the limit derived from the time series analysis of the brightest
mCP candidate. If one keeps in mind that the amplitude in ∆a is much less than in the V and
I bands, the probability of a non-detection is even significantly lower than in the Milky Way.
5.2 Be/shell stars - The case of Pleione
Maitzen & Pavlovski (1987a) presented ∆a measurements of the Be/shell star HR 1180 (Pleione)
within the Pleiades. It is a B8Vpe star known to exhibit prominent long-term photometric and
spectroscopic variations with a period of about 35 yr (Tanaka et al., 2007). In the recent 70
years, Pleione showed twice a cyclic change between a Be-shell phase and a Be phase. For
example, it entered a Be-shell phase in 1972, initiated by the appearance of a wide and shallow
absorption of the Ca II K line. Then, the star developed many shell absorption lines in its
spectrum. At the same time, the star had shown a decrease in its brightness. Pleione is known
to be a speckle and a single-lined spectroscopic binary with an orbital period of 218 d as well as a
large eccentricity of ϵ > 0.7 (Nemravová et al., 2010). However, the astrophysical characteristics
of the shell(s) and the possible circumstellar disk are still a matter of debate.
Measurements of ∆a are clearly correlated with the shell and emission phase of Pleione
(Pavlovski & Maitzen, 1989). A value of +36 mmag was obtained during the shell phase in
December 1984 and then dropped almost to zero in the emission phase. The question arises how
often a Be star in its shell phase mimics a classical CP star. This has obviously an influence on
the incidence of via ∆a detected CP stars in stellar aggregates, for example. Of course, all bonafide
photometrically detected CP candidates should be confirmed via spectroscopy. However, for
14
Table 3: Open clusters observed at ESO and UTSO in 1995 (upper panel) as well as CASLEO
in 1998 and 2001 (lower panel). The ages (log t) and distance moduli (V0 − MV ) were taken
from the literature. The limit of apparent variability (Limit) is according to Sect. 5.3.1. The
errors in the final digits of the corresponding quantity are given in parentheses.
Designation NS NV NF NN JD (start) ∆t Limit log t V0 − MV
[d] [mag]
NGC 2439 C0738−315 115 3 18 4 2449816.51736 7.995 0.022 7.30 13.00(10)
NGC 2489 C0754−299 53 1 13 4 2449818.57083 34.937 0.012 8.45 10.80(10)
NGC 2567 C0816−304 34 − 17 4 2449818.61111 44.868 0.012 8.43 11.10(10)
NGC 2658 C0841−324 84 1 12 3 2449817.56597 18.026 0.018 8.50 12.90(15)
Melotte 105 C1117−632 122 − 15 2 2449816.61111 3.072 0.010 7.77 11.30(10)
NGC 3960 C1148−554 32 − 17 3 2449828.60625 59.865 0.014 8.88 11.10(20)
NGC 5281 C1343−626 16 1 55 6 2449816.78125 48.010 0.008 7.04 10.60(15)
NGC 6134 C1624−490 82 2 32 6 2449821.75069 18.003 0.010 8.84 9.80(15)
NGC 6192 C1636−432 64 − 38 6 2449822.79583 44.949 0.006 7.95 11.15(20)
NGC 6208 C1645−537 15 − 12 2 2449880.69236 2.010 0.020 9.00 10.00(15)
NGC 6396 C1734−349 48 2 18 5 2449821.88958 31.939 0.014 7.40 10.60(15)
NGC 6451 C1747−302 41 2 12 2 2449883.78125 0.988 0.010 8.30 11.65(20)
NGC 6611 C1816−138 45 2 42 5 2449849.79306 38.989 0.016 6.48 11.65(10)
NGC 6705 C1848−063 275 1 43 5 2449822.86250 59.911 0.014 8.40 11.65(20)
NGC 6756 C1906+046 33 3 38 5 2449823.90069 53.944 0.008 8.11 12.60(15)
NGC 3114 C1001−598 181 7 50 4 2451138.82296 2.979 0.022 8.48 9.60(15)
Collinder 272 C1327−610 45 2 22 1 2452144.48472 0.020 0.008 7.11 11.85(15)
Pismis 20 C1511−588 178 2 80 2 2452143.52872 1.045 0.022 6.70 12.55(20)
NGC 6204 C1642−469 268 3 55 1 2452143.63456 0.067 0.020 8.30 10.40(25)
Lyngå 14 C1651−452 60 3 70 1 2452144.58135 0.087 0.008 6.00 12.05(15)
NS: number of investigated stars; NV : number of variable objects; NF : number of frames;
NN : number of nights; ∆t: time base of the observations
more distant Galactic open clusters (Sect. 17.5) and the LMC (Sect. 19.4), the CP candidates
are quite faint, even for 8 meter class telescopes for which observing time is, in addition, quite
rare.
To investigate this issue, Pavlovski & Maitzen (1989) measured several times 40 bright and
well known Be/shell stars via ∆a photometry. From their sample, only two stars (5%) show a
significant positive ∆a value: HD 174638 (+36 mmag, β Lyr) and HD 193237 (+25 mmag, P
Cyg). Both objects are quite outstanding and well investigated. Such objects could be easily
sorted out via CMDs, for example, and should not be confused with CP stars, at all. Although
HD 193237 is classified as supernova, there are strong indications that this object might have
undergone a superoutburst typical of luminous blue variables (Chu et al., 2004). This shows the
potential of ∆a photometry to detect such objects which is especially important for studying
star clusters of the Milky Way and extragalactic systems.
Finally, Pavlovski & Maitzen (1989) concluded from their statistical analysis that the contamination
of CP2/CP4 stars by Be stars with positive ∆a values is practically negligible,
especially if one considers the colour (or Teff) range where CP2/CP4 stars are expected. Furthermore,
they found that the behaviour of Pleione during its shell phase seems to be a rare
phenomenon among Be/shell stars.
5.3 Variable star detection via ∆a photometry
The detection of variable members of open clusters is very important since these objects have
fairly well known astrophysical parameters, such as luminosity and effective temperature. Several
theories (e.g. pulsational and evolutionary models) can be tested with these variable stars.
15
Table 4: Photometric data for the Johnson UBV system taken from WEBDA for the identified
variable stars; the mean reddening values for the open clusters are according to the literature.
The lower panel includes the four variable objects which are most probably not members of
the corresponding cluster. The objects are numbered according to WEBDA or to the internal
numbering system (marked with asterisks).
Name No. E(B − V ) V B − V U − B
NGC 2439 128 0.37 14.72 0.33 0.22
239 14.84 0.63 0.41
741 15.91 1.61
NGC 2489 28 0.40 15.46 0.93 0.21
NGC 2658 56∗
0.44 16.73 0.64
NGC 3114 14∗
0.07 15.51 0.75
143∗
15.83 0.64
193∗
15.70 0.74
233∗
16.29 0.70
272∗
16.17 0.49
273∗
15.86 0.96
274∗
10.19 0.13
Cr 272 1287 0.45 18.43 1.27
1297 14.21 0.57
NGC 5281 1435 0.26 13.47 0.40
Pismis 20 28 1.25 16.04 1.17
NGC 6134 42 0.36 12.40 0.56 0.49
662 15.14 0.50
NGC 6204 92∗
0.45 16.17 1.49
150∗
14.80 1.10
360∗
14.99 1.02
Lyngå 14 115 1.48 14.99 1.38
150 14.78 1.21
NGC 6396 1 0.97 9.79 1.82 −0.06
NGC 6451 199 0.70 14.06 0.62
716 14.46 0.71
NGC 6611 198 0.85 13.21 0.60 −0.06
343 1.16 11.72 0.87 −0.17
NGC 6705 770 0.43 13.72 0.50 0.42
NGC 6756 21 0.70 14.44 1.11
24 14.50 1.11
Pismis 20 27 ≈0 15.43 0.03
Lyngå 14 101 ≈0 14.39 0.62
NGC 6396 20 high 10.62 2.44 2.63
NGC 6756 40 ≈0 15.01 −0.01
In the literature, a huge amount of papers dedicated to the search for new variable stars
in open clusters can be found. In general, two different kinds of surveys are conducted: 1)
the search for special types of variables (Viskum et al., 1997) or 2) selected open clusters are
searched for all kinds of variable objects (Kafka & Honeycutt, 2003).
The search for new variable stars in Galactic open clusters is a serendipitous result from
CCD ∆a photometry (Sect. 17.3). The observations span widely different time intervals (0.02
to 60 d) yielding different possibilities for detecting the whole set of variations. It has to be
emphasized that these observations are not optimized for the detection of variable stars but are
able to find even very low amplitude variables (the typical detection limit reached is between 6
and 22 mmag). It is therefore a very important by-product or spin-off from ∆a photometry.
16
0
5
10
15
20 NGC 2489
0
10
20
30
40
50 NGC 6134
0
4
8
12
16
20
24
NGC 6451
0
5
10
15
20
25
30 NGC 2439
0
2
4
6
8
10 NGC 2567
0
10
20
30 NGC 6192
0
25
50
75
100 NGC 6705
0
15
30
45
60 NGC 3114
0
4
8
12
16
20 NGC 2658
NumberofStars
0
20
40
60
80 NGC 6204
0
4
8
12 NGC 6756
0
2
4
6
8
10 NGC 6611
0
2
4
6
8 NGC 3960
0
1
2
3 NGC 6208
0
5
10
15
20
25 Lyngå 14
0
5
10
15
20 Cr 272
0 4 8 12 16 20 24 28
0
2
4
6
8 NGC 5281
0 4 8 12 16 20 24 28
0
4
8
12 NGC 6396
Three Sigma [mmag]
0 4 8 12 16 20 24 28
0
10
20
30
40
50 Mel 105
0 20 40 60 80 100
0
15
30
45
60 Pismis 20
Figure 3: Histograms of the three sigma standard deviations of all mean photometric values for
the programme clusters; arrows indicate the bona-fide variable stars detected.
5.3.1 Temporal analysis and results
The temporal analysis of the used photometric data is especially sophisticated since the overall
time bases range from 0.020 to 60 days with 12 to 80 data points per individual cluster (Table 3).
The smallest time resolution is about one minute with typically six frames within 30 minutes. As
a consequence of the points discussed in the following, no individual light curves are presented.
A classical time series analysis such as a Fourier technique (Paunzen & Vanmunster, 2016)
cannot be performed since it is not optimized for sparse data sets with widely different time
bases. The following approach was used to get a statistically solid limit for variability.
Since only a limited amount of data is available, all observations were added and analysed
together. For each frame, a “standard mean magnitude” was calculated as the weighted mean
photometric value (the weights are the measurement errors according to the PSF reduction
technique) of all objects (variable and non-variable). The mean atmospheric extinction within
the corresponding 700 Å decreases slightly with λ and may vary during the time of the observations
(Schuster & Parraro, 2001). Furthermore, the quantum efficiency of CCD detectors
increases towards the red region. Therefore, one is confronted with different zero points for the
different standard mean magnitudes. The light curve of an “overall standard star” was used as
comparison in the further analysis.
As a final step, differential light curves of each individual object in comparison to the “overall
standard star” were generated. For all differential light curves, a mean magnitude and its
standard deviation were calculated. An object was defined as variable if
• its standard deviation from the mean exceeds nine times the overall standard deviation of
the cluster
• at least three data points exceed three times its standard deviation.
17
-0.5 0 0.5 1 1.5
(B-V)
0
-6
-4
-2
0
2
4
6
8
Mv
γ Dor
δ Sct
Cephβ
SPB
Cepheids
RR Lyrae
Supergiants
Irregular
Figure 4: The HRD of the variable objects with the parameters listed in Table 4. The ZAMS
was taken from Schmidt-Kaler (1982). The areas of different variable groups are indicated.
The first term is only the formulation of the statistical significance whereas the second guarantees
that bad measurements or possible misidentifications do not affect the conclusions. The mean
values are between 6 and 22 mmag (Table 3). As a test, a phase dispersion minimization analysis
(Stellingwerf, 1978) was performed yielding the same statistical significance of variability. But
the very unfavourable spectral window of the data sets prevents a definite conclusion about the
true periods.
Figure 3 shows the histograms of the three sigma standard deviations of all mean photometric
values of the observed cluster stars. The plotted standard deviations were normalized according
to the errors of the photon noise. The influence of the number of data points on the detection
limit is clearly visible (e.g. NGC 5281). No correlation was found between the amount of
detected variable objects and the value of the detection limit.
5.3.2 Individual variables and Conclusions
Table 4 lists the 35 bona-fide variable objects found in 15 open clusters. The photometric data for
the Johnson UBV system were taken from WEBDA (accessible via http://webda.physics.muni.cz).
Figure 4 shows the HRD of these objects with the parameters listed in Table 4. The ZAMS is
taken from Schmidt-Kaler (1982). One is able to conclude from Table 4 and Fig. 4 that the
following objects are not members of the corresponding open clusters because with the given
(B − V ) colour and reddening, they would lie significantly below the ZAMS (Fig. 4): Pismis
20 # 27, Lyngå 14 # 101 and NGC 6756 # 40. However, with a reddening close to zero, they
are very close to the ZAMS indicating that these objects are foreground stars. NGC 6396 # 20
18
seems to be a highly reddened background star. All other objects are probably members of the
corresponding clusters; although no further membership information was found in the literature.
One has to emphasize that the errors of (B − V ) are of the order of 0.05 to 0.3 mag depending
on the type of measurement technique (photographic, photoelectric or CCD).
The literature was searched if variable objects have been confirmed for the investigated
clusters. Rasmussen et al. (2002), for example, identified the variable stars in NGC 6134 (Table
4) and concluded that these are indeed known δ Scuti type objects with the possibility of a γ
Doradus nature. Since the detection limit of variability for NGC 6134 is defined as 10 mmag,
one can be confident that the employed method is valid for the given data sets.
Another important point is the type of variability. In Fig. 4, the position of known variable
star groups have been indicated. Most of the objects seem to lie within the classical instability
strip. Another large group is located within the area of the irregular variables (e.g. T
Tauri objects). However, for an unambiguous conclusion about the true nature of the detected
variability, follow-up observations, especially spectroscopy, are needed.
None of the objects with a peculiar ∆a value shows evidence of variability which is in
line with the conclusions listed in Section 5.1. This is an independent support that rotational
induced variability of CP stars does not significantly influences the detection probability of ∆a
photometry.
The results of this investigation are another impressive example of how ∆a photometric
observations produce very important spin-off contributions for a completely different research
field.
6 Chemically Peculiar stars of the upper main sequence
The ∆a photometric was designed to detect objects which exhibit a 5200Å flux depression,
namely the chemically peculiar (CP) stars (Sect. 2). However, later it turned out that also
several other objects of all spectral types and luminosity classes have peculiar features in this
spectral region. Here, an overview of the different CP stars, including the group of λ Bootis
stars are given.
The CP stars of the upper MS have been targets for astrophysical studies since the discovery
of these objects by the American astronomer Antonia Maury (1897). Most of this early research
was devoted to the detection of peculiar features in their spectra and photometric behaviour.
The main characteristics of the classical CP stars are: peculiar and often variable line strengths,
quadrature of line variability with radial velocity changes, photometric variability with the
same periodicity and coincidence of extrema. Slow rotation was inferred from the sharpness of
spectral lines. Overabundances of several orders of magnitude compared to the Sun were derived
for Silicon, Chromium, Strontium, and Europium, and for other heavy elements.
Babcock (1947) discovered a global dipolar magnetic field in the star 78 Virginis followed
by a catalogue of similar stars (Babcock, 1958) in which also the variability of the field strength
in many CP stars – including even a reversal of magnetic polarity – was discovered. Stibbs
(1950) introduced the Oblique Rotator concept of slowly rotating stars with non-coincidence
of the magnetic and rotational axes. This model reproduces variability and reversals of the
magnetic field strength. Due to the chemical abundance concentrations at the magnetic poles
also spectral and the related photometric variabilities are easily understood, as well as radial
velocity variations of the appearing and receding patches on the stellar surface.
Preston (1974) divided the CP stars into the following groups:
• CP1: Am/Fm stars without a strong global magnetic field; weak lines of Ca ii and Sc ii,
otherwise strong overabundances;
19
• CP2: “classical” CP stars with strong magnetic fields, also known as the magnetic CP or
mCP stars;
• CP3: HgMn stars, basically non-magnetic;
• CP4: He-weak stars, some of these objects show a detectable magnetic field.
The incidence of CP stars among all MS objects of the same spectral types can reach up to 15%
(Netopil, 2013). Now, some more detail are given for these groups.
CP1 stars: The Am/Fm stars (CP1) are preferably found within close binary systems. The
main characteristics of this group are the lack of magnetic fields, the apparent underabundance
of calcium and scandium compared to the Sun, overabundances of Fe-peak elements, and very
low rotational velocities. Almost all CP1 stars seem to be rather evolved with ages above 400
Myr (Künzli & North, 1998).
The observed abundance pattern is explained by the diffusion of elements together with the
disappearance of the outer convection zone associated with the helium ionization because of
gravitional settling of helium (Michaud et al., 1983). They predict a cut-off rotational velocity
for such objects (≈ 90 km s−1), above which meridional circulation leads to a mixing in the stellar
atmosphere.
CP2 stars: This group of chemically peculiar stars was already described by Maury (1897).
The main characteristics of the classical CP2 stars are: peculiar and often variable line strengths,
quadrature of line variability with radial velocity changes, photometric variability with the same
periodicity, and coincidence of extrema. Slow rotation was inferred from the sharpness of spectral
lines. Overabundances of several orders of magnitude compared to the Sun were derived for
heavy elements such as Silicon, Chromium, Strontium, and Europium.
The strong global magnetic fields exhibit variability of the field strength including even
a reversal of magnetic polarity leading the Oblique Rotator concept of slowly rotating stars
with non-coincidence of the magnetic and rotational axes. This model produces variability and
reversals of the magnetic field strength similar to a lighthouse. Due to the chemical abundance
concentrations at the magnetic poles spectral and the related photometric variabilities are also
easily understood, as are radial velocity variations of the appearing and receding patches on the
stellar surface (Deutsch, 1970).
Kodaira (1969) was the first to notice broad-band flux depressions at 4100, 5200 and 6300Å
during his investigation of the CP2 star HD 221568. Photometrically, the main depressions
(4100 and 5200Å) of another CP2 star were later also found by Maitzen & Moffat (1972) when
they investigated the spectrum-variable HD 125248. These features were later also found to a
weaker extend for other CP stars.
CP3 stars: The HgMn (CP3) stars are generally non-magnetic, slow rotating, B-type stars
with certain chemical abundance anomalies, i.e. large excesses of (up to five orders of magnitudes)
of Mercury and Manganese, but underabundances of Helium and Aluminium. Strong
isotopic anomalies were detected for the chemical elements Calcium, Platinum, and Mercury,
with patterns changing from one star to the next (Cowley et al., 2010). More than two thirds
of the HgMn stars are known to belong to spectroscopic binaries (Hubrig & Mathys, 1995).
It seems that the majority of slowly rotating late B-type stars formed in binary systems with
certain orbital parameters become CP3 stars. There are several mechanism which play a major
role in understanding these extreme peculiarities: radiatively driven diffusion, mass loss, mixing,
light induced drift, and possible weak magnetic fields. However, there is no satisfactory model
which explains the abundance pattern, yet (Adelman et al., 2003).
CP4 stars: As defined by Preston (1974), the CP4 stars comprise helium weak, B-type
objects which often have strong and sharp lines of Gallium, Phosphorus, Titanium, Chromium,
20
and Strontium. They have strong magnetic fields (as the CP2 group) which produce elemental
surface inhomogeneities together with photometric variations. Several objects also show emission
in the optical spectral range and signs of mass loss (Wahlgren & Hubrig, 2004).
λ Bootis stars: This small group comprises non-magnetic, late B- to early F-type, Population
I, luminosity class V stars with apparently solar abundances of the light elements and
moderate to strong underabundances of Fe-peak elements (Paunzen et al., 2002a). Only a maximum
of about 2% of all objects in the relevant spectral domain are believed to be λ Bootis type
stars. Several members of the group exhibit a strong infrared excess, and a disk (Paunzen et
al., 2003b).
To explain the peculiar chemical abundances, Venn & Lambert (1990) suggested they are
caused by selective accretion of circumstellar material. One of the principal features of that
hypothesis is that the observed abundance anomalies are restricted to the stellar surface. On
the basis of this hypothesis Kamp & Paunzen (2002) developed models which describe the
interaction of the star with its local interstellar and/or circumstellar environment, whereby
different degrees of underabundance are produced by different amounts of accreted material
relative to the photospheric mass. The fact that the fraction of λ Bootis stars on the MS is
so small would then be a consequence of the low probability of a star-cloud interaction within
a limited parameter space. For example, the effects of meridional circulation dissolves any
accretion pattern a few million years after the accretion has stopped.
7 Other star groups interesting for the ∆a photometric system
Here, an overview of star groups other than the CP ones which are (possible) targets for ∆a
photometry is given.
7.1 Blue Stragglers
Originally, Blue Stragglers (BS) were discovered as members of open and globular clusters which
are hotter than the turn-off point of the corresponding cluster (Mermilliod, 1982; Simunovic &
Puzia, 2016).
Some main theories with several “flavours” were developed in order to explain the origin of
BS (Stryker, 1993; Santucci et al., 2015):
• They are in a post-MS evolutionary state which coincides with the original MS
• They are normal stars formed long after the members of open and globular clusters
• They have accreted enough interstellar material from nearby stars with large mass loss
rates or from a passing cloud to have moved up the MS
• They have acquired mass by partial or complete mass transfer from a binary companion
• They are the result of stellar collisions and coalescence
• They are undergoing quasi-homogeneous evolution in which substantial mixing which supplies
the core with hydrogen beyond the normal time of exhaustion
None of these theories was proven or rejected by observations, yet. Probably, the phenomenon
is caused not only by one of these theories but by a mixture of several ones.
Ahumada & Lapasset (2007) presented a catalogue of 1887 BS candidates in 427 open clusters.
The extensive list, their characteristics, and statistical analysis of BS in Globular clusters
is reviewed by Knigge (2015).
21
The situation about the definition of Field Blue Stragglers (FBS) is less satisfying because
it is not possible to define a “classical turn-off point” for the field population.
Baade’s original concept of a stellar “population” in the Milky Way was based on a disk (I)
and a halo (II) population. The concept later evolved into a scheme with subdivisions. In one
subdivision, the old metal-weak Population II was divided into halo (extreme) and intermediate
Population II (ip II) objects. The latter was comprised of objects that had a velocity dispersion,
a chemical composition, and a concentration towards the Galactic plane that was intermediate
between those of the halo and the disk populations. The ip II population was later proposed
in order to explain and fit both the global and the local Galactic kinematics. Robin & Crézé
(1986) estimated that about 1.5 % of all stars in the solar neighbourhood are ip II objects.
However, Strömgren (1964) and Blauuw (1965) had already pointed out that, owing to a
steady transition between the populations and also to insufficient precision in their ages, no
clear distinction between the groups could be made. Strömgren (1966) therefore proposed using
the uvbyβ photometric system, as it would be more illuminating. The δm1 index, for instance,
was used to distinguish solar from underabundant objects in the spectral-type domain between
early F and mid G.
Olsen (1979) addressed stars with +0.175 < [m1] < +0.215 mag and [c1] < +0.935 mag not
being ip II as FBS. He was left with a very high percentage of stars according to the normal
field objects (5 %). Carney & Peterson (1981) used the following criteria to find candidates of
this group:
• (B − V )0 < +0.36 mag (reddest turn-off color of globular clusters)
• Close to the MS in order to exclude FHB stars
• High proper motion and/or high radial velocity
Finally, they found only three candidates satisfying all criteria. This might already indicate the
small percentage of true FBS which is not in line with the result of Olsen (1979).
Andrievsky et al. (1995, 1996) derived abundances for 18 stars of the list from Olsen (1980).
They found mildly underabundances and rather low radial velocities for their sample. The mean
value of the iron abundances was derived as [Fe/H] = −0.31(13) dex whereas carbon is slightly
enhanced [C/Fe] = +0.32 dex. The stellar parameters and the location in the HRD supported
rather old ages for these stars (about 4 Gyr).
It has been shown by spectroscopic and ∆a observations that up to 60% of the BS in open
clusters show peculiarities of some kind. However, the absolute percentage is quite diverging
between different references (Abt, 1985; Schönberner et al., 2001). In Sect. 17.4, the observations
and their interpretations are described in more detail.
7.2 Herbig Ae/Be stars
Herbig (1960) proposed a new group of Pre-Main-Sequence (PMS) stars as higher mass counterparts
of the T Tauri stars (Grankin, 2016) later known as Herbig Ae/Be stars. These intermediate
mass (2 − 8M⊙) stars are believed to be still in their radiative phase of contraction onto
the MS. He defined the following criteria for a Herbig Ae/Be star:
• Spectral class earlier than F0
• Strong emission lines, particular those of the Balmer lines
• A location within the boundaries of a molecular cloud
• The star illuminates a nebula
22
It is obvious that the last two criteria ensure the PMS nature of these stars since the remnants
of the protostellar cloud is still detectable. On this base, Finkenzeller & Mundt (1984) found
nearly 60 stars fulfilling the classical criteria. Additional observations in the UV and IR region
revealed further characteristics (Malfait et al., 1998) which lead to two new criteria added to
the classical ones:
• Broad-lined, luminosity class V, IV and III, B- to F-type stars which show or have shown
in the past emission-lines
• The presence of an IR excess due to circumstellar dust
The first criterion should allow to distinguish Herbig Ae/Be stars from evolved stars such as
post-AGB stars which have strong IR excesses due to stellar winds.
Hipparcos photometry (van den Ancker et al., 1998) revealed variations for almost all known
Herbig Ae/Be stars on the time scales of hours to weeks with highly variable amplitudes. Later
on, also stellar magnetic fields and surface spots as for the CP2/4 stars (Sect. 6) were detected
(Järvinen et al., 2016).
Miroshnichenko et al. (1999) presented classification resolution spectroscopic observations of
9 Herbig Ae/Be candidate stars. The found highly variable Fe ii and Ti ii emission lines in the
region between 4900Å and 5500Å. Those emission lines influence all three “classical” (g1g2y)
filters. However, they seem to be more concentrated and stronger in the g2 filter which causes
their detection within the ∆a photometric system.
7.3 Be/shell stars
These stars are defined as non-supergiant B-type which have shown hydrogen emission in their
spectra at least once. Phenomenologically, shell stars are stars with strongly rotationally broadened
photospheric lines and additional narrow absorption lines. Some of the latter appear
roughly at the centre of the photospheric instance of the same atomic transition while those of
low excitation do not have a photospheric counterpart (Cowley et al., 2015).
Studies of Be stars in each of the accessible wavelength domains have revealed unique information:
UV studies have emphasized the duality between Balmer emission line and the star’s
radiative wind flux. X-ray analysis have drawn a distinction between the high energy flux
emitted from interacting binaries and most isolated Be stars (Torrejón et al., 2013).
Due to an equatorial disk produced by stellar winds, emission arises quite regularly. This
disk is believed to be formed from the material ejected from the fast rotating central star. In
addition, photometric variability on different time scales is a common phenomenon caused by
the formation of shock waves within those disks. But also non-radial pulsation and variability
due to rotation are observed (Porter & Rivinius, 2003).
The negative ∆a values found (Sect. 11.9) are probably caused by emission of Fe and Mg
lines in the spectral region from 5167 to 5197 Å (Hanuschik, 1987), which fall exactly within the
g2 filter and its bandwidth (Table 9).
7.4 B[e] stars
The B[e] phenomenon as defined by Conti (1976) is a designation for hot B-type stars whose
spectra show forbidden and permitted emission lines of neutral and singly ionised atoms and
strong infrared excess. These observed properties indicate very extended circumstellar matter
and were discovered in only a small percentage of known B-type stars. The B[e] phenomenon
nowadays incorporates not only B-type stars with forbidden emission lines in their optical spectrum,
but it also includes stars from the pre-main sequence to compact planetary nebulae and
supergiants (Lamers et al., 1998; Kraus et al., 2015).
23
5000 5200 5400 5600 5800
0.0
0.5
1.0
1.5
2.0
2.5
y
g
2
Flux
Wavelength [Å]
HD 45677
V380 Ori
g
1
Figure 5: The spectra of the B[e] stars HD 45677 and V380 Ori from the ELODIE library
together with the g1, g2, and g3/y filters. Because the g1 and g3/y filters are also affected by
emission lines, the usage of colours based on broad band filters is preferable.
This group attracted increasing attention in the last decade. The reasons for that are the
development of new and more efficient ground-based instruments, the availability of space-based
observations, the extension to other than the optical wavelength regions, and the development of
new models. However, the number of objects showing this phenomenon is still very limited. The
detection can be done either by time-consuming spectroscopy (search for the forbidden emission
lines) or photometry (IR-excess, for example). Both methods have their severe limitations due
to the high demand of observing time and the ambiguity of the different photometric diagrams
(Dunstall et al., 2012).
The spectra of two B[e] stars, HD 45677 and V380 Ori, were taken from the ELODIE
(Prugniel & Soubiran, 2001). Figure 5 shows the spectra of these B[e] stars together with
the g1, g2, and g3/y filters. It is clearly visible that the g2 filter measures several forbidden
Fe ii emission lines. Notice how the absolute flux varies for these two objects. However, g1 is
significantly affected by the Hβ line which is in emission whereas within g3/y there are again
some Fe ii emission lines. It seems therefore preferable to use colours based on broad band filters
for which this effect is less pronounced.
From Fig. 5 it is obvious that B[e] stars can be detected via observations in the g2 filter.
This will be especially important for the identification of these stars in the Magellanic clouds
(Sect. 19).
24
7.5 Evolved and Population II stars
In Globular clusters several different highly evolved star groups can be found: red giant and
sub-giant branches (RGBs and SGBs) as well as blue horizontal-branch objects (BHBs and HB).
These groups are defined and characterized as
• (B)HB: horizontal-branch stars in Galactic globular clusters are old, low-initial mass (0.7
– 0.9 M⊙) stars currently burning helium in their core. Owing to their complexity, some
aspects of the formation and internal structure of HB stars have been a matter of debate for
decades (Catelan, 2009). For instance, the blue extension of the HB varies among clusters,
a fact partly associated with the metallicity but not entirely explained by it. A number of
second parameters in addition to metallicity, such as stellar rotation, cluster concentration,
presence of super-oxygen-poor stars, cluster mass, environment of formation, and the
cluster age have been suggested to provide an explanation for this behaviour, but none
has proven completely adequate in describing the complex observational picture.
• SGB: The subgiant branch is a stage in the evolution of low to intermediate mass stars
after the MS until the RGB. As the fraction of hydrogen remaining in the core of a MS star
decreases, the core temperature increases and so the rate of fusion increases. This causes
stars to evolve slowly to high luminosities as they age and broadens the MS band in the
HRD. Once a MS star ceases to fuse hydrogen in its core, the core begins to gravitationally
collapse (Goudfrooij et al., 2015). This causes it to increase in temperature and hydrogen
fuses in a shell outside the core, which provides more energy than core hydrogen burning.
Low- and intermediate-mass stars expand and cool down until at about 5000 K they begin
to increase in luminosity in the RGB. The shape and time scale of the SGB phase varies
for stars of different masses, due to differences in the internal structure. The SGB lasts
for about 12 Myr for a star of 3 M⊙, and only 1 Myr for a star of 6 M⊙. Therefore, this
evolutionary phase is so short that the chance of observing objects in this phase is very
small. This led to the so-called Hertzsprung gap in the CMD of intermediate-age stellar
systems (Adamczak & Lambert, 2014).
• RGB: The red-giant branch is the portion of the giant branch before helium ignition. It
is a stage of stellar evolution that follows the MS and SGB for low- to intermediate-mass
stars. RGB stars have an inert He-core surrounded by a shell of hydrogen fusing via the
CNO cycle (Cohen et al., 2015). Along the RGB, the He-core mass does monotonically
increase due to the conversion of H into He produced by the H-burning shell. Due to the
release of gravitational energy by slow contraction, it tends to heat up. This favours the
persistence of an isothermal core temperature profile. At the same time, with increasing
densities, the neutrino production in the central regions of the core becomes progressively
more efficient. This favours cooling of the innermost layers of the core. This leads to a
feedback of the H-burning shell with the temperature and density of the He-core which
then alters the stellar surface luminosity. The overall metallicity, i.e. C, N, and O, controls
this mechanism which is the so-called He-core mass-luminosity relation for RGB stars. The
RGB phase ends when the off-centre maximum temperature reaches the value to ignite
He-burning via triple-α captures and is called He-Flash.
Mainly on the basis of Hubble Space Telescope (HST) observations, it was found that several
globular clusters have not only at least two MS, which are explained by a different helium content
(Piotto et al., 2007), but also simultaneously different HBs, RGBs, and SGBs (Grundahl et al.,
1998; Piotto et al., 2012).
There are different “jumps” in the BHB distribution as well as peculiar HB extensions, like
the blue-hook (Brown et al., 2001). However, the cause of these phenomena is still not clear,
25
but it is probable connected to the complex star formation history of the individual clusters
(Valcarce et al., 2012).
Gratton et al. (2012) gave an excellent overview of all types of chemical peculiarities for
members of globular clusters. Not only variations in lighter elements (Li, C, N, O, Na, Al, and
Mg), but also of CN and CH were detected. Possible correlations and relations of the individual
abundances for different elements were widely analysed in the context of stellar formation and
evolution. In general terms, one has to distinguish, as for Population I type objects, between
intrinsic and photospheric peculiarities.
An intriguing phenomenon was first reported by Behr et al. (1999) who found large deviations
in element abundances from the expected cluster metallicity for BHB stars in the globular cluster
NGC 6205. For example, Fe was found to be a factor of three enhanced compared to the solar
value, or about 100 times the mean cluster iron abundance. Such atmospheric effects are well
known and studied for the classical CP stars of the upper MS (Sect. 6). Furthermore, in Sect.
14 it was concluded that Fe is mainly responsible for producing a positive ∆a index, but also Cr
and Si are contributors at least for lower effective temperatures. Later on, Khalack et al. (2010)
found clear evidence for vertical stratification of Fe in atmospheres of BHBs. In addition, it was
reported that BHB stars with Teff ≥ 11 500 K have lower rotational velocities than their cooler
counterparts (Behr, 2003b) suggesting that the atmospheres of such stars are stable enough to
have atomic diffusion. The models by Quievy et al. (2009) show that He sinks in stars with low
rotational velocities, which leads to the disappearance of the superficial He convection zone. This
then opens the door for atomic diffusion to play a role. The atmospheric models of Hui-Bon-Hoa
et al. (2000) showed that the observed photometric jumps and gaps for hot BHB stars can be
explained by elemental diffusion in their atmosphere. These models calculate self-consistently
the structure of the atmosphere while taking into account the stratification predicted by diffusion
(assuming equilibrium). They confirm that vertical stratification of the elements can strongly
modify the structure of the atmospheres of BHB stars (LeBlanc et al., 2009). Such structural
changes for the atmosphere lead to the photometric anomalies discussed above. However, the
search for strong magnetic fields in HB stars was not successful (Elkin, 1995).
In overall it can be concluded that these slow-rotating BHB stars are the Population II type
counterparts of the classical CP stars (Sect. 6).
Inspecting the spectral region around 5200Å, where the g2 filter is centred, for RGB, G- and
K-type MS stars (Gray & Corbally, 2009), strong Mg i (5167Å, 5173Å, and 5183Å) and MgH
features are found (Sect. 8.2). This was also the reason why the Vilnius Z filter has been centred
in this region (Sect. 4). Those features strongly vary with the evolutionary status, i.e. for dwarfs
and giants. Johnson et al. (2005) derived magnesium abundances for more than 100 RGB stars
in each of the Galactic globular clusters NGC 5272 and NGC 6205. They found a wide spread
of magnesium abundances within the individual aggregates (about 0.7 dex) and some significant
outliers. So it might be possible to detect strongly deviating elemental abundances of Mg and
luminosity effects with ∆a photometry.
8 An inspection of the wavelength region from 4900 to 5700Å
The original narrow-band ∆a photometric system with its three filters covers approximately the
wavelength region from 4900 to 5700Å. Let us recall here the characteristics of the three filters
(Maitzen & Vogt, 1983): g1 (λc = 5010 Å, FWHM = 130 Å), g2 (5215, 130) and g3/y (5485, 230).
These three filters were always used in two ways/combinations (Sect. 3): a versus (g1 − y)
and y versus (g1 − y) where a = g2 − g1+y
2 . So, in principle, any other colour combination, also
with those from other photometric filter systems, can be applied to study any possible astronomical
objects. Normally, all individual g1, g2, g3/y observations, especially those performed
26
Figure 6: The first notification of significant flux depressions at 4200 Å (2.35 µ−1), 5300 Å
(1.90 µ−1), and 6300 Å (1.55 µ−1) in the spectrum of HD 221568 by Kodaira (1969).
via the CCD technology (Sects. 17.3, 18, and 19), are archived and available for any follow-up
investigation.
In the following, a quantitative overview of the corresponding wavelength region for stars,
quasars, and galaxies is given. For this, spectral libraries are used to show the characteristics
of several different peculiar and “normal” type objects. Furthermore, a summary of the current
knowledge about the 5200Å flux depression is included.
8.1 The 5200Å flux depression
As stated before (Sect. 2), the ∆a photometric system was primarily intended to investigate
the 5200Å flux depression found for CP stars. Within this work, a spectrophotometric investigation
of this region (Sect. 9) and an approach to derive synthetic ∆a values (Sect. 14) are
presented. In these Sections, many details about the characteristics of this flux depression are
listed. Furthermore, several correlations of the depth with astrophysical parameters and the
elemental compositions for different star groups are listed. The interested reader is referred to
these Sections. Here, a short summary of the 5200Å flux depression of CP stars is given.
Kodaira (1969) was the first who noticed significant flux depressions at 4200 Å (2.35 µ−1),
5300 Å (1.90 µ−1), and 6300 Å (1.55 µ−1) in the spectrum of HD 221568 (Fig. 6). The latter is
a magnetic CP2 star with an extremely large amplitude (0.2 mag in B − V ) rotational induced
variability and a period of about 160 d (Ste�pień & Muthsam, 1987). The flux distribution varies
strongly between the red and blue phases. Unfortunately, no ∆a value for it was measured,
yet. For some time, the central wavelength of this depression was believed to be at 5300 Å
(Adelman, 1975) because it is a very broad feature investigated with rather low resolution
27
spectrophotometry only. Maitzen (1976a) was the first who presented evidence that the centre
of the two bluer depressions are actually very close to 4100 and 5200 Å, respectively. Jamar (1977,
1978) detected and investigated similar features in the ultraviolet region at 1400 Å, 1750 Å, and
2750 Å showing that flux depressions are not a phenomenon restricted to the optical.
Several attempts have been made to explain the origin of this feature. Adelman & Wolken
(1976) investigated bound-free discontinuities, Jamar et al. (1978) proposed autoionisation transitions
of Si ii, whereas enhanced line absorption was discussed by Maitzen (1976a) and Maitzen
& Muthsam (1980). The latter presented a comparison of synthesised flux distributions and
observed spectrophotometry. The first attempt in this direction was made by Leckrone et al.
(1974). From their synthetic spectra, Maitzen & Muthsam (1980) recovered a narrow and deep
feature at about 5175 Å and a broad component centred at about 5275 Å. They were not able
to reproduce the flux depression for effective temperatures higher than 8000 K. More recently,
Adelman et al. (1995) have used ATLAS9 model atmospheres (Kurucz, 1993) with enhanced
metallicity (i.e. a solar element abundance distribution where all elements heavier than He had
been scaled by +0.5 or +1.0 dex) and concluded that at least part of the 5200 Å feature in
magnetic CP stars may be due to differential line blanketing. In a follow-up work, Adelman &
Rayle (2000) have extended this study to a larger group of stars and found that solar composition
models may successfully predict the flux distribution of normal and many CP3 (HgMn)
stars, while they fail to do so for a number of CP2 stars, i.e. the group of stars showing the
largest flux depression in the 5200 Å region and thus the largest magnitudes in ∆a.
Khan & Shulyak (2007) found that the majority of the tested chemical elements (within the
limits of abundance values considered) produce less than 1% variations in the model atmosphere
temperature profile. These elements are He, C, N, O, Mg (deficient), Ca, Sr, Eu, and Hg. Several
elements produced moderate changes on the model atmosphere structure (1 – 3%) and the
energy distribution. These elements were Mn, Ni, and Mg (enhanced). The group of elements
which produced large changes in the model atmosphere structure (more than 3%) and energy
distribution consisted of Si, Cr, Fe and scaled abundance patterns.
They found that Fe is the principal contributor into the 5200Å depression for the range of
Teff between 20000 and 8000 K, while Cr and Si are important primarily for low Teff.
8.2 Features of Stars across the HRD
First, the method of spectral classification was developed and used in the second half of the
nineteenth century. Thanks to the invention of photographic plates and the long standing
knowledge of prism, for example, it became a powerful tool quite parallel to photometry. Even
a brief history of its development would fill many pages. The interested reader is referred to the
book by Hearnshaw (2014) who gave an excellent overview about two centuries of astronomical
spectroscopy.
A whole zoo of different systems have been developed from which only the Harvard and
Yerkes systems survived. The latter is associated with the work of Morgan et al. (1943) who
used a prismatic spectrograph covering the region from 3900 to 4900 Å with a dispersion of
115 Å mm−1 at Hγ. During the decades, new developments (for example, grating spectrographs
and the CCD technology) made it necessary to check and revise the original systems. Again,
the interested reader is referred to two excellent books by Jaschek & Jaschek (1990) and Gray
& Corbally (2009) who listed all available information about the spectral classification in great
depth.
It has to be emphasized that the wavelength region for the classical spectral classification is
between 3900 and 4900 Å, respectively. The filters of the ∆a photometric system are actually
redward of this region. This means that the spectral features there are not used for the classification
process. The only exceptions are molecular absorption bands for very cool type stars.
28
5000 5200 5400 5600 5800
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Flux
Wavelength [Å]
B2Ia ve
B2III var
B5V
B8Iae
B9p SiCrEu
B9V
Figure 7: Spectra for selected B-type stars from the MILES library together with the g1, g2, g3/y
filter curves.
29
5000 5200 5400 5600 5800
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Flux
Wavelength [Å]
A0V
A0Ib
LB
Ap
Am
A7V
Figure 8: Spectra for selected A-type stars from the MILES library together with the g1, g2, g3/y
filter curves.
30
5000 5200 5400 5600 5800
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Flux
Wavelength [Å]
F0V
F0p
Fm
F2V w
F5Ib
F7V
Figure 9: Spectra for selected F-type stars from the MILES library together with the g1, g2, g3/y
filter curves.
31
5000 5200 5400 5600 5800
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
Flux
Wavelength [Å]
G0V
G0V we
G3Ib-II CNe
G5V
G8p
G0Ia
Figure 10: Spectra for selected G-type stars from the MILES library together with the g1, g2, g3/y
filter curves.
32
5000 5200 5400 5600 5800
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
K7V
K4Iab
K3II/III CNv
Flux
Wavelength [Å]
K0V
K0III CNpvar
K2II vw
Figure 11: Spectra for selected K-type stars from the MILES library together with the g1, g2, g3/y
filter curves.
33
5000 5200 5400 5600 5800
0
1
2
3
4
5
6
M1Ia/ab
M6III var
M6e
M5V
Flux
Wavelength [Å]
M1V
M2Iab pe
Figure 12: Spectra for selected M-type stars from the MILES library together with the
g1, g2, g3/y filter curves.
34
Those features are, for example, C2 (5164Å), CN (5560Å), MgH (5211Å), TiO (5167, 5448, and
5497Å), and ZrO (5305 and 5379Å).
In the following, the corresponding spectral region is shown for B- to M-type stars of all
types. This is just a short excerpt of many peculiar objects over the whole HRD and by far not
complete. It should show only a cross section of already investigated and potential targets for
the ∆a photometric system.
The spectra were taken from the MILES library which consists of 985 stars spanning a
large range in atmospheric parameters and spectral types (Falcón-Barroso et al., 2011). The
spectra were obtained at the 2.5 m Isaac Newton Telescope at the Observatorio del Roque de
los Muchachos and cover the range from 3525 to 7500Å with an originally estimated spectral
resolution of 2.3Å (full-width half maximum, FWHM). A homogenized compilation of the stellar
atmospheric parameters (Teff, log g, and [Fe/H]) for the stars of this library was presented in
Cenarro et al. (2007). The stellar library is also the basis for our empirical models for stellar
population synthesis (Vazdekis et al., 2010). Both, the stellar library and models can be easily
accessed and manipulated through this website: http://miles.iac.es. All spectra are calibrated
in absolute flux unites and can be directly compared.
Figures 7 to 12 show the corresponding spectra for B- to M-type stars. The individual
spectra were only shifted in the flux unit to present them in a convenient way. Each figure also
includes the g1, g2, g3/y filter curves as a guidance of the covered corresponding spectral regions.
In the following, the different spectral regions are discussed in more detail.
B-type stars (Fig. 7): There are strong variations, especially for the non-MS objects in g1,
visible. Also strong lines for the B2Iave object in the red wing of g3/y are evident. On the other
hand, the flux depression at 5200Å is clearly visible for the B9p SiCrEu (CP2) star whereas no
emission lines for any star are present.
A-type stars (Fig. 8): There is a significant increase of the metallic lines spectrum from
A0 to A7 for the complete spectral region. Also the metallic lines of the A0Ib supergiant are
stronger than for the A0V star, although their v sin i values are comparable. This probably also
causes that some supergiants have positive ∆a values. The metal-weakness of the λ Bootis and
the strong overabundances of the Am (CP1) and Ap (CP2) stars are evident. Other than the
Am star, the Ap object shows the 5200Å flux depression.
F-type stars (Fig. 9): All spectra are very similar in the overall metallic-line strength and
the spectral flux distribution. Only the Fp object shows slightly stronger metal-lines compared
to the corresponding F0V standard star. From the point of view of the ∆a photometric system,
the F-type stars are the least interesting ones to follow in forthcoming projects.
G-type stars (Fig. 10): The first remarkable feature is the change of the flux distribution for
the G8p and G0Ia objects as the g3/y magnitude becomes significant brighter. Such a behaviour
should result in a blueing of the colour. The G0Vwe star and G3Ib-II CNe supergiant clearly
show much weaker metallic-line spectra than the corresponding standard MS stars. These star
groups, especially the weak-lined one, should be easily detectable via ∆a photometry.
K-type stars (Fig. 11): For this spectral region, also a flux depression within the g1 filter
is visible. However, contrary to the CP stars, it is most significant for apparent normal type
MS objects. As for the G-type objects, the weak-lined group seems to by quite outstanding
among the sample. On the other hand, the K4Iab supergiant shows stronger lines as its MS
counterparts. Again, this behaviour is very similar to the hotter supergiants.
M-type stars (Fig. 12): The objects up to a spectral type of M5 (Teff ≈ 3000 K) have quite
a homogeneous flux distribution over the complete spectral region. For cooler temperatures,
the bandheads become very steep with a significant strong flux distribution. This characteristic
might be used to search for M-type stars with large radial velocities. Such shifts should alter
not only the colours but also the a index.
As a summary, it can be said that the additional capabilities of ∆a photometric system are
35
Figure 13: A very high signal-to-noise ratio composite spectrum of the rest-frame ultraviolet
and optical region of a high luminosity quasar together with the identified features (Francis et
al., 1991).
manifold over the complete spectral type range besides maybe for the F-type stars for which
no exceptional outliers were found. Some guidelines for new projects and/or a re-analysis of
archival data are listed in Section 22.
8.3 Features of Quasars
Other than stars, no dedicated observing programme to find and study quasars in the 5200Å
has been conducted, yet. A quasar (also denoted as quasi-stellar object or QSO) is an active
galactic nucleus of very high luminosity. It consists of a supermassive black hole surrounded by
an orbiting accretion disk of gas. As gas in the accretion disk falls toward the black hole, energy
is released in the form of electromagnetic radiation (Liu et al., 2016). Interesting enough, also
optical/ultraviolet variability of these objects has been discovered to be correlated with other
quasar properties, such as luminosity, black hole mass and rest-frame wavelength. To date,
about 450 000 quasars over a very broad range of distances (corresponding to redshifts of up to
7) are catalogued. However, they are faint in the optical region with 3C 273 being the brightest
Quasar known with V = 12.0 mag.
The most prominent emission type features of quasars can be found in the UV region as
shown in Figure 13. The shown spectrum is a composite of 718 individual spectra of quasars
published by Francis et al. (1991). The strongest features have equivalent widths of almost
60Å as listed in Table 5. The latter also includes the calculated redshifts z which shift the
corresponding lines to the centre of the g2 filter. The strongest features cover redshifts from
0.07 to 3.28, respectively.
Finding new Quasars can be done either by searching for the above listed features in the
optical spectral region as done by the Sloan Digital Sky Survey (Pâris et al., 2017) or by analysing
multi-band photometry (Brescia et al., 2013). Having precise photometry from the UV to the
IR region, due to the redshift, the features affect different filters to a certain amount. This
behaviour can be easily simulated. However, it is not straightforward to distinguish redshifted
Quasars from other objects. Brescia et al. (2013) developed a machine learning method that can
36
Table 5: The strongest identified features shown in Fig. 13 together with the equivalent width
and the redshift z shifting them in the centre of the g2 filter.
λrest Species Eqw z λrest Species Eqw z
[Å] [Å] [Å] [Å]
5007 [O iii] 15 0.04 1549 C iv 37 2.36
4861 Hβ 58 0.07 1400 Si iv/O iv] 10 2.71
4340 Hδ 10 0.20 1240 N v 52 3.19
2798 Mg ii 50 0.86 1216 Lyα 52 3.28
1909 C iii] 22 1.72
be used to cope with regression and classification problems on complex and massive data sets in
order to identify Quasars from photometric catalogues. They used the GALEX, SDSS, UKIDSS,
and WISE catalogues which give only 14 000 objects common in all four data bases. This is a
surprisingly low number. The more different filters are available, the better this method works.
A dedicated project searching for new Quasars using photometric observations in the g2
filter seems not efficient because already several deep all-sky survey are available. However, the
observations in the Magellanic Clouds could be used to search for Quasars (Sect. 19). The
data of the Magellanic Quasars Survey (Kozlowski et al., 2013, MSQ) are ideal to test the
method using g2 to identify Quasars. They spectroscopically confirmed 758 Quasars selected
from the third phase of the Optical Gravitational Lensing Experiment based on their optical
variability, mid-IR, and/or X-ray properties. About 50 Quasars are bright enough (I < 18 mag)
to immediately study with the available g2 data. After this pioneer study, the feasibility of
further projects can be evaluated.
8.4 Features of Galaxies
Besides stars, star clusters, and the Magellanic Clouds, galaxies should not be lost out of sight.
With the modern CCD technology and large telescopes, even distant galaxies could be observed
within the ∆a photometric system. Two interesting projects in this respect are the the Advanced
Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA, Moles et al.,
2008) and Cosmic Evolution (COSMOS, Scoville et al., 2007) survey which are described in
Section 21. The first project will observe a total area of four square degrees on the sky with
the focus to study galaxies of all types. There is one filter centred at 5220Å which perfectly
matches g2 but with a broader FWHM of 310Å. The second project is designed to probe the
formation and evolution of galaxies as a function of both cosmic time (redshift) and the local
galaxy environment. The survey covers a two square degree equatorial field with imaging by
most of the major space-based telescopes and a number of large ground based telescopes, with
many ongoing surveys. It includes the “Subaru Telescope Intermediate Band Filter” IA527
which is centred at 5259Å with a FWHM of 242Å.
Because of the availability of filters similar to g2, the spectra of various galaxy types in this
spectral region were investigated in more detail.
The spectral templates of the various galaxies types were taken from Calzetti et al. (1994)
and Kinney et al. (1996). They have a two pixel resolution of 10Å and are calibrated in absolute
fluxes. The spectral templates cover various galaxy morphological types from elliptical
to late type spiral. Starburst templates for low, E(B − V < 0.10 mag, to high, 0.61 < E(B −
V < 0.70 mag, internal extinction are also available. Several of the starburst galaxies used in
the construction of the starburst templates are classified as irregulars. Thus, although irregular
galaxies are no explicitly covered, the starburst templates can be used to cover this morpholog-
37
5000 5200 5400 5600 5800
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Flux
Wavelength [Å]
Sb
Sa
S0
Elliptical
Bulge
Figure 14: Spectral templates for bulge, elliptical, S0, Sa, and Sb galaxies (from bottom to top)
from Calzetti et al. (1994) and Kinney et al. (1996) together with the g1, g2, g3/y filter curves.
38
5000 5200 5400 5600 5800
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Flux
Wavelength [Å]
starburst with E(B-V) < 0.1
starburst with 0.25 < E(B-V) < 0.35
starburst with 0.39 < E(B-V) < 0.50
starburst with 0.51 < E(B-V) < 0.60
starburst with 0.61 < E(B-V) < 0.70
Sc
Figure 15: Spectral templates for Sc and starburst galaxies with different internal extinction
values from Calzetti et al. (1994) and Kinney et al. (1996) together with the g1, g2, g3/y filter
curves.
39
ical type. All details about how these templates were built and which individual galaxies were
used can be found in Calzetti et al. (1994) and Kinney et al. (1996).
It has to be emphasized that none of the parameters such as different metallicities, dust/gas
ratios, star forming episodes, and so on have been taking into account here. These parameters
alter the spectra of galaxies to a certain amount (Möller et al., 1997).
Figures 14 and 15 show the templates for the galaxies divided in those with and without
emission features, respectively. All conclusions drawn below are for a zero redshift. If the latter
is taken into account as non-zero, the analysis of the capability of the ∆a photometric system
becomes much more complex. One example for such an analysis of the COSMOS survey can be
found in Mobasher et al. (2007).
Bulge, elliptical, S0, Sa, and Sb galaxies (Fig. 14): The Sa and Sb spectral templates are
almost indistinguishable from each other. The bulge, elliptical, and S0 show discriminative
features in the g3/y filter. Also the overall flux distributions are slightly different. However the
Sa/Sb and bulge/elliptical/S0 galaxies can be clearly distinguished from each other by the g2
filter.
Sc and starburst galaxies (Fig. 15): When comparing the spectral region of the g2 with those
of the g1 and g3/y filters, it is clear that the classical a index will not work for these galaxies.
There are almost no changes in g2 compared to the adjacent regions visible. The emission
features [O iii] at 4959Å and 5007Å (both sampled by the g1 filter) are varying significantly for
all galaxy types. There are also several strong diversify absorption features (mainly due to Fe
and Mg) between 5380 and 5510Å (g3/y). For these types of galaxies it seems best to use g1
(preferable) or g3/y instead of g2 in order to construct an aGal index as aGal = g1 − B+V
2 , for
example.
For a zero redshift, the ∆a photometric system is able to a-priori distinguish between Sa/Sb
and bulge/elliptical/S0 galaxies on the basis of a classical a versus (g1 − y) diagram. However,
this type of diagram malfunctions to distinguish between different types of Sc and starburst
galaxies which have strong emission lines in the g1 filter. Therefore, a discrimination between
galaxies with and without emission features will not be possible. Taking into account a redshift,
the conceptual formulation becomes quite complex. Depending on the amount of the redshift,
different spectral features can be traced with the different filters. Such an analysis will require
detailed observations of a significant amount of different galaxy types at a wide range of redshift
values. Up to now, no such data sets are available.
9 Spectrophotometry of the 5200Å region for peculiar and normal
type stars
Using spectrophotometry, Kodaira (1969) was the first to notice broad-band flux depressions at
4100, 5200 and 6300Å during his investigation of the CP2 star HD 221568. Photometrically,
the main depressions (4100 and 5200Å) of another CP2 star were later also found by Maitzen
& Moffat (1972) when they investigated the spectrum-variable HD 125248.
A study was conducted to detect CP stars on the basis of spectrophotometric data for which
three different methods were employed that use the flux depression at 5200Å. In addition to the
original method, the a′ system developed by Adelman (1979) and a newly modified method were
investigated. Furthermore, the capability of these systems of finding new, previously undetected,
peculiar stars including metal-weak and emission-type objects of the upper MS was analysed .
Also, the low-mass regime was searched for the behaviour of the a indices in correlation with
the effective temperature and luminosity.
40
-0.03
0.00
0.03
0.06
0.09
0.12
a[mag]
a = -0.0074(4) + 0.035(2) (B - V)
0
N = 437
-0.03
0.00
0.03
0.06
0.09
0.12
a' = +0.0314(6) + 0.012(3) (B - V)
0
a'[mag]
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
-0.03
0.00
0.03
0.06
0.09
0.12
a' mod = +0.0266(5) + 0.027(3) (B - V)
0
(B - V)
0
[mag]
a'mod[mag]
Figure 16: Regression of 437 normal stars with reference to the different a indices.
9.1 Data and reduction
The source of spectrophotometric data is the stellar catalogue by Kharitonov et al. (1988). It
contains data for 1159 bright stars of different spectral types in the wavelength range from 3200 to
7600Å, with a spectral resolution of 50Å. Each star was observed at least three times, on different
nights. The root mean square (rms hereafter) relative error of the measurements is between 2%
and 4% per 50Å bandpass. Stars with only two-digit measurements in the wavelength region
around 5200Å were not considered in the analysis because of the statistical inaccuracy of these
measurements. Early-type supergiants were excluded because of their strong photometric and
spectroscopic variability. The remaining data of 1067 stars were used to synthesize different
peculiarity indices. The methods used to detect CP stars are designed to have magnitudes
as input. Therefore the intensity and flux values given in the catalogue were converted into
magnitudes.
One hast to be aware that there are more extensive corresponding catalogues with higher
resolutions available in the literature, for example the one by Burnashev (1985). This author, for
example, also used at that time unpublished data by Kharitonov et al. (1988), but interpolated
the data to a resolution of 25Å. However, the here used catalogue is the basis of a list of
spectrophotometric standards published by Glushneva et al. (1992). Therefore the quality of
the data is beyond any doubt. In addition, the spectral resolution is similar to that used for the
Gaia mission (Jordi et al., 2010).
Spectrophotometric observations of classical CP stars were published before, for example by
Maitzen & Muthsam (1980) and Adelman et al. (1989). However, all these analyses concentrated
either on individual stars or on the comparison with results from synthetic spectra.
The goal of this analysis is not only to detect CP stars, but also to compare the findings
41
with already existing ∆a photometry and spectrophotometry. For this purpose, three different
systems were employed (Sect. 4).
1. The ∆a photometric system by Maitzen (1976a): For simplicity, the three filters were
represented by Gaussian curves with a FWHM of 130Å and a transmission maximum of
100% each. The fact that these simulated filters, in contrast to the original definition of
g1, g2 and y, all have the same transmission curves, probably does not significantly affect
∆a, because its value is always the difference between a peculiar star and the corresponding
normal star with the same colour index. To convolve the Gaussian curves with the
measurements of the spectrophotometric catalogue, transmission values of 50Å (bins) of
the simulated filters, corresponding to the measurements with 50Å spectral resolution,
had to be determined. This was achieved by segmenting the Gaussian curves into 5Å
bins, which were then numerically integrated. The percentage of transmission, relative
to the maximum, could now be calculated by applying the mean value theorem. For the
transmission values of the 50Å bins, to be multiplied with the measurements, simply ten of
the 5Å bin transmission values were summed. This approach enables to adapt the central
wavelengths of the filters in 5Å steps to figure out the optimal filter positions. The central
wavelengths of the filters were optimised with respect to a low variance of a values for normal
stars and secondly the highest possible a values of CP2 stars. The best compromise
of filter positions found for the spectrophotometric data is 5020Å for g1, 5215Å for g2, and
5470Å for y. These filter positions are very close to those of the revised ∆a system by
Maitzen (1980b). The values of the simulated filters were calculated by multiplying the
transmission values of the 50Å bins with the corresponding measurements of the catalogue
and adding the results.
2. The ∆a′ index by Adelman (1979): This index is described in more detail in Section 4.
3. The ∆a′mod index: Very early in the process of evaluating the spectrophotometric data
the central wavelengths of the spectrophotometric data did not fit those of the ∆a′ index
very well. To calculate the a′ index, the measurements closest to the defined wavelengths
were used. This resulted in inaccurate results, because the central measurement was shifted
from the deepest part of the depression to the red side of the spectra and in some stars
the Hβ line influenced the continuum value on the blue side. To address this problem two
values next to each other were linearly interpolated to obtain central wavelengths closer
to the predefined wavelengths of the ∆a′ index, as well as to improve the error by a factor
of
√
2. This new index is referred to as ∆a′mod and is defined as
a′
mod = m5250 − [m4750 + 0.453 · (m5850 − m4750)]. (11)
The calculation of the indices a′ and the a′mod was straightforward. They were obtained by
simply applying the values of the corresponding measurements to the formula.
As next step, the indices had to be corrected with the a, a′, and a′mod obtained from nonpeculiar
stars of the same temperature. For this purpose, all stars hotter than F5 were selected
to calculate a0, a′
0 and a′
0mod.
According to Maitzen (1976a), the indices are expected to be very well correlated with the
colour index (B − V )0. To deredden the programme stars, use was made of photometric data
in the Johnson, Geneva, and Strömgren systems, compiled from the General Catalogue of Photometric
Data (GCPD, Mermilliod et al., 1997). For the first two systems, the well-known calibrations
based on the X/Y parameters (Cramer, 1999) and Q-index (Gutierrez-Moreno, 1975),
respectively, which are applicable for O/B type stars were applied. Objects with available Strömgren
data were treated with the routines by Napiwotzki et al. (1993), which allow dereddening
42
-0.09
-0.06
-0.03
0.00
0.03
0.06
0.09
a[mag]
3 = ±0.023 mag
-0.09
-0.06
-0.03
0.00
0.03
0.06
0.09
3 = ±0.036 mag
a'[mag]
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
-0.09
-0.06
-0.03
0.00
0.03
0.06
0.09
3 = ±0.032 mag
(B - V)
0
[mag]
a'mod[mag]
Figure 17: Peculiarity indices of 631 stars in the spectral-type range from O6 to F5. The filled
circles denote stars that are detected as peculiar within at least one index.
of cooler-type stars. For about 60 % of the targets it was possible to determine reddening values,
transformed to E(B − V ) with the ratios summarised by Netopil et al. (2008). If several estimates
for a particular object were available, a mean value was calculated. Since all objects are
rather bright and therefore close-by, a strong reddening especially for cool-type stars is hardly
expected. Therefore non-reddening was adopted for these when no Strömgren photometry was
available, which is justified by the obtained overall mean E(B − V ) = 0.02(6) mag.
To find the normality lines, an iterative linear regression of a, a′ and a′mod versus (B − V )0
was performed. In each iterative step, the outliers that lay more than 5σ from the normality
line were discarded. After three iterations, the errors did not significantly decrease any more.
In total, the normality lines is defined from 437 stars and a 3σ of 23, 36, and 32 mmag was
obtained, respectively. Figure 16 shows the regression of the peculiarity indices versus (B −V )0.
The three ∆a indices were calculated by subtracting the corresponding a0, a′
0 and a′
0mod
from the a, a′ and a′mod values for the same (B − V )0. Figure 16 shows the peculiarity indices
versus (B − V )0. All stars above the threshold of 3σ are expected to be chemically peculiar,
whereas those below are emission-type and/or metal-weak objects. The region of (B − V )0 in
which CP2 stars are expected (hotter than spectral type F5) contains 631 stars (Fig. 17).
At (B − V )0 of about 1.5 mag, corresponding to a spectral type M0, the indices a, a′ and
a′mod lose their correlation with (B − V )0 although they are nearly linearly correlated at bluer
colour indices. This may indicate a dependency of a, a′ and a′mod on the luminosity class of
the stars (see Fig. 18).
43
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
a[mag]
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3a'[mag]
-0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
(B - V)
0
[mag]
a'mod[mag]
Figure 18: Different a indices of 1067 stars from the catalogue by Kharitonov et al. (1988)
plotted versus (B − V )0.
9.2 Results
The findings of this investigation are summarized in Tables 6 and 7. The first table lists all
well-known CP stars taken from the catalogue by Renson & Manfroid (2009). The second
table includes apparently normal-type objects (according to spectral classification) hotter than
spectral type F5 that have ∆a values both higher and lower than the 3σ thresholds. The tables
contain the HD number, spectral type, the ∆a values of each applied method, and the CP class
(Table 6 only) of the stars. For comparison with existing peculiarity measurements, they also
include published ∆a values (Sect. 10) and ∆(V 1 − G) (Sect. 4) values.
9.3 Known peculiar objects
First of all, the 55 CP stars listed in Table 6 that are included in the catalogue by Renson &
Manfroid (2009) were analysed. Altogether, 19 stars were detected beyond the 3σ threshold by
any of the systems. The modified system of Adelman yields 18 stars above 3σ for this sample.
This is the highest ratio of spectrophotometric to otherwise identified peculiar stars of the three
applied detection methods.
In Fig. 19, the observed ∆(V 1 − G) versus the synthetic ∆a′mod values for the sample is
presented. The observed ∆a values were not used because there are too few available. There
is a clear correlation of the observed and synthesized values. The five outliers (HD 11415, HD
115735, HD 189849, HD 201601, and HD 206088) are described below.
The CP1 (Am) stars have, with some rare exceptions, observed ∆a values well below
+10 mmag and are normally inconspicuous in the ∆(V 1 − G) index. However, four stars were
detected, three above and one below, the 3σ threshold; these are
• HD 29479: a moderate overabundance of Fe-peak elements and [Ba/H] = +1.77 dex com-
44
-20 -10 0 10 20 30 40 50 60
-60
-40
-20
0
20
40
60
80
3
5
4
a'mod[mmag]
(V1 - G) [mmag]
1
2
1 HD 11415
2 HD 115735
3 HD 189849
4 HD 201601
5 HD 206088
Figure 19: Observed ∆(V 1 − G) versus synthetic ∆a′mod values (∆a and ∆a′ behave very
similar) for the CP star sample. The outliers are discussed in the text.
pared with that of the Sun was reported by Iliev et al. (2006)
• HD 76756: α Cancri is one of the prototype Am stars, with no other conspicuous features
• HD 173648: this is a hot Am star with overabundances of most Fe-peak elements, and
considerable overabundances of Sr, Y, Zr, and Ba as well as some rare earths (Adelman et
al., 1999)
• HD 189849: a weak magnetic field of about 250 G was detected on a 20σ level (Bychkov
et al., 2009), so it might be misidentified.
It seems that some very peculiar CP1 stars are detectable via spectrophotometric observations
and the ∆a peculiar indices.
The magnetic CP2 stars are mainly detectable via ∆a photometry, which is reflected in the
results. Figure 20 shows the spectrophotometric data of standard star HD 102647 (A3 V) and
HD 118022 (A2 Cr Eu Sr) for the whole spectral range (upper panel) and the region where the
∆a system is situated (lower panel). The UV excess (Sokolov, 2006) and the 5200Å depression,
both typical for CP stars, are clearly visible for HD 118022. All strong positive photometric
detections are reproduced by the synthetic investigation. There are two objects, that have
significant negative synthetic ∆a values, but have statistically insignificant observational values:
• HD 201601: γ Equulei is a well-studied rapidly oscillating Ap star with a strong magnetic
field and a very peculiar abundance pattern (Perraut et al., 2011).
• HD 206088: a very peculiar object, in a transition between CP1 and CP2 shows strong
variability in the infrared (Catalano & Renson, 1994).
45
The spectrophotometry of both objects might be severely influenced by the unusual elemental
peculiarity and the variability.
Among the apparent non-magnetic CP3 (HgMn) stars, no detection in any system was found.
This is perfectly in line with the results from Section 11.5.
The sample includes only three well-known CP4 stars of which two (HD 11415 and HD
115735) show significant negative synthetic ∆a′ and ∆a′mod values. Both objects are known to
have strong emission lines according to Kohoutek & Wehmeyer (1999) which explains the result.
9.4 Apparent normal-type objects
Table 7 lists the apparently non-CP stars detected via synthetic photometry. This sample can
be divided into emission-type and metal-weak objects as well as inconspicuous stars.
The hot-emission-type stars are defined as dwarfs that have shown hydrogen emission in
their spectra at least once. Due to a developed equatorial disk that is produced by stellar winds,
emission arises quite regularly. In addition, photometric variability on different time scales is a
common phenomenon caused by the formation of shock waves within those disks. The phases of
emission are replaced by shell and normal phases of the same object, leading to a transition from
negative to positive ∆a values (Pavlovski & Maitzen, 1989). Among the metal-weak objects,
the most prominent subgroup are the λ Bootis stars (Sect. 6). The ∆a observations of the two
groups are summarized in Section 11.
In the sample of inconspicuous objects, two β Cephei pulsators (HD 19374 and HD 29248)
were detected with significantly high positive ∆a values. These objects are early-type-B stars
with light and radial velocity variations on time scales of several hours (Stankov & Handler,
2005). Since these objects are quite rare, fewer than 200 Galactic objects are known, it would
be interesting to find out whether they can be detected via ∆a photometry. Unfortunately,
no observations in this respect have been performed so far. The remaining objects have two
characteristics in common:
1. Except for one object (HD 22951), all of them are very fast rotators (v sin i ≥ 150 km s−1)
which is atypical for CP stars.
2. Almost all objects are in binary systems, which might distort the spectrophotometry.
For the following objects additional interesting characteristics were found in the literature:
• HD 24554: Schröder & Schmitt (2007) found strong X-ray emission indicating an undetected
binary nature of the object.
• HD 28052: This is the second-brightest X-ray source in the Hyades and a possibly quadruple
system with at least one component of δ Scuti type (Simon & Ayres, 2000).
• HD 83808: This spectroscopic binary system is listed as CP1 candidate in Renson &
Manfroid (2009).
• HD 107700: Griffin & Griffin (2011) analysed this close-binary system and found a slight
metal-weakness for both components.
• HD 119765: Renson & Manfroid (2009) listed it as questionable CP candidate without
any designation to a specific subgroup.
For these samples, ∆a′ is superior to the other two systems. For almost all of the newly discovered
peculiar objects among the normal-type objects, photometric ∆a and/or spectroscopic
observations are needed to clarify their nature.
In addition, nine cool-type objects (0.5 < (B − V )0 < 1.5 mag) were also identified that significantly
deviate in the positive direction. Those stars are
46
Table 6: Synthetic (∆a, ∆a′, and ∆a′mod) and observed (∆a obs and ∆(V 1 − G)) peculiarity
indices in mmags for well-established CP (flag “∗”) stars taken from Renson & Manfroid (2009).
The synthetic photometric values for detected objects are given in boldface italics.
HD SpType ∆a ∆a′ ∆a′mod ∆a obs ∆(V 1 − G) CP group
6116 A3−A9 +8 +20 +16 − −8 1
20320 A2−A9 −6 −13 −14 −3 0 1
27045 A3−F3 −3 +1 −4 − −1 1
27962 A1−A4 +13 +26 +31 − −2 1
28355 A5−F1 −1 +2 +2 − −3 1
29140 A3−A7 +12 +25 +23 − −6 1
29479 A3−A9 +6 +37 +28 − −2 1
40536 A4−F1 −3 +18 +16 +7 +7 1
41357 A4−F2 −4 +6 −1 − −1 1
76756 A3−F1 +17 +34 +39 − +2 1
116657 A1−A7 −6 +19 +25 +10 − 1
125337 A2−A7 −11 −8 −9 − −7 1
141795 A2−A8 −1 −6 +3 − −7 1
173648 A4−F1 +3 +40 +34 − −2 1
173654 A2−A7 +3 +17 +13 − −11 1
189849 A5−A9 −17 −40 −40 − +2 1
197461 A7−F0 dD −6 −10 −7 − +1 1
198743 A3−F3 +8 +5 −9 − −1 1
207098 A5−F4 dD −4 +7 +1 − +5 1
223461 A3−F0 +3 +7 +8 − −1 1
10221 A0 Si Sr Cr +12 +25 +33 − +17 2
11502/3 A1 Si Cr Sr +10 +45 +43 +39 +17 2
15089 A4 Sr −1 −4 0 − +4 2
19832 B8 Si +14 +43 +40 +10 +17 2
26571 B8 Si +2 −25 −20 +14 −10 2
32549 B9 Si Cr +10 +50 +52 +25 +17 2
32650 B9 Si +8 +12 +12 − +11 2
34452 B9 Si +36 +65 +78 − +54 2
40312 A0 Si +7 +30 +25 − +17 2
68351 A0 Si Cr +24 +58 +53 +24 +24 2
90569 A0 Sr Cr Si +26 +42 +57 +36 +26 2
112185 A1 Cr Eu Mn +18 +35 +34 − +6 2
112413 A0 Eu Si Cr +13 +19 +22 +40 +26 2
118022 A2 Cr Eu Sr +43 +78 +77 +51 +34 2
120198 A0 Eu Cr Sr +1 +40 +39 +38 +31 2
137909 A9 Sr Eu Cr +39 +21 +47 +25 +4 2
148112 A0 Cr Eu −6 +7 +8 − +13 2
170000 A0 Si +7 +6 +6 − − 2
183056 B9 Si +13 +23 +20 − +2 2
201601 A9 Sr Eu −14 −54 −48 +10 +4 2
206088 A7−F3 Sr +1 −50 −48 +7 +2 2
358 B9 Mn Hg 0 −7 −6 − +5 3
23950 B9 Mn Hg Si +3 −19 −14 − 0 3
33904 B9 Hg Mn −1 +3 +3 − −4 3
35497 B8 Cr Mn +3 +4 +3 − −7 3
77350 B9 Sr Cr Hg −4 +10 +9 +1 +5 3
78316 B8 Mn Hg 0 +18 +20 +12 +6 3
106625 B8 Hg Mn +3 −18 −11 − −9 3
129174 B9 Mn Hg −4 +4 +1 − 0 3
143807 A0 Mn Hg −7 +13 +3 − +6 3
145389 B9 Mn Hg +15 +8 +19 − +4 3
220933 A0 Hg Mn −3 −2 +7 − −5 3
11415 B3 He wk. +13 −41 −34 − +28 4
23408 B7 He wk. Mn +13 −9 −9 +5 +3 4
115735 B9 He wk. −11 −42 −49 +2 −2 4
47
Table 7: Synthetic (∆a, ∆a′, and ∆a′mod) and observed (∆a obs and ∆(V 1 − G)) peculiarity
indices in mmags for apparent non-CP stars detected via synthetic photometry. The synthetic
photometric values for detected objects are given in boldface italics. The upper panel lists
well-known emission-type and metal-weak objects.
HD SpType ∆a ∆a′ ∆a′mod ∆a obs ∆(V 1 − G)
5394 B0.5 IVe +17 −37 −21 +5 +1
6811 B7 Ve −10 −45 −41 −5 +2
18552 B8 Ve +40 +100 +97 − −2
22192 B5 Ve −9 −49 −44 − −4
23016 B8V (e) −16 −38 −30 − −6
32537 F1 Vp MgII 4481Å weak −10 −51 −31 − −7
34078 O9.5 Ve, var. +4 −57 −52 − −10
35439 B1 Vpe −11 −34 −49 +5 +3
67934 A0 Vnp MgII 4481Å weak −1 +40 +13 − −4
74873 kA0.5hA5mA0.5V λ Boo −18 −37 −25 − −15
111604 A5 Vp λ Boo −11 −34 −39 − −2
112014 A0 IIsp Mg,Si weak −9 −39 −30 − +2
193237 B1 ep +6 −97 −14 +25 +17
209409 B7 Ive −18 +53 +24 − +4
210839 O6 If(n)p(e) +6 −69 −55 − −19
217891 B6 IIIe +4 +65 +48 −1 +4
17769 B7 V +18 +41 +49 − −3
19374 B1 V β Cep +50 +62 +91 − −5
22951 A1 Vn +32 +33 +33 − −7
24554 A1 V +32 −6 −10 − −
28052 F0 V +32 +17 +19 − +6
28149 B5 V +42 +28 − −
29248 B2 III β Cep +4 +44 +32 − −9
35671 B5 V SB +18 +51 +35 − −5
35770 B9.5 Vn +26 +40 +33 − −4
70011 B9.5 V −2 +40 +22 − +2
76582 A7 V +24 +18 +25 − −6
83808 F8-G0III + A7m +18 +18 +34 − −10
107700 G7III + A3IV +29 +1 +18 − −4
119765 A0 V −7 −50 −33 +1 −
139891 B6V SB2 +11 +41 +28 − −
166182 B2 IV +6 +38 +27 − −3
178596 F2 IV-V −3 −45 −28 − −8
188260 B9.5 III −15 −47 −38 − −
188350 A0 III −13 −49 −42 − −8
212120 B6 V, ell. var. −45 −15 −41 − −2
222603 A7 V +7 −69 −36 −5 −4
48
3000 4000 5000 6000 7000 8000
0.2
0.4
0.6
0.8
1.0
HD 102647, A3 V
HD 118022, A2 Cr Eu Sr
RectifiedIntensity
Wavelength [Å]
4800 5000 5200 5400 5600
0.3
0.4
0.5
0.6
0.7
0.8
RectifiedIntensity
Wavelength [Å]
Figure 20: Spectrophotometric data of HD 102647 (A3 V) and HD 118022 (A2 Cr Eu Sr) for
the whole spectral range (upper panel) and the region where the ∆a system is situated (lower
panel). The UV excess and the 5200Å depression, both typical for CP stars, are clearly visible
for HD 118022.
• HD 19373: Canto Martins et al. (2011) analysed the chromospheric activity of the G0 V
object.
• HD 26965: This is a young triple binary system including flare-type objects (Pettersen,
1991).
• HD 35369: Prugniel et al. (2011) found an underabundance of [Fe/H] = −0.22 dex compared
with the Sun.
• HD 49878: There are no detailed investigations for this K-type giant available in the
literature.
• HD 68375: Takeda et al. (2008) investigated it in more detail, and found no peculiarities.
• HD 82635: This is a highly chromospherically active RS CVn type giant (Strassmeier et
al., 1994).
• HD 158899: According to Antipova et al. (2004), this is a moderate Barium star classified
as K3.5 III Ba0.1. This group of chemically peculiar stars consists of G- to K-type giants,
whose spectra indicate an overabundance of s-process elements.
• HD 192577: It is a ζ Aurigae type eclipsing binary of spectral type K4 I (Eaton, 2008).
49
• HD 194093: Gray (2010) presented photometric and spectroscopic time series of this
variable star. The variations are found on all time scales up to several hundred days.
The a indices are linearly correlated with Teff up to a spectral type of M0. For cooler-type
objects, there is a strong indication of an additional luminosity effect that is superimposed on
the temperature dependency.
9.5 Conclusions
The spectrophotometric data of the stellar catalogue by Kharitonov et al. (1988) were used to
synthesize three different “a systems”. These data cover the complete spectral range from lowto
high-mass objects. Excluding low-quality data and early-type supergiants, 1067 stars were
used to synthesize different peculiarity indices. The main results are
• Most of the known classical magnetic CP stars were detected.
• A list of about 50 normal-type objects across the complete spectral range was presented
that were detected.
• The most efficient a system is very similar to that previously employed by Maitzen (1980b).
• The normality line of the a system correlates with Teff up to a spectral type of M0.
The analysis showed that spectrophotometric data can be used for calculating synthetic a indices
and for detecting peculiar objects across the complete spectral range up to M0. These findings
are also interesting in the light of the discussion presented in Sect. 8.2 about the 5200Å region
of stars across the HRD.
10 A catalogue of ∆a measurements for Galactic field stars
The prerequisite for investigating larger samples of CP stars (including the generally fainter star
cluster members) is an unambiguous detection. Looking into catalogues of CP stars, especially
the magnetic ones, it immediately becomes obvious that there are many discrepancies even at
classification dispersions. The reasons for discrepant peculiarity assessments are mainly to be
found in the differences in observing material (density of spectrograms, widening of spectra,
dispersion, and focussing), but also intrinsic variability of peculiar spectral features (e.g. silicon
lines).
Besides the use of (very time consuming and magnitude limited) high dispersion spectroscopy,
photometry has shown a way out of this dilemma, especially through the discovery of
characteristic broad band absorption features, the most suitable of them located around 5200Å
(Kodaira, 1969).
Since its introduction in 1976, many papers presenting ∆a photometry of galactic field and
especially open clusters have been published. Until the late 90s, all observations were performed
with photomultipliers.
All but two (Vogt et al., 1998; Paunzen et al., 2005b) publication about ∆a photometry of
galactic field stars were explicitly devoted to CP stars or related groups selected on the basis
of several relevant catalogues. Superficial “normal” type objects were only observed in order to
define the normality line for the specific set of data.
All available ∆a data of bright Galactic field stars that have been published in the literature
over more than two decades were compiled, in order to make a sound statistical analysis of detection
probabilities for all kinds of peculiar objects, as well as luminosity class I/II supergiants
(Sect. 11). This is especially important for observations in star clusters (Sects. 17 and 18) and
50
Table 8: The number of individual ∆a measurements from the given reference. The used filter
systems are according to Table 9.
Ref. Nobs. System Ref. Nobs. System
Maitzen (1976a) 168 1 Pavlovski & Maitzen (1989) 40 4
Maitzen (1980a) 10 2 Schnell & Maitzen (1994) 3 5
Maitzen (1980b) 8 2 Schnell & Maitzen (1995) 14 5
Maitzen & Segewiss (1980) 21 2 Maitzen et al. (1997) 6 6
Maitzen (1981) 20 2 Maitzen et al. (1998) 131 7
Maitzen & Vogt (1983) 342 3 Vogt et al. (1998) 803 3
Maitzen & Pavlovski (1989a) 16 4 Paunzen et al. (2005b) 99 5
Maitzen & Pavlovski (1989b) 31 4
extragalactic systems (Sect. 19). The knowledge of how many peculiar stars for a certain detection
limit are expected in comparison with the actually observed number, serves as important
information for a statistical analysis, such as the incidence of CP stars that depend on different
local environments.
10.1 Selection, preparation, and homogenization of the data
The following sources of ∆a photometry for galactic field stars were used: Maitzen (1976a,
1980a,b, 1981), Maitzen & Segewiss (1980), Maitzen & Vogt (1983), Maitzen & Pavlovski
(1989a,b), Pavlovski & Maitzen (1989), Schnell & Maitzen (1994, 1995), Maitzen et al. (1997,
1998), Vogt et al. (1998), and Paunzen et al. (2005b). The number of individual measurements
are given in Table 8. Some references already list (b − y)0 magnitudes, these were used. Objects
were only included which have Strömgren indices available.
All but Maitzen et al. (1997, CCD) were conducted with photomultipliers and classical
aperture photometry (one star at one time). The different filter sets of these observations are
listed in Table 9. The only important difference is the filter set used by Maitzen et al. (1997)
together with the CCD equipment. Although the bandwidths of g1 and y were exchanged, the
overall values of ∆a are in very good agreement with those of the photoelectric system.
The Johnson, Geneva, and Strömgren (if not listed in the original source of the ∆a photometry)
colours were taken from the General Catalogue of Photometric Data (GCPD, Mermilliod
et al., 1997). Usually, the reddening for objects within the solar neighbourhood is estimated
using photometric calibrations in the Strömgren uvbyβ system (Strömgren, 1966; Crawford &
Table 9: Filter systems used for the ∆a measurements.
System g1 g2 g3/y
λc λ1/2 λc λ1/2 λc λ1/2
1 5020 130 5240 130 5485 230
2 5010 130 5215 130 5485 230
3 5020 130 5240 130 5505 230
4 5026 111 5238 138 5466 230
5 5017 120 5212 120 5494 228
6 5027 222 5205 107 5509 120
7 5017 110 5212 120 5473 188
51
180 210 240 270 300 330 0 30 60 90 120 150 180
-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Galacticlatitude
Galactic longitude
Figure 21: The galactic distribution of the sample including 1561 individual objects. There is a
clustering of objects at 190o < l < 280o, the almost reddening free (up to 500 pc from the Sun)
third galactic quadrant.
Mander, 1966; Crawford, 1975, 1979; Hilditch et al., 1983). The validity of these procedures
for CP stars was shown, for example, in Netopil et al. (2008). However, these relations have
to be used with some caution when applied to magnetic CP2 stars, because all calibrations are
primarily based on the β index. But due to variable strong magnetic fields, the β index can
give erratic values (Catalano & Leone, 1994) Another effect taken into account is a “blueing”
effect, which occurs in bluer colours due to stronger UV absorption than in normal type stars,
which can be erratically interpreted as strong reddening (Adelman, 1980). An independent way
to derive the interstellar reddening is to use galactic reddening maps, which are derived from
open clusters as well as from galactic field stars. For this comparison, the model proposed by
Chen et al. (1998) was used to derive the interstellar reddening for all program stars. The values
from the calibration of the Strömgren uvbyβ and the model (Chen et al., 1998) agree within an
error of the mean of ±1.9 mmag for the complete sample.
In order to check this procedure, the raw data of Maitzen (1976a) were used to derive the
normality line of these data. He used a combined normality line for the (b − y) and (b − y)0
values under the assumption that the reddening in the solar neighbourhood is negligible. The
deduced results confirm his A0 parameter with a slight adjustment of the A2 value from 0.06 to
0.066, which means a correction of ∆a in the order of only one mmag. This leads to confidence
in the applied dereddening procedure.
As the next step, the intrinsic consistency of the different reference for objects in common
was checked since the filter systems are slightly different (Table 9). Besides a possibly wrong
identification or typographical errors, the variability of ∆a itself has to be taken into account.
Several CP stars show variability in correlation with strong magnetic fields and rotation. These
52
2 3 4 5 6 7 8 9 10
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
Numberofstars
V [mag]
-150 -75 0 75 150 225 300 375
(b - y)
0
[mmag]
#
tot
= 1561
Figure 22: The distribution of Johnson V and Strömgren (b − y)0 of the sample.
variations were also detected in the ∆a photometric system (Sect. 5).
The published (b − y)0 and ∆a values were checked in this respect and no significant trends
were found. All references agree, in a statistical sense, within one sigma of the correlation
coefficients. No significant outliers were found. Therefore, the values of objects with more than
one measurement were averaged without using any weights, resulting in 1561 individual galactic
field stars. This almost doubles the sample used by Vogt et al. (1998) with an available ∆a
value. This sample consists of “normal” type and peculiar stars of all kinds.
Figure 21 shows the distribution of the galactic coordinates for the sample. There is a
clustering of objects between 190o < l < 280o (third galactic quadrant) because of the systematic
investigation in the southern hemisphere by Vogt et al. (1998). In this region, the reddening is
almost negligible for distances up to 500 pc (Chen et al., 1998). But no unknown bias has been
introduced, because the CP stars are distributed uniformly in the solar neighbourhood (Gómez
et al., 1998).
The sample covers −0.15 < (b − y)0 < +0.4 mag (Fig. 22), which corresponds to the spectral
range from B0 to F8 (Crawford, 1975, 1979). The peak of the distribution is at (b −
y)0 = −0.05 mag or B9 at the MS. At this spectral type, the number of CP2 stars reaches an intrinsic
maximum. The Johnson V magnitude distribution shows two maxima around V = 6 mag
and 8 mag and extends from 1.5 < V < 10.5 mag. The first peak is a consequence of the systematic
investigation of all bright stars by Vogt et al. (1998) whereas the second one is due to the
chosen sample by Maitzen & Vogt (1983). They have investigated the list of astrophysically
interesting stars by Bidelman & MacConnell (1973), which was published prior to the Michigan
spectral survey, while both are based on the same spectroscopic material.
53
-120 -80 -40 0 40 80 120 160 200 240 280 320
-40
-36
-32
-28
-24
-20
-16
-12
-8
-4
0
4
8
12
16
20
24
28
32
36
40
a[mmag]
(b - y)
0
[mmag]
Outliers not in Renson & Manfroid (2009)
Figure 23: The mean values and the corresponding root mean square scatter for all normal type
objects with ∆a measurements. The straight lines are the 3σ fits through the errors, whereas
the asterisks denote the outliers of objects not included in the catalogue of RM09 discussed in
Section 11.2.
11 The detection probability of the ∆a system for Population I
stars
With the sample of 1561 Galactic field stars (Sect. 10), a statistically sound analysis was
performed. There are two stars in the sample that exhibit positive ∆a values, for which it was
not possible to designate a distinctive membership in a certain class of CP stars. Certainly,
these two objects deserve further interest:
HD 68161: Eggen (1980) lists a photometric spectral type of B7III, whereas the spectroscopic
type is B8Ib/II (Houk & Swift, 1999). This is a strong indication that this star is of CP2 type,
because the silicon lines are also used to derive the luminosity classification.
HD 225253: several deviating classifications in the literature were found, B8III (Jaschek et al.,
1969), B8IV/V p(mild) (Maitzen, 1980a) and B7 UV gallium (Jaschek & Jaschek, 1987). With
a ∆a value of +18 mmag, this object is obviously chemically peculiar.
Let us recall the definition of the different (quality) flags for CP stars by Renson & Manfroid
(2009, RM09 hereafter). In general, a flag indicates the degree of confidence for the CP nature
of the star. A slash (/) denotes a star that was improperly considered to have an Ap, HgMn
or Am nature. Question marks (?) mean doubtful cases (2314 stars, among which are 311 Ap
stars detected by photometric criteria, and not yet confirmed by ordinary spectroscopy). On
the contrary asterisks (*) denote well-known confirmed Ap, HgMn or Am stars (only 426).
54
For the further analysis of the CP stars, only well-known confirmed objects were used. This
is the most homogeneous sample of CP stars available in the literature. Of course, one could
add further stars to this list on the basis of more recent published single papers. But this would
decrease the homogeneity of the sample. However, a list of further confirmed CP stars on the
basis of the ∆a index was derived (Table 11). These stars are already included in RM09, but
without an asterisk flag. They should be included with such a flag in the next updated version
of RM09.
11.1 The normal type objects
The selection of apparent normal type objects is a rather difficult task because of undetected
peculiarities of all kinds which might introduce an unknown bias. All objects not listed in the
catalogue by RM09 were chosen, because they compiled stars which have been identified as
peculiar at least once in the literature, even though they might turn out to be “normal” after
all. As a next step, stars classified as λ Bootis (Paunzen et al., 2002a), Be/shell stars, and super
giants of luminosity classes I and II were excluded. For this purpose the spectral classifications
given in the Michigan catalogues of two-dimensional spectral types (Houk & Swift, 1999, and
references therein) and the extensive list of Skiff (2016) were used. Known binary systems of all
kinds were not automatically excluded.
In total, 673 objects with luminosity classes V, IV, and III were selected on this basis.
These stars were divided into subsamples according to their (b − y)0 values (−0.125 < (b −
y)0 < +0.315 mag) with a bin size of 20 mmag, which corresponds to ±1 spectral subclasses.
The intervals are defined in the sense [a,b]. For each subsample the mean ∆a value and the
corresponding standard deviation of the mean for all objects within it was calculated. One
object, HD 102870 (F8 V), falls outside the above given bins because it is too cool with (b −
y)0 = +0.356 mag. Figure 23 shows the results, with mean values uniformly distributed around
zero. The straight lines ±13 ± 0.01(b − y)0 are linear fits through the mean values adding
3σ in both directions. The mean value of σ is 5(2) mmag in the interval from −0.125 < (b −
y)0 < +0.315 mag which corresponds to spectral types between B0 and F5. This is in line with
the published values in Maitzen (1976a) and Vogt et al. (1998). The detection limit for the
sample increases from ±12 to ±16 mmag towards cooler objects (Fig. 23 and Sect. 9). There
are two main reasons for this behaviour: 1) (g1 − y) is no longer only an indicator of the Teff
because of significantly increasing line blanketing as (b − y) and 2) the strong general increase
in metallic lines towards later spectral types. Since most of the “normal” type stars are brighter
than V = 7 mag (Fig. 22), it was checked if the detection limit changes if only fainter “normal”
objects are used. Although one is confronted with poor number statistics, no correlation was
found.
The observed scatter around the normality line has several causes. Besides the instrumental
limitations (e.g. photon noise and variable sky transparency), which account for about 3 mmag
(Maitzen, 1976a), the intrinsic variations due to the natural bandwidth of the main sequence is
important. In Sect. 14, a synthetic ∆a photometric system based on modern stellar atmospheres
and the filter transmission curves of “System 3” in Table 9 was investigated. The models are in
the temperature range from 7000 to 15000 K and surface gravities from 2.5 to 4.5 dex. A natural
bandwidth of about 4 mmag within these models was found. A metallicity range from −0.5 to
+0.5 dex creates an overall bandwidth (= 2σ) of 10 mmag (Sect. 14.1.4). This is more or less
exactly the value one finds for the sample of normal type, galactic field stars. In open clusters for
which the metallicity is rather uniform, lower detection limits are expected if neglecting strong
differential reddening (Sect. 17).
The results of the statistics for the different groups are listed in Table 10. The detection
rates as functions of the corresponding 3σ limits are shown in Figure 24.
55
Table 10: Limits in mmag for detecting the individual groups of objects. For example 41% of
all CP1 stars can be detected with a 3σ limit of +5 mmag. In addition, the mean group ∆a, the
maximum values for group members ∆am, and the number N of well-established members for
the analysis are listed.
+5 +10 +15 +20 ∆a ∆am N
[%] [%] [%] [%] [mmag] [mmag]
CP1 41 21 3 3 +3.5 +22 29
CP2 96 92 85 71 +31.3 +79 129
CP3 56 19 − − +4.3 +11 16
CP4 79 71 43 21 +18.8 +31 14
I/II 52 17 7 − +4.0 +19 29
−5 −10 −15 −20
[%] [%] [%] [%]
λ Boo 95 65 35 20 −16.2 −35 20
Be 20 5 2 − −0.5 −19 64
11.2 Outliers not included in RM09
Eight objects (four each with positive and negative ∆a values) are located outside the 3σ limit
(Fig. 23) and are not included in RM09.
First of all, the four objects with negative ∆a values are discussed in more detail:
HD 2834 ((b − y)0 = +8 mmag, ∆a = −16 mmag): a known spectroscopic binary system that is
also part of a visible double system.
HD 4158 (+210, −37): a metal weak, cool star classified as hF3mF0V (wk met) by Paunzen et
al. (2001).
HD 6173 (+102, −23): although previously thought to be a member of the λ Bootis group, it
was classified as A0IIIn (Paunzen et al., 2001).
HD 97937 (+188, −16): a metal weak (F0V m−1.5), intermediate Population II type object
(Gray, 1989).
HD 114911 (−48, −15): a young, early type quadruple system which exhibits X-ray emission
(Hubrig et al., 2001).
The four objects with positive ∆a values lie only marginally above the 3σ limit (Fig. 23):
HD 31726 (−110, +14): a B1V star which exhibits rather normal silicon line strengths (Massa,
1989).
HD 49028 (−61, +13): a close visual binary system with a B7III and a F3V Fe−2 component
(Corbally, 1984).
HD 65908 (−44, +13): Bowyer et al. (1995) reported a clear flux detection in the far-ultraviolet
for this star which might indicate a previously unknown binary nature.
HD 73451 (+275, +16): a known spectroscopic binary system with an early A- and a G-type
component (Cowley et al., 1969).
These objects deserve a further analysis using photometric and spectroscopic data to determine
why they exhibit a non-standard ∆a value.
11.3 CP1 stars
In the investigated sample, there are only 29 well established CP1 stars yielding a slightly
positive mean value (+3.5 mmag) and quite extreme values (+22 mmag) for some members
(e.g. HD 184552). But the detection capability is only 21% for a limit of +10 mmag (Table
56
Table 11: Confirmed CP stars listed in RM09 with the (b−y)0 and ∆a values taken from Section
10.
HD RM09 Spec. (b − y)0 ∆a HD RM09 Spec. (b − y)0 ∆a
[mmag] [mmag] [mmag] [mmag]
315 30 B9 Si −71 +31 43901 11660 F0 Sr Cr Eu +132 +26
2957 760 B9 Cr Eu −20 +36 44290 11750 B9 Cr Eu −26 +36
5601 1480 A0 Si −56 +49 44293 11760 A0 Cr −89 +55
6164 1580 A0 Si −12 +40 44456 11800 A0 Si Sr −9 +50
6322 1620 A0 Sr Cr Eu −23 +22 44947 11910 A3 Sr Eu Si +105 +21
6783 1760 B8 Si −57 +53 44953 11930 B8 He wk. −86 +17
8783 2110 A2 Sr Eu Cr +72 +23 45439 12040 B9 Si −60 +19
16145 4060 A0 Cr Sr Eu +28 +35 45530 12070 A0 Si −30 +36
18610 4670 A2 Cr Eu Sr +114 +48 45583 12120 B9 Si −65 +58
19712 4880 A0 Cr Eu −60 +43 45698 12150 A2 Sr Eu +69 +16
21590 5400 B9 Si −43 +31 46462 12430 B9 Si −75 +25
23207 5900 A2 Sr Eu +106 +28 47116 12650 B9 Si −50 +35
27463 7050 A0 Eu Cr +22 +28 47714 12810 B8 Si −64 +35
28299 7230 B8 Si −57 +31 47802 12860 B9 Si −60 +30
28365 7280 B9 Si −71 +18 48729 13000 A0 Si −35 +26
29435 7530 B9 Si −46 +22 50166 13690 A0 Si −22 +30
29925 7690 B9 Si −61 +46 50221 13750 B9 Si −69 +28
32145 8190 B7 Si −72 +37 50403 13790 A2 Sr Eu +98 +20
32432 8250 B9 Si −32 +31 50461 13810 B9 Si Cr −51 +52
34427 8760 A0 Si −14 +25 50825 13960 B8 Si −29 +36
34435 8770 A2−A7 +70 +17 51172 14100 B9 Si −58 +33
34631 8840 B9 Si −64 +24 51650 14210 B9 Si −4 +33
34719 8850 A0 Hg Si Cr −38 +44 51684 14220 F0 Sr Eu Cr +154 +20
34736 8860 B9 Si −64 +17 52589 14400 B8 Si −62 +42
35353 9030 A0 Sr Cr Eu +94 +23 52696 14460 A3 Sr Eu Cr +97 +23
36668 9560 B7 He wk. Si −59 +26 52847 14500 A0 Cr Eu +102 +62
37140 9910 B8 Si Sr −66 +31 52993 14550 B9 Si −64 +29
37189 9940 A0 Si −9 +23 53116 14620 A0 Sr Eu −46 +50
37210 9950 B8 He wk. Si −61 +22 53204 14630 B9 Si −30 +21
37642 10150 B9 He wk. Si −84 +34 53662 14740 A0 Si −36 +19
37713 10170 B9 Si −64 +15 53851 14780 B9 Si −63 +29
37808 10210 B9 Si −73 +27 54832 14980 B9 Si −64 +42
38170 10256 B9 −33 +23 55309 15040 B9 Si −60 +48
38698 10400 A0 Si −13 +54 55395 15070 B9 Si −65 +22
38719 10410 A0 Cr Sr Eu +11 +38 55540 15100 A0 Eu Cr −68 +70
39082 10500 B9 Sr Cr Eu −63 +42 56022 15250 A0 Si Cr Sr −25 +16
39353 10570 B8 Si −57 +17 56273 15300 B8 Si −59 +25
39575 10600 A0 Si Cr Eu −74 +55 56336 15350 B9 Si −63 +32
40071 10680 B9 Si −50 +42 56632 15450 B9 Si −41 +22
40277 10730 A1 Sr Cr Eu +41 +20 56809 15480 B9 Sr Cr Eu −3 +29
40383 10780 B9 Si −42 +31 56882 15520 F0 Sr Cr Eu +109 +27
40711 10880 A0 Sr Cr Eu +95 +43 57526 15710 B9 Si −38 +40
40759 10900 A0 Cr Eu −13 +27 58292 15910 A0 Si −27 +34
41403 11080 B9 Sr Cr Eu −16 +48 60559 16550 B8 Si −62 +23
42326 11280 A0 Eu Cr +8 +42 61382 16840 B9 Si −23 +23
42335 11290 A0 Si +72 +16 62530 17150 B9 Eu Cr −31 +34
42536 11340 A0 Sr Cr −4 +22 62535 17160 A0 Si −35 +40
42576 11360 B9 Si Cr −16 +20 62556 17180 A0 Eu Cr +35 +18
43408 11520 B9 Sr Eu −23 +28 62640 17220 B9 Si −80 +19
57
Table 11: continued.
HD RM09 Spec. (b − y)0 ∆a HD RM09 Spec. (b − y)0 ∆a
[mmag] [mmag] [mmag] [mmag]
63401 17480 B9 Si −73 +27 82154 23360 B9 Si −51 +59
63759 17570 A2 Sr Cr Eu +51 +22 82567 23480 B9 Si −62 +26
64881 17800 A0 Si −55 +32 83266 23750 A0 Si Cr Sr −48 +55
64901 17810 A0 Si −63 +38 83625 23850 A0 Si Sr −67 +40
66051 18190 A0 Si −29 +30 85892 24520 B8 Si −61 +27
66195 18240 A0 Sr Eu Cr +43 +39 86170 24620 A2 Sr Eu Cr +71 +23
66350 18320 A0 Eu Cr −30 +37 86976 24850 A5 Sr Eu Cr +133 +20
66624 18410 B9 Si −85 +28 88385 25310 A0 Cr Eu Si −2 +50
66698 18430 A0 Eu −26 +21 89103 25530 B9 Si −54 +59
67165 18510 A0 Si −44 +36 89192 25580 A0 Cr Eu Si +9 +27
67330 18590 A0 Si −13 +38 89217 25590 B9 Si −50 +26
67835 18700 B8 Si −65 +17 89385 25650 B9 Cr Eu Si −26 +40
68161 18840 B8 −44 +22 89393 25660 A0 Sr Cr Eu +134 +42
68292 18860 B9 Si −73 +35 89519 25720 B9 Eu Cr Sr −33 +24
68476 18960 B9 Si −53 +22 89680 25750 A0 Cr +33 +21
68998 19120 A5 Eu Cr Sr +130 +18 90264 25960 B8 He wk. −68 +17
69067 19150 B8 Si −62 +39 90612 26020 B8 Si −60 +47
70464 19440 B9 Si −68 +30 91089 26200 B9 Si −69 +16
70507 19470 B9 Si Cr −60 +24 91134 26210 B9 Si −48 +29
70749 19520 B8 Si −54 +23 91239 26240 A0 Eu Cr Si −33 +44
70847 19570 B8 Si −66 +16 92379 26610 B8 Si −56 +35
71808 19820 B9 Si −54 +36 93500 27010 B9 Cr Eu Sr −19 +15
72055 19900 B8 Si −58 +23 93821 27150 B9 Si −40 +16
72295 19980 A0 Sr Eu Cr −23 +35 94455 27260 A0 Cr Eu Sr +112 +38
72611 20120 A0 Eu Cr Sr −62 +49 94873 27350 B8 Si −49 +19
72634 20130 A0 Eu Cr Sr −11 +26 95198 27420 B9 Si −34 +31
72881 20200 B9 Si −61 +35 95413 27490 A0 Si −52 +44
72976 20250 B9 Si −58 +37 95442 27500 A0 Sr Cr Eu +13 +24
73737 20560 B9 Si −25 +46 95569 27530 B9 Si +121 +29
74067 20630 A0 Cr Si −50 +37 95699 27560 F0 Sr Eu Cr +75 +36
74555 20830 A0 Cr Eu +6 +23 96910 27960 B9 Si Cr Eu −24 +61
74888 20950 B9 Si −64 +22 97394 28090 A5 Eu Cr Sr +121 +39
76104 21290 B9 Si −39 +39 97986 28260 B8 Si −48 +30
76439 21510 B9 Si −69 +19 98340 28350 B9 Si −38 +19
76650 21610 B9 Si −64 +25 98457 28360 A0 Si −39 +22
76897 21690 B9 Si −32 +25 98486 28370 B9 Si −60 +23
77609 21960 B9 Eu Sr −29 +32 101600 29270 A0 Si +22 +21
77653 21970 B9 Si −70 +26 101724 29330 B9 Si −78 +16
77689 21980 B9 Si −77 +38 103302 29780 A0 Sr Cr Eu +4 +33
78201 22150 A0 Sr Eu −27 +23 103457 29820 A0 Si −7 +35
78568 22260 B9 Si −62 +16 103498 29830 A1 Cr Eu Sr −9 +46
79066 22420 A9− dD +202 −16 104810 30330 B8 Si −65 +19
79976 22750 B9 Sr Cr Eu −15 +16 105379 30460 A0 Sr Cr +27 +16
80282 22830 A0 Si −73 +30 105457 30490 A0 Si +56 +50
81141 23030 B9 Si −58 +25 105770 30610 B9 Si −68 +18
81289 23080 A2 Eu Sr Cr −5 +25 106204 30700 B9 Si −46 +25
81588 23190 A5 Sr Cr Eu +118 +18 109809 31860 B9 Si −48 +24
81847 23260 B8 Si −65 +47 112252 32600 B9 Si −42 +19
82093 23340 A2 Sr Eu Cr +5 +41 112528 32730 A3 Sr Eu Cr +188 +24
58
Table 11: continued.
HD RM09 Spec. (b − y)0 ∆a HD RM09 Spec. (b − y)0 ∆a
[mmag] [mmag] [mmag] [mmag]
115440 33340 B9 Si −61 +42 156853 44120 B8 Si −58 +31
115599 33420 A2 Si +158 +22 156869 44130 A0 Sr Cr Eu +41 +25
116235 33550 A2−A8 +52 +16 157678 44280 B9 Si −66 +16
116423 33580 A0 Eu Sr Si +87 +48 157751 44320 B9 Si Cr −29 +44
116890 33720 B9 Si −68 +17 158128 44450 B9 Si −41 +36
117057 33780 B9 Si −69 +17 158175 44480 B8 Si −55 +42
118913 34340 A0 Eu Cr Sr +17 +44 158450 44620 A0 Sr Cr Eu +234 +22
119308 34460 B9 Sr Cr Eu −26 +36 159545 44900 B9 Si −47 +31
120059 34630 B8 Si −15 +15 159846 44970 B9 Si −58 +23
121661 34970 A0 Eu Cr Si +27 +39 160127 45090 A2 Sr Eu Cr +128 +31
122208 35050 A2 Sr Cr Eu +45 +42 161277 45440 B9 Si −42 +33
123627 35410 A3 Sr Eu Cr +144 +20 161349 45470 B9 Si −67 +16
125532 35850 B8 Si −67 +38 164224 46430 B9 Cr Eu −31 +44
126876 36120 B8 Si −62 +20 166053 46770 B9 Si −73 +16
127453 36240 B8 Si −57 +33 166921 46960 B8 Si −47 +28
127575 36280 B9 Si −60 +48 168856 47330 B9 Si −63 +38
129899 37030 A0 Si −26 +44 169021 47410 B9 Si −63 +27
130335 37110 A2 Si +120 +33 172690 48380 A0 Si Sr Cr +24 +18
131505 37350 B9 Si −68 +18 173406 48570 B9 Si −59 +24
132322 37580 A7 Sr Cr Eu +118 +25 173562 48600 A0 Cr Eu +38 +21
133281 37840 B9 Si −63 +38 174638 48890 B8 He −75 +36
135415 38460 B8 Si −61 +31 174646 48910 B9 Si −58 +25
137160 38970 A0 Sr Eu Cr +47 +25 174779 48940 A0 Si −45 +49
137193 38980 B9 Si −46 +39 176555 49260 B9 Si −58 +24
138758 39500 B9 Si −38 +53 181550 50290 B9 Si Cr −39 +31
138773 39520 A0 Si +81 +27 184020 50800 A0 Sr Cr Eu −15 +18
141461 40170 B9 Si −60 +29 189502 52540 A0 Si Sr Cr −48 +39
141641 40220 B8 Si −78 +21 191439 53340 B9 Cr Eu Sr −25 +46
143473 40620 B9 Si −67 +45 191796 53460 A0 Eu Cr −35 +39
144231 40860 B9 Si −22 +42 196425 54740 A7−F2 +121 +17
144748 41020 F0 Sr Eu Cr +85 +35 196606 54840 B9 Si −55 +20
146971 41510 A0 Sr Cr Eu +147 +16 196655 54880 A2− +46 +34
148848 42060 A0 Si Cr Sr +134 +51 197417 55030 A0 Cr Eu +32 +54
149764 42360 A0 Si +10 +21 200405 55830 A2 Sr Cr +13 +38
149831 42400 B9 Si −70 +22 200623 55940 A2 Sr Eu Cr +67 +25
150040 42450 A0 Si +37 +20 203585 56690 A0 Si −37 +21
150323 42500 B6 Si −61 +40 204131 56860 B9 Si Cr Sr −10 +15
150486 42560 B9 Si −40 +22 204541 56970 A2−F1 +138 +17
150714 42640 A0 Si +88 +24 204815 57030 A0 Si +16 +40
151742 42930 B9 Si −51 +25 207188 57640 A0 Si −41 +37
151965 43000 B9 Si −78 +35 209339 58240 B0 He −120 −26
152366 43130 B8 Si −53 +42 209845 58400 A1−F1 +79 +15
153707 43400 B8 Si −37 +20 212432 58920 B9 Si −54 +22
154253 43610 A0 Sr Cr Eu +106 +20 213232 59100 A4 Sr +63 +17
154308 43620 A0 Cr Eu Sr +95 +47 215966 59650 B9 Eu Cr −13 +31
154458 43660 B9 Si −66 +35 217792 60045 F0− +191 −15
155127 43810 B9 Eu Cr Sr −14 +45 225253 61770 B8 Ga −46 +18
155778 43990 B8 Si −40 +24 258583 12260 A0 Si −20 +18
156300 44040 B9 Si −34 +29 17100 A0 Si −19 +46
59
10). Some of the most outstanding objects have already been discussed by Vogt et al. (1998).
In Sect. 14, detailed synthetic ∆a values for the CP1 group are presented concluding that
the 5200 Å flux depression is only marginally detectable for these objects. This means that the
most significant elements contributing to this feature (e.g. Iron and Chromium) are not strongly
enhanced compared to the overall strength of the metallic-lines in CP1 stars.
11.4 CP2 stars
Most of the former ∆a observations were dedicated to this group because of the high efficiency at
detecting CP2 stars. This is also reflected by the results listed in Table 10. About 92% of all CP2
objects can be detected with a limit of +10 mmag, whereas the mean value is +31.3 mmag with
an extreme value of +79 mmag. This sample includes all well-established CP2 stars classified in
RM09 and marked with an asterisk. The sample was not subdivided into hotter Si and cooler
CrEu(Sr) objects, because the definition is not quite clear yet (Bychkov et al., 2003).
11.5 CP3 stars
All CP3 stars listed by Adelman et al. (2003) with ∆a measurements (10 objects) are included
in the analysis. The mean value of all objects is +4.3 mmag but with a very low maximum
of +11 mmag (Table 10). The detection limit drops from 56% to 19% for +5 and +10 mmag,
respectively. This is comparable to the values found for the CP1 group. This similar behaviour
can be explained because both groups are apparently non-magnetic.
11.6 CP4 stars
The percentage of detection (71%) at +10 mmag is lower than that of the CP2 group. But one
can conclude that a statistically significant amount of magnetic CP stars can be detected with
the ∆a photometric system.
Within the sample, there are also three helium rich objects: HD 37017 (∆a = +2 mmag),
HD 37479 (+10), and HD 64740 (−1). Zboril et al. (1997) analysed a sample of 17 helium rich
objects and concluded that several stars exhibit strong emission together with stellar activity.
This might be the reason why such a wide range of ∆a values was observed similar to Be/shell
stars.
11.7 λ Bootis stars
The group of λ Bootis stars is an especially excellent example of how ∆a photometry can preselect
candidates for spectroscopic observations, for example, in young open clusters. Paunzen et
al. (2001) presents spectral classification of 708 stars selected to be good photometric candidates
only on the basis of Strömgren indices. From those, only 26 turned out to be new members of
the λ Bootis group.
Within the presented analysis, twenty well-established members of the λ Bootis group with
∆a measurements were found. The group mean value is −16.2 mmag, and a maximum of
−35 mmag (Table 10) shows the high efficiency of this photometric system. Even with a detection
limit of −10 mmag, almost 2/3 of all bona-fide λ Bootis stars can be detected.
11.8 Supergiants
The only notice about a positive detection of supergiants was given by Vogt et al. (1998), who
investigated two cool supergiants and found a substantial positive deviation from the normality
line.
60
-20 -15 -10 -5 0 5 10 15 20
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
CP1
CP2
CP3
CP4
I/II
Boo
Be
Detectedobjects[%]
a [mmag]
Figure 24: The detection probability of the different investigated groups as listed in Table 10.
The current analysis was restricted to objects classified as luminosity class I or II in the
literature. It has to be emphasized that such objects are, in general, easily sorted out within
colour-magnitude diagrams of different photometric systems. However, the results from Sect.
13 show that isochrones with the ∆a photometric system together with the location of objects
with respect to the normality line are capable of sorting out fore- and background objects very
efficiently.
The analysis of supergiants in open clusters is important in several respects. Most of these
objects are within binary systems and exhibit variability on several time scales (Corliss et al.,
2015). Furthermore, their membership is crucial for isochrone fitting because of the sensitivity
of the determined age on the existence of a “giant clump” (Eigenbrod et al., 2004). Since all
known CP stars have luminosity classes IV or V (Gómez et al., 1998), supergiants selected by
their location in a CMD with a significant positive ∆a value can be easily tested for membership
in an open cluster (Sect. 17.3). In total, 29 supergiants from O9.5II (HD 47432) to F4Iab (HD
61715) are included in the investigated sample with a mean value of +4.0 and a maximum value
of +19 mmag (Table 10).
11.9 Be/shell stars
The phases of emission are replaced by shell and normal phases of the same object. This episode
was analysed for the case of Pleione using ∆a photometry (Sect. 5.2). In the shell phase it
reached a ∆a value of +36 mmag, which dropped to +4 mmag within one year. However, the
behaviour of Pleione seems quite extreme and outstanding, because no other similar object has
been detected so far (Vogt et al., 1998). The contamination of classical CP stars due to Be stars
in a shell phase is, therefore, only marginal (Sect. 5.2).
61
Since Pavlovski & Maitzen (1989) already presented a paper with measurements of 40 apparent
Be/shell type stars, the investigated sample is rather large, 64 objects in total. The mean
value is close to zero (−0.5 mmag) with extremes of −19 mmag (emission phase) and +36 mmag
(shell phase).
11.10 Newly confirmed CP stars
In Sect. 11.1, the detection limit of apparent peculiar was estimated as increasing from ±12 to
±16 mmag towards the coolest objects (spectral type F5). These values are only valid for the
sample of 1561 Galactic field stars as presented in Section 10.
Taking a limit of ±15 mmag for the whole investigated range, 294 peculiar objects were
detected. This stars together with the spectral information from RM09 are listed in Table 11.
There are only three stars with significant negative ∆a values among the sample:
• HD 79066: This star was classified as δ Del type (Cowley, 1973) which are a group of
giants of late A- to early F-type, with weak Ca ii lines.
• HD 209339: classified as O9.7 IV by Sota et al. (2014) which probable shows emission lines.
• HD 217792: a metal-weak binary system (Gray & Garrison, 1989) with a debris disk (Chen
et al., 2014).
Only six bona-fide CP1 objects (the references of the classification are listed below) with a
significant positive ∆a values were found:
• HD 34435: Jaschek & Jaschek (1960)
• HD 116235: LeBlanc et al. (2015)
• HD 196425: Abt et al. (1979)
• HD 196655: Bidelman (1985)
• HD 204541: Bertaud (1970)
• HD 209845: Gray et al. (2003)
These stars are good candidates to search for an organized and stable stellar magnetic field in
CP1 objects.
Besides HD 68161 and HD 225253 which are discussed in Sect. 11, six He-peculiar objects
(HD 36668, HD 37210, HD 37642, HD 44953, HD 90264, and HD 174638), and only one marginal
CP3 star (HD 34719) are listed in Table 11. The latter is a very peculiar object with a strong
magnetic field (Kudryavtsev et al., 2006).
As expected, the large majority of objects (275) with significant positive ∆a values are CP2
stars. They are included in RM09 but not marked as “well established”. These objects are
obviously magnetic CP stars (Sect. 14.9.2). Although several of these stars have already been
assigned to the CP2 group, the results can be seen as further proof of membership.
11.11 Comparison with the Geneva ∆(V 1 − G) and Z indices
These two indices (∆(V 1 − G) and Z) are described in Section 4. Let us recall that Z is only
useful defined for stars hotter than A0.
The samples for all star groups including the normal type objects as described before (Table
10) were taken and searched for all objects with available Geneva photometry in the General
Catalogue of Photometric Data (GCPD, Mermilliod et al., 1997). In the following, only stars
62
were included in the analysis for which both, ∆a and Geneva photometry, is available. The
detection limit for the ∆a photometric system was set to ±15 mmag which is a very conservative
value based on the statistics listed in Sect. 11.1.
Hauck & North (1982) concluded that apparent normal stars have mean ∆(V 1−G) values of
−5 mmag and are not uniformly distributed around zero. Therefore, first it was checked if this
offset is also visible for the sample as defined in Section 11.1. In total, 635 stars are included
in this sample. As for the ∆a photometry, the ∆(V 1 − G) values were binned according to
their (b − y)0 values (−0.125 < (b − y)0 < +0.315 mag) with a bin size of 20 mmag. Only very
few normal type stars exceed ∆(V 1 − G) > +2 mmag, whereas many normal type objects have
values lower than −10 mmag with a mean value of −7.3 mmag for the complete sample. The
mean value of σ in the complete interval is 4(1) mmag. Therefore, significance limits of +5 and
−19 mmag for ∆(V 1 − G) and the complete range were taken.
For Z, only the range −0.125 < (b − y)0 < −0.005 mag (approximately stars hotter than A0)
was investigated in the same way. The mean value was determined as +1.3 mmag with a mean
value of σ of 4(1) mmag which yields a detection limit of ±12 mmag. One has to keep in mind
that the sign of Z is opposite which means that CP stars have significant negative Z values.
Table 12 shows the results according to the defined detection limits and the samples.
The incidence of apparent normal type stars which are still outside the detection limits is
comparable low (1 to 3%).
The ∆a and ∆(V 1 − G) indices are able to detect all investigated star groups with more or
less the same statistical significance. The slope for the complete sample of CP2 stars in a ∆a
versus ∆(V 1 − G) diagram is +0.73(5) and a zero point of −7(2) mmag as well as −0.88(6) for
Z, respectively.
For λ Bootis stars the detection capability is similar to that of ∆a. But for the Be/shell
stars, the ∆(V 1 − G) and Z indices are even more sensitive.
12 An empirical temperature calibration for the ∆a photometric
system
One of the most important observational diagnostic tools of astrophysics is the HRD allowing
to study the correlation between the effective temperature and the absolute magnitude (or luminosity)
of astronomical objects. Virtually all stellar astrophysical models are tested according
to the HRD.
The absolute magnitudes of stellar objects can be derived directly via parallax measurements,
appropriate photometric indices (e.g. Strömgren β) or on a statistical basis in open and globular
clusters. The errors of such combined estimates are already rather small (< 0.1 mag).
As a consequence, an empirical effective temperature calibration of main sequence, luminosity
class V to III B-, A- and mid F-type stars for the ∆a photometric system is established. It
provides the index (g1 − y) which shows an excellent correlation with (B − V ) as well as (b − y)
and can be used as an indicator for the effective temperature. This is supplemented by a very
accurate colour-magnitude diagram, y or V versus (g1 − y), which can be used, for example, to
determine the reddening, distance and age of an open cluster.
A division between the calibration for B-type and cooler stars was done because of the
widely different available reddening free and temperature sensitive indices in the the Strömgren
uvbyβ, Geneva 7-colour, and Johnson UBV systems. In addition, for B-type stars: 1) there are
reddening free parameters available allowing to check the dereddening procedure for (g1 − y)
and 2) the stellar interiors for these objects are very similar over the whole spectral range. For
A-type to early F-type objects, on the other hand, calibrations have to be more sophisticated
due to the increase of line blanketing and luminosity effects.
63
Table 12: A comparison of the detection capability of the ∆a and Geneva ∆(V 1−G), as well as
Z indices for the objects with available Geneva 7-colour photometry. No objects of the CP1 and
λ Bootis group are within the range of valid Z values (defined for stars hotter than A0). One
has to keep in mind that the sign of Z is opposite which means that CP stars have significant
negative Z values.
Ntot N∆(V 1−G) N∆a N∆(V 1−G) N∆a
− + − + [%] [%]
CP1 28 − 1 − 1 4 4
CP2 129 2 101 − 110 80 85
CP3 16 − − − − − −
CP4 13 − 4 − 5 31 38
I/II 29 2 − − 2 7 7
λ Boo 17 11 − 12 − 65 71
Be 59 1 2 1 1 5 3
normal 635 7 3 4 1 2 1
Ntot NZ N∆a NZ N∆a
− + − + [%] [%]
CP2 78 71 − − 71 91 91
CP3 15 − − − − − −
CP4 13 3 − − 5 23 38
Be 59 5 4 1 1 16 3
normal 354 5 4 1 − 3 1
The photometric calibration of effective temperatures is still a very tricky business with several
pit falls. The applied calibrations do severely depend on the investigated spectral range and
the physics introduced in the models. Smalley & Kupka (1997) give an excellent overview of
how convection, for example, can lead to significant deviations for A-type and cooler stars. The
statistical calibration of effective temperatures via photometric indices has been done since the
introduction of photometric systems (Johnson, 1958; Strömgren, 1966, and references therein).
The applied calibrations become more precise and sophisticated as the theoretical stellar atmospheres
and the input physics became more realistic. Furthermore, the amount of available
photometric and spectroscopic data increases constantly.
With the established intrinsically consistent, empirical, effective temperature calibrations for
B-type to mid F-type stars, it is now possible to study individual objects in very distant galactic
open clusters and extragalactic systems.
12.1 The B-type stars
In Sect. 14, a synthetic photometric ∆a system is established which confirmed the observed
dependency of the a index as a function of various colour indices sensitive to the effective temperature
and surface gravity variations within the Strömgren uvbyβ and Johnson UBV photometric
systems using fluxes from ATLAS9 model atmospheres as well as most recent atomic
line data together with opacity distribution function for individual chemical compositions. Furthermore,
in Sect. 13 isochrones are presented, taking into account mass loss during the main
sequence evolution on the basis of modern equations of state including partial ionization through
Saha’s approximation, the pressure of gas and radiation as well as the equations for degenerate
64
4.0 4.5 5.0 5.5 6.0 6.5 7.0
0
10
20
30
40
50
60
Numberofstars
V [mag]
-0.28 -0.24 -0.20 -0.16 -0.12 -0.08 -0.04
0
10
20
30
40
50
60
(B - V)
0
[mag]
Numberofstars
Figure 25: The distribution of Johnson V and (B − V )0, see Sect. 12.1.2, for the sample of 225
main sequence B-type objects.
electrons.
As next step, an empirical effective temperature calibration for main sequence (luminosity
class V to III) stars in terms of (g1 −y)0 is established. This is most important for studying very
distant galactic open clusters and extragalactic systems for which, in general, no photometric
data within a standard system are available. The absolute magnitudes and thus luminosities
can be easily estimated via y and the appropriate isochrones.
For the empirical temperature calibration, a homogeneous sample of bright (V < 7 mag),
apparently normal type objects, from Section 10 was taken. In total, 225 stars were used to
derive effective temperatures within the Strömgren uvbyβ, Geneva 7-colour and Johnson UBV
systems which were then applied to establish a calibration in terms of (g1 − y)0. The final
calibration is valid for effective temperatures between 33 000 and 10 000 K and yields a statistical
mean error of 238 K for the whole spectral range.
12.1.1 Sample of program stars
The “normal” B-type objects were selected fulfilling the following criteria:
• classification as B-type, luminosity class V to III
• no significantly deviating ∆a values, i.e. ±10 mmag
• not listed in the catalogue of Ap and Am stars by Renson & Manfroid (2009, RM09)
65
• available data within the Johnson, Strömgren, Geneva, and ∆a photometric system
Binary systems of all kinds and high v sin i stars were a-priori not excluded. The Johnson,
Geneva, and Strömgren colours were taken from the General Catalogue of Photometric Data
(Mermilliod et al., 1997, GCPD). The ∆a photometry is from Section 10.
The following stars have inconsistent photometric measurements and were therefore excluded:
HR 345, HR 1375, HR 1617, HR 2870, HR 3470, HR 8854, and HR 8887. From the available
data, it was not possible to decide if measurement errors, a wrong identification or a binary
nature causes these discrepancies.
The final list comprises 225 objects that satisfy the criteria. The complete list of program
stars is only available in electronic form. This table includes the identification of objects, the (g1−
y)0, (B−V )0, X and (u−b) values, V magnitudes, effective temperature with the corresponding
errors (Sect. 12.1.3), v sin i values, and spectral types, respectively.
The distribution of Johnson V and (B − V )0, see Sect. 12.1.2 for the estimation of the
reddening, for the sample is shown in Figure 25. The peak of the (B − V )0 values is at about
−0.10 mag (B8, Table 13) which reflects the coincidence that the CP stars which were measured
within the ∆a photometric system peak also at this effective temperature (Schneider, 1993) and
the normal type objects, used in this investigation, served as standard stars.
12.1.2 The estimation of the reddening
The reddening for B-type stars within the solar neighbourhood is, in general, estimated using
photometric calibrations in the Strömgren uvbyβ (Crawford, 1978) and the Q parameter within
the Johnson UBV system (Johnson, 1958). These methods are only based on photometric
indices and do not take into account any distance estimates via parallax measurements.
The reddening in the Strömgren uvbyβ photometric system is based on the comparison of
the reddened (b − y) and c1 with the unreddened (u − b) and β indices (Crawford, 1978). The
procedure of the Q method is straightforward and has been described in much details by Johnson
(1958). Here are the basic correlations from this reference:
Q = (U − B) − 0.72 · (B − V ) (12)
E(B − V ) = (B − V ) − 0.332 · Q (13)
Throughout these sections, the following relation is used: AV = 3.1E(B − V ) = 4.3E(b − y).
Figure 26 shows the comparison of the derived AV values for both methods. The agreement
is very good indicating that photometric measurements within the Johnson and Strömgren
systems are intrinsically consistent. Otherwise, a severe deviation from the linear correlation
would occur. The distribution of the adopted values (mean of both methods) shows that most
of the program stars have an absorption which is below 0.1 mag.
However, the interstellar reddening was also derived using the model proposed by Chen et
al. (1998) who combined galactic reddening maps, which are derived from open clusters as well
as from galactic field stars with published empirical reddening laws from the literature. As
input parameters, the galactic coordinates and the distance from the Sun (i.e. derived from
Hipparcos parallax measurements) are needed. The error of the latter severely influences the
error of the derived reddening. For program stars with distance errors smaller than 15%, a very
good agreement with the results of the photometric calibrations has been found.
12.1.3 The calibration of the effective temperature
To reach the final goal, an empirical effective temperature calibration of (g1 − y)0 for B-type
stars, this astrophysical parameter was calibrated for the sample using the published calibrations
in the Geneva, Strömgren, and Johnson photometric systems. Those calibrations are, in general,
66
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
20
40
60
80
Numberofobjects
AV
(adopted) [mag]
AV
(Q)[mag]
AV
(uvby ) [mag]
Figure 26: The correlation of the absorption AV estimated from the Strömgren uvbyβ and the
Q method (upper panel). The statistical error for both methods is indicated with the symbol
in the lower left corner. The distribution of the adopted AV values is shown in the lower panel.
derived independently from each other which allows to detect possible inconsistencies due to,
for example, spectroscopic binaries. The applied calibrations are now discussed in more details.
Geneva system: detailed calibrations were published by Cramer (1984, 1999); Künzli et al.
(1997). They are all based on the reddening free parameters X and Y which are valid for
spectral types hotter than approximately A0. The results are therefore independent of the
estimation of AV for the program stars.
Strömgren system: the most recent and widely used reference is Napiwotzki et al. (1993). For
stars hotter than 11000 K, the unreddened [u − b] and for cooler B-type objects, the a0 index
are used to calibrate the effective temperature. The latter is not reddening free.
Johnson system: first of all, the Q values for luminosity class III and V objects were calculated
according to the Tables listed by Schmidt-Kaler (1982). The (B−V )0 values for those luminosity
classes were transformed into effective temperatures using the results by Code et al. (1976, Table
7). As final correlation a polynomial fit for dependence of the effective temperature on Q is
derived as
log Teff = 3.983(5) − 0.31(3) · Q + 0.33(3) · Q2
(14)
which is valid for all B-type, luminosity class III to V objects. This relation has to be treated as
an averaged statistical result. If one uses the individual measurements from Code et al. (1976)
for the ten stars that are in the relevant effective temperature and luminosity regime (Sect.
67
0.0 0.2 0.4 0.6 0.8 1.0 1.2
10000
15000
20000
25000
30000
35000
Teff
[K]
(u - b) [mag]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
X [mag]
-0.30 -0.25 -0.20 -0.15 -0.10 -0.05
10000
15000
20000
25000
30000
35000
Teff
[K]
(B - V)
0
[mag]
-0.10 -0.08 -0.06 -0.04 -0.02
(g
1
- y)
0
[mag]
Figure 27: Mean relation between the effective temperature and (u − b), X, (B − V )0 as well as
(g1 − y)0 for B-type, luminosity class V to III objects.
12.1.1), the following relation is derived:
log Teff = 3.994(29) − 0.25(15) · Q + 0.38(15) · Q2
(15)
A comparison of these two relations gives ∆Teff = +141(147) K.
The individual effective temperature values within each photometric system were first checked
for their intrinsic consistency and then averaged. These final values together with the standard
deviations of the means are listed in the electronically available table. No outliers in any photometric
system were detected.
12.1.4 The calibration procedure for the ∆a photometric system
The starting point is one set of (g1 − y) measurements, for example, of an open cluster. Here
one faces the first problem because the zero points of data sets from different instruments and
filter systems may vary. An overview of several used ∆a filters is listed in Section 10.
First of all, the reddening coefficient k of the relation E(g1 −y) = k ·E(B −V ) was estimated
which can then be transformed to other photometric systems. The correlation coefficients for
(B − V ) versus (g1 − y) are derived and then applied to (B − V )0 using the estimated reddening
for each individual star as well as (g1 − y) to derive (g1 − y)0 and thus E(g1 − y). The final
value, k = 0.39(2) is in excellent agreement with those values derived from open cluster data.
As next steps, the individual indices are dereddened and the linear correlations between
those parameters are established. A “standard (g1 − y) system” is defined which is set to
68
-1000
-500
0
500
1000
Teff
[K]
(u - b) X
0 100 200 300 400
-1000
-500
0
500
1000 (B - V)
0
Teff
[K]
v sin i [km s
-1
]
0 100 200 300 400
(g
1
- y)
0
v sin i [km s
-1
]
Figure 28: No systematic correlation of ∆Teff and the v sin i values were found for (u − b), X,
(B−V )0 as well as (g1 −y)0. The well-known effect of the rotational velocity on the photometric
indices is therefore less significant than the precision of the method itself.
(B − V )0 = (b − y)0 = (g1 − y)0 = 0 as following:
(B − V )0 = −1.413(7) + 2.82(1) · (g1 − y)0 (16)
(b − y)0 = −0.664(5) + 1.333(9) · (g1 − y)0 (17)
This system was also kept for the the calibration of the A-type to early F-type stars (Sect. 12.2).
Figure 27 shows the relation between the effective temperature and the different temperature
sensitive indices for the four investigated photometric systems. The temperature range from
approximately 33 000 to 10 000 K which covers the main sequence B-type stars. However, there
are only four stars with temperatures hotter than 25 000 K (B1.5 V). The temperature relations
were checked with and without those four data points and no significant differences were found.
The final calibrations are given as:
log Teff = +4.520(3) − 0.754(15) · (u − b) + 0.413(2) · (u − b)2
− 0.108(11) · (u − b)3
(18)
= +4.546(3) − 0.698(13) · X + 0.367(17) · X2
− 0.092(6) · X3
(19)
= +3.956(5) − 1.04(7) · (B − V )0 + 2.89(24) · (B − V )2
0 (20)
= +3.909(7) − 6.47(48) · (g1 − y)0 − 47(9) · (g1 − y)2
0 − 425(60) · (g1 − y)3
0 (21)
with the mean of the errors for the whole sample of ∆Teff[(u − b), X, (B − V )0, (g1 − y)0] =
[157,146,333,238 K]. These are statistical errors and should be treated as such. The mean relations
between the effective temperature and (B − V )0, (u − b), X as well as (g1 − y)0 depending
on spectral types are listed in Table 13. The agreement with standard values for those indices
from the literature (Code et al., 1976; Crawford, 1978; Cramer, 1999) is excellent.
69
Table 13: Mean relation between the effective temperature and (B − V )0, (u − b), X as well as
(g1 − y)0 for B-type, luminosity class V to III objects.
Spec. Teff (B − V )0 (u − b) X (g1 − y)0
B0 32000 −0.292 0.020 0.060 −0.102
B1 26000 −0.257 0.151 0.210 −0.090
B2 23000 −0.236 0.239 0.310 −0.082
B3 18000 −0.189 0.448 0.557 −0.065
B5 16000 −0.164 0.570 0.705 −0.056
B6 14500 −0.142 0.688 0.850 −0.049
B7 13500 −0.125 0.785 0.970 −0.043
B8 12500 −0.105 0.901 1.113 −0.036
B9 10800 −0.064 1.155 1.411 −0.021
(A0) 9800 −0.031 1.338 1.603 −0.011
It is known that high rotational velocities can alter the photometric indices significantly
(Collins et al., 1991). The break-up velocity ranges from about 540 to 400 kms−1 for B0 to B9
stars (Townsend et al., 2004). However, the inclination i is the crucial point for the comparison
of these models with observations. One only has to recall the case of the prototype A0 star Vega
that has a very low v sin i of 22 kms−1 but an equatorial velocity of 160 kms−1 (Hill et al., 2010).
The papers by Glebocki & Stawikowski (2000); Abt et al. (2002) were searched for available v sin i
values for the program stars, and averaged individual measurements from the different sources.
In total, there are measurements for 175 stars of the sample available with the highest value of
390 kms−1 for HR 3502. Figure 28 shows the diagrams of ∆Teff = Teff(orig) −Teff(calib) versus
v sin i for the different indices. There is no obvious correlation between these two parameters
in any of the diagrams evident. The effect of the rotational velocity is therefore less significant
than the precision of the method itself. Or in other words, the well-known alteration of stellar
colours caused by high rotational velocities (Collins et al., 1991) cannot be distinguished from
the overall statistical errors resulting from the calibration process.
The overall procedure of deriving the effective temperatures for main sequence B-type objects
in the ∆a photometric system should be as following:
• Estimate the reddening, for example via isochrones for open cluster members
• E(g1 − y) = 0.39 · E(B − V )
• Apply the reddening correction for all individual indices
• Transform the (g1 − y)0 via the standard relations
• Check the intrinsic consistency of all available measurements according to the spectral
type - effective temperature - photometric indices correlation
• Apply the effective temperature calibration
The estimated effective temperature from the ∆a system can in addition compared with calibrated
values from other photometric indices.
12.2 The A-type and mid F-type stars
Here, the A-type to mid F-type objects are investigated that exhibit an increase line blanketing
and luminosity effects without the availability of any a-priori reddening-free parameter. Only
70
3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
0
10
20
30
40
50
60
70
Numberofstars
V [mag]
-0.1 0.0 0.1 0.2 0.3 0.4
0
10
20
30
40
50
Numberofstars
(B - V)
0
[mag]
Figure 29: The distribution of Johnson (B −V )0 (lower panel) and V (upper panel) for the used
sample of 282 main sequence A- to mid F-type objects. The distribution of (B − V )0 shows two
maxima at spectral types of about A0 and F0.
Strömgren β does, in general, not depend on the extinction. However, it is sensitive not only
to the effective temperature alone but also to the luminosity (Gerbaldi et al., 1999). Based on
the methods used in Sect. 12.1, the following parameters were used for this purpose: (b − y)0,
(B2 − V 1)0, and (B − V )0. The scatter of the derived effective temperatures for spectral types
between A0 and A3 is not larger than that for later type stars because the sample of bright
galactic-field stars is almost free of reddening.
Applying the same selection criteria as for the B-type stars (Sect. 12.1.1) yields 282 luminosity
class V to III A-type to mid F-type objects. The derived mean errors for the effective
temperature calibrations within all photometric systems are smaller than those for the B-type
stars.
12.2.1 Sample of program stars
The selection criteria and the sources of photometry for the A-type to mid F-type objects are
exactly the same as listed in Section 12.1.1.
The final list includes 282 objects. This table includes the identification of objects, the
complete Strömgren uvbyβ, (g1 −y)0, (B −V )0, and (B2−V 1)0 values, V magnitudes, E(b−y)
values, effective temperature with the corresponding errors, v sin i values, and spectral types,
respectively.
The distribution of Johnson V and (B − V )0 for the sample is shown in Figure 29. The
estimation of the reddening is explained in more detail in Section 12.2.2. The distribution of V
is comparable to the one for the B-type sample peaking at V = 6.25, mag, whereas the one for
71
(B − V )0 exhibits two maxima at spectral types of about A0 (+0.0 mag) and F0 (+0.3 mag, see
also Table 14). However, there is a statistically significant number of objects in the complete
investigated spectral range.
12.2.2 The estimation of the reddening
The sample comprises stars later than a spectral type of A0. A typical A0 main sequence object
has a mean absolute magnitude of about +0 mag. A visual magnitude of 7 mag (Fig. 29) then
corresponds to a distance of 250 pc, for which the reddening can be almost neglected in all
directions (Neckel et al., 1980).
The following photometric calibrations in the Strömgren uvbyβ system were used to estimate
the reddening according to the valid spectral range that is estimated by the standard relations
of the different indices:
• A0 − A3: Crawford (1978); Hilditch et al. (1983)
• A3 − F0: Crawford (1979); Domingo & Figueras (1999)
• later than F0: Crawford (1975); Schuster & Nissen (1989)
The calibrations are not very reliable for stars with spectral types between A0 and A3 (Gerbaldi
et al., 1999), mainly because for these stars, the reddening-free parameter β is no longer a
temperature indicator alone but is also sensitive to the luminosity, therefore the standard relation
of (b−y)0 versus m0 as listed by Hilditch et al. (1983) and their method of calibration were used.
Only some objects that fall outside the given relation were dereddened using the calibration by
Crawford (1978).
Furthermore, the interstellar extinction model by Chen et al. (1998) used to derive the
reddening for all program stars as described in Section 12.1.2. The values from the calibration
of the Strömgren uvbyβ and the model by Chen et al. (1998) agree very closely. As expected,
all objects have a calibrated total absorption AV of less than 0.35 mag with 233 (82% of the
complete sample) stars even lower than 0.05 mag. Taking the following relations into account:
AV = 3.1E(B − V ) = 4.3E(b − y) = 4.95E(B2 − V 1) = 7.95E(g1 − y), (22)
the effect of the reddening on the calibration for the sample can be neglected and does not
introduce a significant error source.
12.2.3 The calibration of the effective temperature
As for the B-type sample, the first step was to derive the effective temperature for each individual
star within the Geneva, Strömgren, and Johnson photometric systems. For this purpose the
reddening relations as listed in Eq. 22 was used to calculate the unreddened indices that are
necessary to make the proper calibration as listed.
Geneva system: the calibration by Künzli et al. (1997) is the most recent for the investigated
spectral range. For intermediate stars hotter than 8500 K, they used the parameters pT and pG,
which are linear combinations of the seven Geneva colors. Those two indices can be dereddened
with the following relations: pT0 = pT − E(B2−V 1) and pG0 = pG − 1.1E(B2−V 1). For cooler
objects, the grids of m2 and d versus (B2 − V 1)0 served as a calibration tablet. The definition
of these indices are listed in Golay (1994).
Strömgren system: Napiwotzki et al. (1993) investigated several calibrations based on a0 and r∗
for hotter, as well as β, and c0 for cooler objects yielding a rather unsatisfactory result. Finally,
they established a Teff versus (b − y)0 relation (Eq. 10 therein), which was applied to sample
here.
72
-0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30
6000
7000
8000
9000
10000
11000
Teff
[K]
(b - y)
0
[mag]
-0.18 -0.12 -0.06 0.00 0.06 0.12 0.18 0.24
(B2 - V1)
0
[mag]
-0.1 0.0 0.1 0.2 0.3 0.4
6000
7000
8000
9000
10000
11000
Teff
[K]
(B - V)
0
[mag]
-0.03 0.00 0.03 0.06 0.09 0.12 0.15 0.18
(g
1
- y)
0
[mag]
Figure 30: Mean relation between the effective temperature and (b − y)0, (B2 − V 1)0, (B − V )0,
as well as (g1 − y)0 for A-type to mid F-type, luminosity class V to III objects.
Johnson system: the semi-empirical Teff versus (B − V )0 relation as listed in Gray (2008, Eq.
15.14) was used. It is based on synthetic colours from theoretical stellar atmospheres that are
normalized to observations of spectroscopic binary systems, as well as bright stars. It is given
as
log Teff = + 3.988 − 0.881(B − V )0 + 2.142(B − V )2
0 − 3.614(B − V )3
0 +
+ 3.2637(B − V )4
0 − 1.4727(B − V )5
0 + 0.2600(B − V )6
0 (23)
and is valid for all A-type to mid F-type, luminosity class III to V objects. It superseded the
relation listed in Code et al. (1976).
The individual effective temperature values for the three photometric systems were first
tested for their intrinsic consistency and then averaged. No statistical significant outliers in any
photometric system were detected.
12.2.4 The result for the ∆a photometric system
The relation between the mean effective temperature and the different temperature sensitive
indices for the four investigated photometric systems is shown in Figure 30. The errors are
constant over the complete spectral range. There is a larger scatter only for the Geneva (B2 −
V 1)0 index at effective temperatures hotter than 9000 K. This region was checked with the grids
of pT0 and pG0 originally used. It is exactly where both indices become zero for the Main
Sequence and small shifts result in larger uncertainties. It therefore seems to be an intrinsic
73
numerical problem of the grids themselves; however the overall statistical error of (B2 − V 1)0
is satisfying. The final calibrations parameterized as third-degree polynomials are:
log Teff = + 3.9793(4) − 1.34(2) · (b − y)0 + 4.90(15) · (b − y)2
0 − 8.06(38) · (b − y)3
0 (24)
= + 3.8853(4) − 0.459(5) · (B2 − V 1)0 + 1.02(2) · (B2 − V 1)2
0 −
− 2.36(16) · (B2 − V 1)3
0 (25)
= + 3.9825(4) − 0.670(10) · (B − V )0 + 1.05(7) · (B − V )2
0 −
− 0.98(12) · (B − V )3
0 (26)
= + 3.9817(8) − 1.79(5) · (g1 − y)0 + 8.14(77) · (g1 − y)2
0 − 19(3) · (g1 − y)3
0 (27)
with the mean of the errors for the whole sample of ∆Teff[(b−y)0, (B2−V 1)0, (B−V )0, (g1−y)0] =
[66,100,71,134 K]. These are statistical errors for the complete sample. The errors for individual
stars are, of course, larger than that. Note that the error for the Johnson (B − V )0 calibration
is surprisingly small. It shows the overall robustness of broad-band indices against metallicity
and luminosity effects, which makes them superior for statistical analysis of larger samples over
a wide spectral range. However, it has to be emphasized that it is a-priori not possible to apply
dereddening methods in the Johnson UBV system for stars cooler than B9 (Johnson, 1958).
The statistical error for (g1 − y)0, 134 K, is significantly smaller than the one for the hotter
stars (238 K). But one has to keep in mind that the absolute errors are over the complete spectral
range from early B-type to F-type constant, but only the relative one, as listed, is decreasing.
Table 14 lists the mean relations between the effective temperature and (B − V )0, (b − y)0,
(B2 − V 1)0, as well as (g1 − y)0, depending on spectral types. Only standard spectral types of
the Yerkes system (Jaschek & Jaschek, 1990) are given. The (B−V )0 and (g1 −y)0 values for A0
are, within the error limits, identical to those derived for the B-type sample, which guarantees
an intrinsic consistent calibration from B0 to F5 for the ∆a photometric system.
The effect of high v sin i objects on the derived calibrations was checked in the same manner
as described in Section 12.1.4. This might be an issue for early A-type objects only because
the rotational velocities decrease significantly for cooler objects (Zorec & Royer, 2012). Again,
no statistical significant effect of the rotational velocity, which can be distinguished from other
error sources, was found on the precision of the calibration.
The detailed calibration procedure for determining the effective temperature within the ∆a
photometric system is given in Section 12.1.4. Here, only a short overview of the main method
is given. After the estimation of the reddening E(g1 −y), the dereddened standard (g1 −y)0 has
to be calculated and the calibration for the appropriate spectral region applied. As a final check,
a comparison with the values for other photometric systems, if available, should be performed.
13 Theoretical isochrones for the ∆a photometric system
Theoretical isochrones for the photometric ∆a system were calculated to derive astrophysical
parameters such as the age, reddening, and distance modulus for star clusters. Using the stellar
evolutionary models by Claret (1995), a grid of isochrones with different initial chemical compositions
for the ∆a system was generated. The data of 23 open clusters (Sect. 17) were used to
fit these isochrones with astrophysical parameters (age, reddening, and distance modulus) from
the literature. As an additional test, isochrones with the same parameters for Johnson UBV
data of these open clusters were also considered. The fits show a good agreement between the
observations and the theoretical grid. The accuracy of fitting isochrones to ∆a data without the
knowledge of the cluster parameters is between 5 and 15 %.
74
Figure 31: Theoretical relationship between (g1 − y)0 and the effective temperature for models
with solar abundance, vt = 2 kms−1, l/Hp = 1.25 and log g = 4.5 dex. For models with Teff ≤
8500 K, an alternative theory of convection was adopted.
75
Figure 32: The empirical (g1 − y)0 and (B − V )0 data and the respective theoretical predictions
(continuous line). The theoretical value was obtained by averaging the whole grid of stellar
atmosphere models.
76
-0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
MV
[mag]
g1
- y [mag]
7.0
7.5
8.0
8.5
9.0
9.5
Figure 33: Theoretical isochrones for different ages and solar abundance for the evolutionary
models described in Section 13.1.
Figure 34: Isochrones for NGC 6611 and NGC 6705 with the parameters listed in Table 15.
77
Table 14: Mean relation between the effective temperature and (B − V )0, (b − y)0, (B2 − V 1)0,
as well as (g1 − y)0 for A-type to mid F-type, luminosity class V to III objects. Only spectral
types according to the Yerkes system (Jaschek & Jaschek, 1990) are listed.
Spec. Teff (B − V )0 (b − y)0 (B2 − V 1)0 (g1 − y)0
A0 10000 −0.025 −0.015 −0.160 −0.010
A2 8750 +0.067 +0.031 −0.093 +0.025
A3 8300 +0.112 +0.055 −0.060 +0.042
A5 7900 +0.161 +0.082 −0.024 +0.062
A7 7500 +0.221 +0.120 +0.022 +0.087
F0 7050 +0.304 +0.185 +0.087 +0.125
F2 6750 +0.368 +0.238 +0.141 +0.155
F3 6650 +0.390 +0.254 +0.159 +0.165
F5 6450 +0.433 +0.284 +0.196 +0.184
Table 15: 23 published open clusters with ∆a CCD photometry taken from Section 17. The
metallicity for all clusters is (within the errors) solar according to DAML02 (Dias et al., 2002).
Cluster log t mV − MV E(B − V ) NStars Cluster log t mV − MV E(B − V ) NStars
Collinder 272 7.20 13.06 0.47 111 NGC 6134 8.97 11.07 0.40 102
Lyngå 14 6.71 14.29 1.48 (var) 53 NGC 6192 7.95 13.00 0.68 98
Melotte 105 8.30 12.70 0.36 114 NGC 6204 7.60 11.50 0.43 319
NGC 2099 8.50 11.67 0.30 41 NGC 6208 9.00 10.54 0.18 41
NGC 2169 7.70 10.57 0.12 13 NGC 6250 6.50 11.18 0.38 48
NGC 2439 7.20 14.23 0.41 113 NGC 6396 7.20 13.34 0.96 (var) 105
NGC 2489 8.45 12.00 0.40 59 NGC 6451 8.13 13.74 0.67 146
NGC 2567 8.43 11.40 0.13 50 NGC 6611 6.90 13.72 0.86 (var) 79
NGC 2658 9.10 11.67 0.04 55 NGC 6705 8.30 12.73 0.43 312
NGC 3114 8.10 10.02 0.07 271 NGC 6756 8.10 14.67 0.80 65
NGC 3960 8.80 12.74 0.30 93 Pismis 20 6.60 15.30 1.24 (var) 238
NGC 5281 7.10 11.35 0.26 30
13.1 Models, data selection, and isochrone fitting
The stellar models used to calculate the isochrones have been described in more detail by Claret
(1995). Here a short overview of the input physics is given. The chemical composition is (X, Z)
= (0.70, 0.02) though different combinations of X and Z can also be used following the metallicity
indicator of each cluster. The equation of state takes into account partial ionization through
Saha’s approximation, the pressure of gas and radiation as well as the equations for degenerate
electrons. For less massive stars, a special treatment of the equation of state was adopted
through the CEFF package (Däppen, 2000). Radiative opacities were computed with the OPAL
code. The mixing length theory was used to describe convection and moderate overshooting
with αov = 0.2 was considered for convective cores. The models take into account mass loss
during the main sequence as well as during the red giant phase.
The filter transmission functions of g1 and y are the same as those used in Section 14. Synthetic
colour calculations were performed using the properties of the mentioned filters, in order
to establish the connection between observed and theoretical quantities. A similar procedure as
described by Castelli (1999) was adopted. The original ATLAS9 models Kurucz (1993), with a
microturbulence velocity of 2 kms−1, −5.0 ≤ log [M/H] ≤ +1, and mixing-length parameter α
= 1.25 were the basic tools to derive the synthetic colours. For Teff ≤ 8500 K, the calculations
listed in Sect. 14 were adopted due to problems detected in the convection model, precisely
in the specific intensities (Claret, 1995). These models were computed adopting the Canuto &
78
Mazzitelli (1991) prescription. The implementation of this alternative theory of transport of
energy by convection does not significantly affect the hotter models, as expected. In fact, the
differences in the respective colour indices are of the order of 1 to 3 mmag, as described and
calculated in Section 14. As an example of synthetic colour calculation, Fig. 31 shows the dependence
of (g1 − y)0 with the effective temperature for models with log g = 4.5 dex. Similar results
are obtained for different values of log g, microturbulent velocities and/or metallicity. Figure 32
shows a comparison between empirical data and theoretical colour indices. The continuous line
indicates the average of all theoretical models (in log g). The zero-point was corrected by adding
0.31 to the theoretical (g1 − y) values. The final isochrones, considering the adequate values of
log g for each class of luminosity, are shown in Fig. 33 for different ages from log t = 7.0 to 9.5,
respectively.
In Sect. 14 it is shown that metallicities different from solar values shift the normality line
by about 3 to 6 mmag for [Z] = ±0.5 dex. Such an effect is, in general, a factor of two smaller
than the intrinsic measurement errors and not detectable. Nevertheless, the DAML02 database
Dias et al. (2002) was searched through for available metallicities of the open clusters listed
in Table 15. For none of the investigated clusters, a value significant different than solar was
found within the given error. Therefore it is expected that all programme clusters have solar
metallicity.
The published ∆a CCD photometry together with the Johnson UBV ones of 23 open clusters
(Sect. 17) was taken to test these isochrones. These open clusters have widely different ages
and reddening which makes them excellent test cases (Table 15).
The isochrone fitting was performed in two steps. First, the (g1 − y) values were dereddened
according to E(g1 − y) = 0.4 · E(B − V ) and an individual isochrone was calculated according
to the ages (taken from the literature) listed in Table 15. The data were then plotted with the
appropriate distance modulus. In order to test the parameters from the literature, the same
procedure was performed for Johnson UBV colours. Figure 34 shows the examples of NGC
6611 and NGC 6705 for both photometric systems, respectively. The isochrones fit, in general,
the data very well.
As second step, the ∆a data were fitted to the isochrones without an a-priori knowledge of
the reddening, age and distance modulus. Here the same problems and error sources are evident
as for the classical photometric systems since no colour-colour diagram is available. Nevertheless,
it was possible to reproduce the parameters from the literature with an accuracy between 5 and
15 % depending on the age, available giant members and the presence of differential reddening.
14 Synthetic ∆a photometry
A synthetic photometric system was developed which can be used to explore the capability of
model atmospheres with individual element abundances. This can be used to predict photometric
∆a magnitudes which measure the extent of the flux depression around 5200Å found in different
types of CP stars (Sect. 6).
One of the main conclusions drawn from the explanation of the 5200Å flux depression (Sect.
8.1) has been the necessity to build specific model stellar atmospheres for CP stars using state-ofthe-art
opacity data. The increase in available computer power and advances in computational
algorithms during the last two decades have now brought this problem into the realm of workstations
and personal computers. Moreover, stellar atmosphere modelling can take advantage
of data bases for atomic line transitions devoted to stellar atmosphere applications such as Kurucz
(1992) and the VALD project (Kupka et al., 1999). Among the current projects for the
computation of model atmospheres there are several which can calculate models with individual
abundances on workstations or personal computers. Two of them are based on an opacity sampling
approach. ATLAS12 by Kurucz (2005), for which applications were presented by Castelli
79
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
4800 5000 5200 5400 5600 5800
relativetransmissivity
λ [Å]
g1
g1 * PMT * mirror
g2
g2 * PMT * mirror
y
y * PMT * mirror
Figure 35: Filter transmission functions and effective transmission of the synthetic photometric
system after convolution with the profiles of the response function of a 1P21 RCA photomultiplier
tube (PMT) and a typical mirror reflection efficiency function. The latter two are taken from
the uvby.for programme of Kurucz (1993).
& Kurucz (1994), is particularly suitable for B- to K-type stars at or close to the main sequence.
The MARCS project in Uppsala (Bengt Gustafsson and his group) is aimed at the cool part
of the HRD and can produce model atmospheres for stars with spectral types later than A0
(Gustafsson et al., 2008). However, for the computation of small grids of model atmospheres
with individual abundances, which are required when varying Teff or log g during the initial
analysis of a single star or several sufficiently similar stars, the opacity distribution function
(ODF) approach remains preferable due to its higher computational efficiency. Piskunov &
Kupka (2001) have presented a new software toolkit based on this approach using a modified
version of the ATLAS9 code of Kurucz (1993). It is suitable for spectral types from early B-type
to early F-type stars at or close to the main sequence.
14.1 The normality line
First, the observed dependency of the a index as a function of various colour indices sensitive
to the effective temperature of stars as well as its average scatter expected from surface gravity
variations within the main sequence band was investigated. The behaviour of the so-called
“normality line” of ∆a systems used in photometric observations of CP stars (Sect. 3) is well
reproduced. The metallicity dependence of the normality line of the ∆a system was computed
for several grids of model atmospheres where the abundances of elements heavier than He had
been scaled ±0.5 dex with respect to the solar value. A lowering of ∆a magnitudes for CP
stars within the Magellanic Clouds by ∼ −3 mmag relative to those in the solar neighbourhood
80
assuming an average metallicity of [Fe/H] = −0.5 dex was estimated. Using these results on the
metallicity bias of the ∆a system one finds the observational systems in use suitable to identify
CP stars in other galaxies or distant regions of our own galaxy and capable to provide data
samples on a statistically meaningful basis.
14.1.1 The synthetic ∆a filter system
Relyea & Kurucz (1978) have discussed in detail how to calculate synthetic colours from model
atmosphere fluxes computed with the ATLAS code. The main idea is to convolve the emergent
surface fluxes predicted from model atmospheres with several functions representing filter transmission,
relative absorption of all other devices in the optical path (including telescope mirrors),
and detector sensitivity.
Figure 35 shows the response functions of the applied synthetic photometric system. The
steep decay of the response function of the 1P21 RCA photomultiplier from 58% at 5000Å to
29% at 5500Å and a mere 10% at 6000Å explains the smaller effective sensitivity of the system
in the y-band relative to the g1-band in comparison with the transmission functions of the filters
themselves. Here it has to be noted that the transmission functions for the g1 and g2 filters were
taken from calibration measurements of one of the filter sets used in earlier observations (System
“2” in Maitzen & Vogt, 1983), while the y filter transmission (difference less than 1 % to that of
Maitzen & Vogt, 1983) and the mirror reflection efficiency and detector response functions were
taken from the uvby code of Kurucz (1993). Maitzen & Vogt (1983) used the response function
of an EMI 6256 photomultiplier for their calibrations which has essentially the same shape but
a different absolute sensitivity as the 1P21 one in the relevant wavelength region. This offset in
the absolute sensitivity does not affect the synthetic magnitudes since only differences between
individual filters were used.
Only photoelectric ∆a measurements (Sect. 10) were used for the comparisons here. However,
there are also a lot of CCD ∆a measurements available by now (cf. Sect. 18). A classical
photomultiplier is almost insensitive at approximately 6000Å whereas a CCD is very sensitive in
the red region. This implies an almost linear increase of the response function from g1 to y. In
the new CCD system, the FWHM of the g1 and y filters are 222Å and 120Å, respectively. This
guarantees that the total flux of each filter after the convolution with the response function is
comparable with that one of the “old” system.
14.1.2 Calibration relations
The overall success of the ATLAS9 model atmospheres of Kurucz (1993) to reproduce photometric
colours and spectrophotometric fluxes of standard stars of spectral types B and A (Castelli &
Kurucz, 1994; Smalley & Dworetsky, 1995; Castelli et al., 1997) and also for some of the CP stars
(Adelman & Rayle, 2000) promotes them as a logical choice when testing a synthetic photometric
system. Several grids of ATLAS9 model atmospheres were computed with the Stellar Model
Grid Tool (SMGT, see Heiter et al., 2002b, for a description) using the line opacities and the ATLAS9
code of Kurucz (1993), unaltered except for the convection treatment (Smalley & Kupka,
1997; Heiter et al., 2002b). In fact, both Smalley & Kupka (1997) and Heiter et al. (2002b) recommend
the use of a convection model in ATLAS9 which predicts inefficient convection for mid
to late A-type stars (Teff 8500 K). Therefore, the model of Canuto & Mazzitelli (1991) were
used which allows a better reproduction of Strömgren colours of A-type stars than the original
models of Kurucz (1993), as shown in Smalley & Kupka (1997). For models with Teff > 8500 K,
where convection has only negligible influence on temperature gradients and colours, our models
are virtually identical to those from the original grids published by Kurucz (1993). Anyway,
a comparison with model atmospheres based on different convection models was done and the
conclusion was drawn that for any of the convection treatments available for ATLAS9 (Castelli
81
0.580
0.585
0.590
0.595
0.600
0.605
0.610
0.615
−0.2 −0.1 0.0 0.1 0.2 0.3 0.4
a[mag]
B−V [mag]
models
models with log(g)=4 dex
fit for models with log(g)=4 dex
(a)
0.580
0.585
0.590
0.595
0.600
0.605
0.610
0.615
0.00 0.05 0.10 0.15 0.20 0.25
a[mag]
b−y [mag]
models
parabolic least square fit
models with log(g)=4 dex
(b)
0.580
0.585
0.590
0.595
0.600
0.605
0.610
0.615
−0.04 −0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
a[mag]
g1−y [mag]
models
models with log(g)=4 dex
fit for models with log(g)=4 dex
(c)
0.580
0.585
0.590
0.595
0.600
0.605
0.610
0.615
0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30
a[mag]
[u−b] [mag]
models
parabolic least square fit
models with log(g)=4 dex
(d)
Figure 36: Temperature and gravity dependence along the main sequence for various observational
indicators of Teff. Colours were computed from ATLAS9 type model atmospheres with
Teff=[7000,15000] K for log g = [3.5,4.5] dex and solar metallicity. For the upper right panel,
models were restricted to (b − y) ≥ −0.02 while for the lower right panel, models were restricted
to [u-b] ≤ 1.38. The zero point of the (g1 − y) colour was set to coincide with the zero point of
(b − y) at a log g of 4 dex (a constant of 0.269 had to be added to the output value of (g1 − y)).
Models with log g of 4 dex have been connected by straight lines to indicate the shape, zeropoint,
and slope of the normality line. For the cooler models (towards the right-hand side within
each panel) the true ZAMS and thus the normality line a0 are located slightly below this line
(cf. Fig. 37). For the left-side panels a cubic least square fit through the log g = 4 dex models
is displayed, while right-side ones include a parabolic fit through all the models displayed.
82
et al., 1997; Heiter et al., 2002b) the a values change only by up to +3 mmag for the coolest
models in the grids and remain completely unaltered for models with Teff > 8500 K. Thus,
no important bias is introduced into our calibration tests by selecting a particular convection
model. The ATLAS9 grids have a spacing of ∆ log g = 0.5 dex which is slightly too coarse
for the purpose. Hence, also intermediate models were included in the computations by using
a spacing of ∆ log g = 0.25 dex. A log g–range from 2.5 dex to 4.5 dex and a Teff–range from
7000 K to 15 000 K (with a spacing of 250 K) was studied. Model atmospheres assuming one of
the following three metallicities were investigated: −0.5, 0, and +0.5 dex, where [M/H] = 0 dex
represents solar abundance and elements heavier than He are scaled by ±0.5 dex in the other
cases. A constant value of 2 km s−1 as in the standard grid of Kurucz (1993) was used for the
microturbulence.
To transform the theoretical colours into the frame of observed colours, Kurucz (1993) corrected
the zero-point of his synthetic uvby system so as to match c1, m1, and (b − y) of Vega.
A similar procedure is necessary to compare calculated a values from the synthetic ∆a system
directly to observations. A value of 0.6 was added to the synthetic a value computed from convolving
the effective transmission functions with the fluxes from ATLAS9 model atmospheres.
The numerical values obtained are then close to (Maitzen & Vogt, 1983, see their Table 1 and
Equation 1). One gets a ∼ 0.594 mag for a main sequence star with (b−y) = 0.000 mag and solar
metallicity from the synthetic photometric system. For the ∆a system itself the specific value of
a and thus any zero-point correction related to it are irrelevant, because the quantity of interest
is the difference of a measured a value to the normality line a0 (Sect. 3). Hence, it is much more
important to show that the synthetic ∆a system recovers the observed dependencies of the ∆a
index from different indicators of effective temperature, surface gravity, and metallicity.
Figure 36 illustrates the temperature (and gravity) dependence of the a index as a function
of various experimental indicators of Teff. For (B − V ) and (g1 − y) the entire temperature
range is displayed while a cut-off was introduced for the other two cases through requiring that
(b − y) −0.02 (i.e. Teff 11 000 K) and [u-b] 1.38 (i.e. Teff 9250 K). Models with
log g = 4 dex have been connected with straight lines to provide a proxy for the normality line
a0 of the synthetic photometric system. Note that the output colours have been rounded to
1 mmag accuracy as in Kurucz (1993). The actual run of the colours is continuous and smaller
magnitude differences can hardly be assigned a real physical meaning within the current state
of modelling.
For the comparison of the synthetic ∆a system to observational ones, the results for Galactic
field stars (Sect. 10) were used. The differences for the ∆a values were found to be in the range
of 2 to 3 mmag. The following relation for the normality line was found:
a0 = G0 + G1(b − y) + G2(b − y)2
(28)
with G0 = 0.594, and where 0.086 < G1 < 0.105 as well as −0.050 < G2 < −0.150 hold for
−0.120 < (b − y) <+0.200 mag. The 1σ level around the normality line was found to be between
2.9 and 5.1 mmag. These values are a superimposition of the internal measurement errors and the
(observed) natural bandwidth. On the other hand, the colours from model atmospheres ranging
the main sequence band from log g of [3.5,4.5] dex for all models with a Teff of [7000,15000] K
and solar metallicity, and for which (b − y) ≥ −0.02 mag, yield a G0 = 0.591 (with less than
0.5 mmag error), while G1 = 0.0985 ± 0.0056 and G2 = −0.044 ± 0.030, when fitting a least
square parabola through the model colours (see Fig. 36). Hence, the (b − y) dependence of the
experimental ∆a systems is reproduced very well.
For the [u − b] relation, Maitzen (1985) lists G1 = 0.024 for 22 bright unreddened stars with
a 1σ level of 4.5 mmag. For this correlation, the results in Fig. 36 imply a more flat dependence
of G1 = 0.0098 ± 0.0018 (and a G2 of −0.0022 ± 0.00097). However, the rather small slope is
very sensitive to the precise definition of the sample: including giants with log g 2.5 dex would
83
0.580
0.585
0.590
0.595
0.600
0.605
0.610
0.615
700080009000100001100012000130001400015000
a[mag]
Teff [K]
models, log(g) = [2.5,3.5)
models with log(g) = 4 dex
models, log(g) = [3.5,4.5]
Figure 37: Luminosity dependence of the a index. Colours from ATLAS9 type model atmospheres
with Teff=[7000,15000] K for log g = [2.5,4.5] dex and solar metallicity. Models above
the main sequence band and thus at lower surface gravity are indicated by different symbols.
Asterisks indicate the overlap of both ranges. Output accuracy is limited to 1 mmag. Models
with log g = 4 dex have been connected by straight lines to indicate the normality line a0.
raise G1 to 0.0161, whereas reducing the range of [u − b] from an upper limit of 1.38 to 1.20
while keeping only the main sequence band models with log g 3.5 dex, as in the first case,
would increase it to G1 = 0.0211 ± 0.0028. Thus, within the overall uncertainties expected for
such kind of a weak dependence on [u − b] the latter is reproduced sufficiently well.
Figure 36 also shows the correlation of a with the temperature indicators (B − V ) and
(g1 − y). Their dependency can easily be studied as before, but is unlikely to reveal more information
beyond the uncertainties introduced by the colour transformation required to compare
the different filter systems used in observations and the synthetic systems of Kurucz (1993).
14.1.3 Luminosity effects
Because each of the colour relations presented in Fig. 36 is also affected by surface gravity
within the range of effective temperatures populated by the CP stars, the direct dependence of
a on Teff was investigated as well (see Fig. 37). Clearly, models with lower surface gravity have
higher a values. The effect of surface gravity on the a index is largest for the late B-type stars
with effective temperatures around Teff ∼ 10 500 K. The width of the band of standard stars as
induced by surface gravity for a given metallicity is between 2 and 5 mmag. This confirms the
results of Sect. 14.1.2 and is in agreement with the observational data quoted therein.
One hast to note here that the step size in log g for model sequences shown in both Figs. 37
and 38 is 0.25. However, as the output of the photometric indices has been truncated to 1 mmag,
84
0.580
0.585
0.590
0.595
0.600
0.605
0.610
0.615
700080009000100001100012000130001400015000
a[mag]
Teff [K]
[M/H] = +0.5 dex
[M/H] = 0.0 dex
[M/H] = −0.5 dex
Figure 38: Metallicity dependence of the a index. Colours from ATLAS9 type model atmospheres
with Teff=[7000,15000] K for log g = [3.5,4.5] dex. Metallicities are scaled with respect
to the solar abundances used in Kurucz (1993). Again, models with log g = 4 dex have been
connected by straight lines to indicate the normality line a0.
it turns out that the ∆a dependence on log g is too weak to show up more prominently. Hence,
many models overlap in the Figures due the assumed output accuracy. The sensitivity of ∆a to
log g slightly depends on Teff and metallicity, as the number of apparent points in Figs. 37 and
38 reveals as well.
14.1.4 Metallicity effects
Metallicity has an effect on the a index which is actually more important than that of luminosity
(surface gravity). Figure 38 compares the main sequence band for solar metallicity with
models having over- and underabundances of ±0.5 dex for all elements heavier than He. An
underabundance of −0.5 dex as in the Magellanic Clouds (Dirsch et al., 2000) yields a shift of
the normality line of −3 mmag. The size of this shift is quite constant over the entire Teff range
relevant for CP stars and also within the entire luminosity range expected for the main sequence
band. On the other hand, an overabundance of +0.5 dex yields a larger shift of between +3 and
+6 mmag with a maximum for the late B-type stars. This behaviour gives already some hint
on the nature of the flux depression at 5200Å in agreement with Adelman & Rayle (2000) who
found that line opacities of ATLAS9 models with metal overabundances of +0.5 and +1.0 dex
predict some extra line blanketing in this region. In turn, due to the good agreement of ATLAS9
model fluxes in this wavelength region with observations for mildly peculiar stars, which have
underabundances or overabundances of up to about 0.5 dex (Adelman & Rayle, 2000), and due
to the satisfactory agreement of the derived synthetic ∆a system with systems used in observa-
85
tions, an important conclusion can be drawn: application of ∆a photometry to the Magellanic
Clouds (Sect. 19.3) will lead only to a small bias, with a size of about −3 mmag relative to the
observations made for the solar neighbourhood, and the same will hold for more remote targets
that have a similar metallicity range.
14.2 The cool CP and λ Bootis stars
After establishing the synthetic ∆a photometric system (Sect. 14.1.1), model atmospheres
were computed with individual abundances for a representative sample of CP stars. This will
either confirm or redetermine their input parameters through comparisons with photometric,
spectrophotometric, and high resolution spectroscopic data. The final models obtained from this
procedure were used to compute synthetic ∆a indices which were compared with observations.
The determination of abundances for CP stars is not straightforward. Their magnetic fields
together with inhomogeneous surface abundance distributions makes a reliable analysis very
difficult. One of the main conclusions drawn from previous works on this field has been the
necessity to build specific model stellar atmospheres for CP stars using state-of-the-art opacity
data. The increase in available computer power and advances in computational algorithms
during the last two decades have now brought this problem into the realm of workstations and
personal computers. Moreover, stellar atmosphere modelling can take advantage of data bases
for atomic line transitions devoted to stellar atmosphere applications such as Kurucz (1992) and
the VALD project (Kupka et al., 1999). Among the current projects for the computation of
model atmospheres several are based on an opacity sampling approach. The PHOENIX code
(Hauschildt et al., 1999) has been developed for computations of model atmospheres throughout
the entire HRD. However, for the computation of small grids of model atmospheres with individual
abundances the opacity distribution function (ODF) approach remains preferable due to
its higher computational efficiency. The main limitation of this approach is that it is unsuitable
for taking vertical stratification into account. However, as it was decided to consider models
with a chemically homogeneous composition first to explore capabilities and limitations, and to
provide a starting point for more elaborate analyses later on, the approach of Piskunov & Kupka
(2001) was taken to construct model atmospheres with individual abundances for CP stars.
The observed behaviour of ∆a is reproduced for several types of CP stars: models for Am
stars show negligible (or marginally positive) values of a few mmag, while for λ Bootis stars –
and for metal deficient A-type stars in general – negative values (as low as −12 mmag in one
case) were obtained. For the coolest CP2 stars with effective temperatures below about 8500 K,
mild (∼ +10 mmag) to moderately large (∼ +30 mmag) flux depressions in agreement with
observations were obtained. However, ∆a values for slightly hotter members of the CP2 group
(for which still Teff < 10 000 K) are underestimated from these new models. The effect of the
microturbulence parameter on the ∆a index is revisited and its different role in various types of
CP stars for reproducing the flux depression at 5200Å is explained.
14.2.1 Model atmospheres for CP stars
The model atmospheres applied in this study have been computed with a variant of the ATLAS9
model atmosphere code which uses line and Rosseland mean opacities calculated for individual
chemical composition, as described in Piskunov & Kupka (2001). The models assume plane
parallel geometry, hydrostatic equilibrium, local thermal equilibrium (LTE), horizontal homogeneity,
and a homogeneous chemical composition. An opacity distribution function (ODF) approach
(Kurucz, 1970) is used for the computation of line opacities for these models. Piskunov
& Kupka (2001) have also confirmed the equivalence of their model atmospheres to those of
Kurucz (1993), if identical element abundances are used. Further model atmospheres have been
computed using the standard ATLAS9 code (except for the treatment of convection, see below)
86
and the line opacities of Kurucz (1993) with a solar (Anders & Grevesse, 1989) or scaled solar
abundance. These were used to initiate our computational procedure and to provide a reference
for the effect of including an individual chemical composition in the modelling of the atmosphere
of each target star.
The new model atmospheres with individual chemical composition differ from those used in
earlier studies such as Maitzen & Muthsam (1980) by enhanced numerical resolution and the
usage of much more accurate and complete atomic line data provided such as Kurucz (1992)
and the VALD project (Kupka et al., 1999). Recent enhancements to line opacities include the
contributions of rare earth elements from neutral, singly, and doubly ionised stages, of strong
and intermediately strong lines from iron peak elements, and the addition of millions of weak
lines from predicted energy levels of iron peak elements (Kurucz, 1992). The new line data
allows to take full advantage of the higher resolution and the better signal to noise ratio of modern
spectroscopic observations. Contrary to earlier studies reduced overabundances have been
found when using the current atomic data for both the analysis of individual spectral lines and
the construction of model atmospheres. For example, compare the abundance analysis of γ Equ
(HR 8097) by Adelman (1973a) and Ryabchikova et al. (1997), who also give examples of how
including the effects of hyperfine and Zeeman splitting naturally yields even lower overabundances.
The new line data provide sufficiently accurate description of line blanketing to allow
a much better though not yet fully satisfactory match of the spectral flux distribution from the
far UV to the infrared. This has been confirmed by detailed comparisons with flux observations
of Vega (Castelli & Kurucz, 1994; Piskunov & Kupka, 2001). It has also been found to hold at
least as long as chemical peculiarities are moderate enough to be accounted for by simply scaling
the solar metallicity (Adelman & Rayle, 2000) and convection is not strong enough to form a
granulation pattern as in the solar case. See also the discussion on the effects of convection
treatments in Smalley & Kupka (1997).
However, despite the success of the revised atomic data in explaining the spectrophotometry
of stars with a chemical composition similar to the Sun apart from a scaling factor, even an overall
fit of the flux distribution using model atmospheres with scaled solar chemical composition is
generally not sufficient to match flux depressions observed in CP stars such as the 5200Å feature
(Adelman & Rayle, 2000). Moreover, extreme peculiarities may even change the atmospheric
structure (Piskunov & Kupka, 2001). For that reason it was decided to compute models with
individual chemical compositions for our study (Table 17) following the computational procedure
described in detail in Piskunov & Kupka (2001). In general, for larger deviations a reanalysis of
the element abundances may have to be considered to obtain a model which predicts fluxes and
rectified spectra that match the observational data. In the case of HR 7575, for which a larger
change in log g was favoured, it was verified that the derived element abundances from the final
model are still within the error range expected for the original model.
In some cases, abundances and input Teff and log g had to be changed, although mostly
within the limits mentioned above. The model construction was iterated this way until a more
satisfactory match with the observations had been achieved. The best matching model atmospheres
obtained from this procedure were used to compute synthetic ∆a indices and the latter
were compared with the observed ∆a data. In a final stage, detailed synthetic spectra for the
region measured by the ∆a system were computed and compared with observations to probe the
reliability of the chemical composition and fundamental parameters used as well as the obtained
model atmosphere structure, and in particular to detect the main contributing species to the
enhanced line blanketing in the region of the 5200Å flux depression.
For this procedure the use of Balmer line profiles was avoided in order to constrain the
model parameters due to the uncertainties in the broadening mechanisms and the effects from
the convection treatment found for stars with Teff < 9000 K (Smalley et al., 2002). Further
uncertainties are introduced by the complex dependence of the Balmer lines on both Teff and
87
Table 16: Cool CP stars for this study (upper panel). The spectral type classification has been
taken from Renson & Manfroid (2009) and Gray & Corbally (1993). Values for Teff and log g
are those redetermined in Section 14.3. Data for the surface magnetic field and microturbulent
velocities ξt are taken from the sources given in the last column: (1) Ryabchikova (2017, priv.
comm.), (2) Ryabchikova et al. (1999a), (3) Kato & Sadakane (1999), (4) Caliskan & Adelman
(1995). For β CrB, 33 Lib, and HR 7575, ξt has been enhanced to account for magnetic
intensification effects (cf. Sect. 14.2.1 and Ryabchikova et al., 1999a). Additional target stars,
of λ Bootis type, are listed in the lower panel. In their case, model data and fluxes have been
taken from Heiter et al. (1998).
HD Star name Spectral type Peculiarity Teff log g ξt Bs Ref
[K] [dex] [km s−1] [kG]
108642 HR 4750 hA2mF0 CP1 8200 4.0 4.0 ∼ 0 1
108651 17 Com B hA2mF1 CP1 7900 4.3 4.0 ∼ 0 1
137909 β CrB A9 SrEuCr CP2 8000 4.3 4.0 5.7 2
137949 33 Lib F0 SrEu CP2 (roAp) 7550 4.3 4.0 4.9 2
188041 HR 7575 A6 SrCr CP2 8700 4.5 1.75 3.6 2,3
196502 73 Dra A2 SrCr CP2 8900 4.0 2.0 2.0 2
201601 γ Equ A9 SrEu CP2 (roAp) 7700 4.2 2.0 4.0 2
204411 HR 8216 A6 Cr CP2 8400 3.5 2.0 0.5 4
183324 35 Aql A0 Vb λ Boo 9300 4.3 3.0 ∼ 0
192640 29 Cyg A0.5 Va− λ Boo 7800 4.0 3.0 ∼ 0
log g in that region (Heiter et al., 2002b), and particularly by their ambiguity near the Balmer
maximum which may lead to severe errors when deriving fundamental parameters (Smalley et
al., 2002).
One has to point out at this stage effects of a magnetic field on the atmospheric structure,
with the exception of the enhanced line blanketing created by the Zeeman splitting of lines were
considered. The latter has been modelled by a pseudo-microturbulence in stars with known
large magnetic fields (> 2 kG). This concept dates back to Adelman (1973b) and Hensberge &
De Loore (1974). Due to indications of strong stratification in the coolest stars of the sample
(Ryabchikova et al., 2005) it was assumed that convection has a negligible influence on the
temperature gradient in all our sample stars. Hence, similar to Piskunov & Kupka (2001), for
most calculations the convection model of Canuto & Mazzitelli (1991, CM) was used, because it
predicts the most inefficient convection among the various models available for use with ATLAS9
(Heiter et al., 2002b). As a consequence, the temperature gradients obtained for the investigated
CP stars are either nearly or even completely radiative. This and several other limitations of the
modelling approach and its ability in explaining the observational data are discussed in more
detail in Section 14.6.
14.2.2 Selected sample of stars
To find out whether model atmospheres based on individual element abundances are capable
to reproduce the 5200Å feature, and in particular the ∆a index, well studied members from
the major groups of CP stars were selected to perform case studies. The sample of stars was
supposed to fulfill the following requirements: a) multiband photometry for at least the Johnson
UBV and Strömgren uvbyβ – and preferably also for the Geneva 7-colour system – had to
be available, as well as b) spectrophotometric measurements ranging from the near UV to the
88
Table 17: Individual abundances (in dex, relative to total number of atoms for the Sun) for
all CP1 and CP2 stars discussed; the solar values are from Anders & Grevesse (1989). Last
digits for Dy, Er, Yb, and Lu have no significance. Only Yb and Lu for HD 137909, Yb for
HD 137949, as well as Dy and Er for HD 201601 are based on actual abundance determinations
of these heaviest elements. The Ne abundance has not been determined for any of the target
stars and thus exhibits the scaling factor used for other undetermined element abundances. The
solar He abundance was assumed in all model atmosphere calculations.
Elem. 108642 108651 137909 137949 188041 196502 201601 204411 Sun
He +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 −1.05
C −0.39 −0.23 −0.72 −0.70 −0.50 −0.50 −0.52 −0.70 −3.48
N +0.50 +0.50 −0.93 −0.60 −0.50 −0.50 −0.60 −0.60 −3.99
O −0.63 −0.43 −0.89 −0.39 −0.50 −0.50 −0.79 −1.30 −3.11
Ne +0.50 +0.50 +0.50 +0.50 +0.50 +1.00 +0.50 +0.50 −3.95
Na +0.38 +0.24 +0.28 −0.19 +0.50 +1.00 +0.44 +0.50 −5.71
Mg −0.28 −0.31 +0.50 +0.50 +0.01 +1.00 +0.17 −0.38 −4.46
Al +0.50 +0.50 +0.50 +0.50 +0.50 +1.00 +0.64 +0.50 −5.57
Si +0.21 +0.43 −0.31 −0.01 +0.50 +0.01 +0.07 −0.05 −4.49
S +0.50 +0.50 +0.50 +0.50 +0.50 +1.00 +0.09 +0.50 −4.83
Ca −0.47 −0.25 +0.18 +0.08 +0.78 −0.50 +0.21 +0.44 −5.68
Sc −0.34 −0.27 +0.50 +0.50 −0.02 −1.25 −0.51 −0.70 −8.94
Ti +0.01 +0.09 +0.50 +0.50 +0.77 +0.33 +0.06 +0.51 −7.05
V +0.52 +0.57 +0.50 +0.94 +0.50 −0.04 +0.96 −0.30 −8.04
Cr +0.23 +0.40 +1.77 +1.62 +2.31 +2.67 +0.89 +1.33 −6.37
Mn +0.63 +0.65 +0.50 +0.50 +2.07 +0.37 +1.02 +0.61 −6.65
Fe +0.07 +0.08 +0.27 +0.02 +0.86 +1.07 +0.07 +0.33 −4.37
Co +0.68 +0.59 +0.50 +0.50 +0.50 +0.44 +1.11 +0.58 −7.12
Ni +0.67 +0.72 +0.50 −0.01 +0.38 +0.58 −0.14 +0.05 −5.79
Cu +0.93 +0.73 +0.50 +0.50 +0.50 +1.00 +0.50 +0.50 −7.83
Zn +0.42 +0.35 +0.50 +0.50 +0.50 +1.00 +0.50 +0.50 −7.44
Sr +0.83 +0.55 +0.50 +0.50 +0.51 +1.00 +2.18 +0.60 −9.14
Y +0.94 +0.70 +0.50 +0.50 +0.50 +0.04 +1.43 −0.14 −9.80
Zr +0.88 +0.32 +0.50 +0.50 +0.50 +0.75 +0.76 +0.40 −9.44
Nb +0.50 +0.50 +0.52 +0.52 +0.50 +1.00 +1.77 +0.52 −10.62
Mo +0.50 +0.50 +0.50 +0.50 +0.50 +1.00 +1.87 +0.50 −10.12
Ba +0.60 +0.80 +0.51 +0.31 +0.50 +1.00 +0.85 +0.97 −9.91
La +1.05 +1.01 +2.32 +2.32 +2.76 +0.67 +1.23 −0.28 −10.82
Ce +1.67 +1.93 +2.99 +2.49 +2.73 +0.77 +1.29 +0.50 −10.49
Pr +0.50 +0.50 +2.03 +2.13 +2.28 +1.48 +1.35 +1.79 −11.33
Nd +0.89 +0.97 +2.09 +2.19 +0.50 +1.00 +1.37 +1.00 −10.54
Sm +0.85 +0.82 +2.44 +2.94 +0.50 +1.00 +1.51 +0.74 −11.04
Eu +1.38 +1.39 +3.03 +2.53 +4.63 +2.73 +1.33 +0.33 −11.53
Gd +1.25 +1.27 +0.52 +0.52 +3.75 +1.44 +1.57 +0.52 −10.92
Dy +0.54 +0.54 +0.54 +0.54 +0.54 +1.00 +1.80 +0.54 −10.94
Er +0.51 +0.51 +0.51 +0.51 +0.51 +1.01 +1.11 +0.51 −11.11
Yb +0.56 +0.56 +2.46 +2.16 +0.56 +1.00 +0.56 +0.56 −10.96
Lu +0.58 +0.58 +1.28 +0.58 +0.58 +1.08 +0.58 +0.58 −11.28
89
red region. Moreover, c) an abundance analysis and determination of fundamental parameters,
preferably based on model atmospheres and atomic data similar to Kurucz (1993), and d) most
importantly, measurements of the ∆a index had to be available. For about half of the target
stars also new spectra were taken to analyse the contributing species in and around the 5200Å
region. In a few cases it was possible to supplement these data by spectrophotometric scans of
the region such as have frequently been used in earlier studies of the 5200Å feature (Maitzen &
Muthsam, 1980). Section 14.5.4 includes two examples to judge the amount of line-blanketing
accounted for by the new model atmospheres. To minimise the influence of reddening we have
chosen only bright, close-by target stars. Hence, E(B − V ) is most likely less than 0.01 mag for
all objects we have studied here.
In Table 16 the basic parameters of all target stars for this study are listed which have a Teff
of less than 10 000 K. They comprise two CP1 stars, four very cool CP2 stars (mid A- to late
A/early F- type), and two slightly hotter CP2 stars with a very strong 5200Å feature.
In addition, two λ Bootis stars (35 Aql and 29 Cyg) are listed. For 35 Aql and 29 Cyg these
underabundances amount to −1.5 dex and −2.0 dex for the iron peak elements with respect to
solar values. Thus, they represent the opposite case to the CP1 and CP2 stars. For both stars
neither further investigations of their basic parameters nor model computations were necessary,
because they had already been done by Heiter et al. (1998) with exactly the same software tools
used here. Hence, it was possible to directly use the output fluxes calculated from their model
atmospheres for this study of the ∆a index. Refer to Heiter et al. (1998) for further details on
parameter determinations of these stars, in particular for metallicities and model calculations.
14.3 Individual models: parameter determination with observed fluxes
In the following, the consistency checks and improvements of the parameter determinations for
our CP1 and CP2 target stars based on the new model atmospheres with individual abundances
are described. The complete list of element abundances as used for the final models is given
in Table 17. Synthetic as well as observed multiband photometry of the targets have been collected
in a separate table available on request from the author, as the main focus has been the
investigation of the capability of the models to reproduce observed spectrophotometry. The observational
data for the comparison with model atmosphere fluxes was taken from the literature.
If more than one measurement was found, the values were averaged. The errors of the means
are in general smaller than those of individual measurements, although for some stars there is
considerable variation over their rotational period (see also discussions in Sects. 14.4 and 14.5.3).
It has to be emphasized that almost all spectrophotometric observations are normalised to the
flux at 5000Å which is rather close to the investigated 5200Å depression. This might introduce
an error source when comparing those data to synthetic spectra. Therefore also a comparison
of these data with a normalisation at 5556 Å was performed and no significant differences were
found, as it is discussed in Section 14.3.1.
14.3.1 CP1 stars
Detailed model atmospheres for two Am stars were computed: HR 4750 (HD 108642) and
17 Com B (HR 4751, HD 108651). Both are members of the Coma cluster (Guerrero et al.,
2015). HR 4750 is an SB 2 type binary (Boesgaard, 1987) with a period of 11.78 days while
17 Com B is of SB 1 type with a period of 68.29 days (Savanov, 1996) and is occasionally
misclassified as an Ap star.
Table 18 lists the fundamental parameters of both stars obtained from photometry and from
the spectroscopic analysis of Savanov (1996). Microturbulent velocities of 5 to 6 km s−1 were
found for a number of atomic species. For both objects, the starting point was a solar composition
as in Kurucz (1993) and Anders & Grevesse (1989), for which elements heavier than He had
90
Table 18: Comparison of the spectroscopic results of Savanov (1996) for Teff (in K) and log g (in
dex) of our target CP1 stars with photometry. The uvbyβ photometry from Paunzen (2015) and
the calibrations by Napiwotzki et al. (1993) and Smalley (1993) were used for the photometric
parameter determinations. The microturbulent velocity ξt is given in km s−1 as found by Savanov
(1996) from Fe ii lines.
HD uvbyβ Savanov (1996)
Teff log g [M/H] Teff log g ξt
108642 8087 4.01 0.25 8200 4.0 5.3
108651 8068 4.20 0.36 8000 4.3 5.6
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5000Å
λ [Å]
HD 108651 = HR 4751 = 17 Com B
observations, BV
model, individual compos., 8000 K
model, individual compos., 7900 K
(a)
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5556Å
λ [Å]
HD 108651 = HR 4751 = 17 Com B
observations, CB
observations, BV
model, individual compos., 8000 K
model, +0.5 dex, 8000 K
(b)
Figure 39: Spectrophotometric observations of 17 Com B are compared to fluxes from model
atmospheres with individual chemical compositions for two values of Teff: 7900 K and 8000 K.
Note the effect of different normalisations: the standard one at 5000Å (left panel) is compared
to an alternative one at 5556Å (right panel).
in addition been scaled by +0.5 dex. This composition was modified by using the element
abundances obtained from the spectroscopic analysis published in Table 6 of Savanov (1996)
wherever possible, with the exception of (the less reliable result for) Al. For O an additional,
more recent result based on the same observations was used. In most cases where both neutral
and singly ionised species of an element had been analysed, their average was used, except for
Si and Cr, where results from singly ionised species were preferred (changes would have been
negligibly small for the applications, if averages were considered for them instead). A value of
4 km s−1 for the microturbulence parameter for any of our model atmospheres for HR 4750 and
17 Com B (Table 16) was taken, as it provides a safe lower estimate for the different atomic
species and is readily available also from the model grids published by Kurucz (1993).
Because the agreement between photometric and spectroscopic values of Teff and log g is quite
good (Table 18), the latter ones were taken to compute models as well as synthetic photometric
91
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5556Å
λ [Å]
HD 108642 = HR 4750
observations, CB
model, individual compos., 8200 K
model, +0.5 dex, 8200 K
Figure 40: Spectrophotometric observations of HR 4750 from Clampitt & Burstein (1997) are
compared to fluxes from model atmospheres with an individual chemical composition and with
a composition scaled with respect to the solar one.
colours with the chemical composition as just described. The synthetic photometric colours for
all the models for HR 4750 and 17 Com B turned out to be in agreement with observations to
within the uncertainties of colour transformations for individual stars.
Figure 39 compares the spectrophotometric observations of Böhm-Vitense & Johnson (1977)
for 17 Com B with fluxes from model atmospheres with individual chemical compositions for
two values of Teff: 7900 K and 8000 K. The upper panel of the figure assumes that fluxes are normalised
at 5000Å such that mag(Fν) equals zero. This choice represents the standard convention
in visual spectrophotometry. With this normalisation, a slightly lower Teff of 7800 K to 7900 K
appears preferable to the value of 8000 K used in the abundance analysis of Savanov (1996).
However, as the normalisation to an alternative wavelength of 5556Å reveals (right panel), a
lowering of Teff by 100 K or even more might actually turn out to be just an overcompensation
of the normalisation procedure with its finite accuracy. This claim is corroborated by a comparison
to observations by Clampitt & Burstein (1997) in the same panel: note that the apparently
92
beneficial effect of normalising the Böhm-Vitense & Johnson (1977) data at the wavelength of
5556Å is questionable, because a shift in the opposite direction is needed to improve the match
with the data of Clampitt & Burstein (1997) which had originally been normalised to 5556Å.
Consequently, because of the limitations of the present spectrophotometric data, modifications
of the normalisation wavelength are not likely to provide any improvements of the analysis and
it was decided to use the traditional wavelength of 5000Å as the normalisation point for all
subsequent work.
Figure 40 displays a comparison of spectrophotometric observations of HR 4750 from Clampitt
& Burstein (1997) with the model fluxes. Note that the luminosity of the late F- or early G-type
companion of HR 4750 is much smaller than that of the Am type primary of the system. For
fundamental parameters chosen as in Table 16, i.e. with Teff and log g from Savanov (1996) as
well as a ξt of 4 km s−1, the match appears slightly better than for 17 Com B (right panel of
Fig. 39). Note that the fluxes from a model based on individual abundances and one based
on a solar composition scaled by +0.5 dex can hardly be distinguished on the level of current
spectrophotometric precision. The same can be concluded for the case of 17 Com B. Hence, it
was decided to use the parameters in Table 16 and the abundances described in this Subsection
in the studies of the 5200Å depression.
14.3.2 CP2 stars with Teff 8500 K
The SrEu subclass of CP2 stars includes the magnetic CP stars which have some of the lowest
Teff among all CP stars. Two of them were chosen for this study: 33 Lib (HD 137949) and γ Equ
(HD 201601). Both also belong to the rapidly oscillating Ap (roAp) stars (Bigot & Kurtz, 2011)
which are characterised by oscillations with amplitudes of about a few mmag and periods of
less than 25 minutes. To complement the sample two further objects were included which are
quite distinct from each other. β CrB (HD 137909) shares many similarities with roAp stars, in
particular its range of colour indices and low effective temperature while HR 8216 (HD 204411)
is distinguished from these three by its higher Teff and the much lower overabundance of Eu.
For the initial model atmosphere of β CrB, Teff, log g, (pseudo-) microturbulence, and the
chemical composition were taken from Ryabchikova et al. (1999a) supplemented by additional
element abundances determined by Ryabchikova (2017, priv. comm.; see also Table 17). Scaled
solar abundances as in the model of Ryabchikova et al. (1999a) have been assumed for all the
other elements. After comparing fluxes from model atmospheres with individual composition to
the observations of Adelman et al. (1989), it was found that a slightly increased Teff allows a
better match with the data. The upper left panel of Fig. 41 shows the fluxes of the observations
as well as those of the best fitting models obtained with either composition. Their parameters
are summarised in Table 19. Clearly, the model with individual composition achieves a much
better match for the entire range from the Balmer jump to about 6500Å than its counterpart
with a scaled solar metallicity. Changing Teff for the scaled composition cannot emulate this
effect, because the predictions of the UV fluxes get worse. On the other hand, a Teff of 7750 K
for the model atmosphere with individual composition yields worse results than our choice of
8000 K in both the UV and blue region as well as in the red region and most of the near IR.
A slightly higher Teff of 7850 K would match the far red/IR region best, but would not be
as satisfactory for the remaining part of the visual region, nor the UV, compared to the hotter
model shown in Figure 41. Hence, the latter represents the best model which can be found under
the assumption of chemical homogeneity to within a fitting uncertainty of ±100 K. Overall, the
new model is a considerable improvement over its predecessor: if abundances are assumed to be
merely scaled solar ones, it is difficult to match more than one or two spectrophotometric regions
of β CrB with a size of a few 100Å simultaneously. The new model matches a region of 3000Å
ranging from the UV to the red quite satisfactorily. None among the chemically homogeneous
93
Table 19: Parameters for model atmospheres of CP2 stars with a scaled solar composition
(Anders & Grevesse, 1989), which has been used in spectroscopic analyses in the literature, are
compared to those derived for the models with individual chemical composition. Teff is given
in K, other parameters are in dex. Literature parameters are from Ryabchikova et al. (1999a),
except for HD 204411 (Caliskan & Adelman, 1995), and for the second rows for HD 188041 and
HD 196502, which contain the results from Lyubimkov (1986) and Kato & Sadakane (1999),
respectively. For the microturbulence ξt see Table 16. Details on individual abundances are
found in the text and in Table 17.
HD Literature parameters This analysis
Teff log g [M/H] Teff log g [M/H]
137909 7750 4.3 +0.5 8000 4.3 ind.
137949 7350 4.4 +0.5 7550 4.3 ind.
188041 8500 4.5 +0.5 8700 4.5 ind.
8500 3.5 +1.0
196502 8700 3.8 +1.0 8900 4.0 ind.
8150 3.6 +0.0
201601 7700 4.2 +0.5 7700 4.2 ind.
204411 8400 3.3 +0.5 8400 3.5 ind.
models is able to match the slope of the near IR region from 6800Å to 7800Å as well as the
visual region at the same time.
For 33 Lib, abundances and initial model data were taken from Ryabchikova et al. (1999a)
with additional element abundances from Ryabchikova (2017, priv. comm.; see Table 17 for a
summary). The latter are based on a revision of the results of Gelbmann (1998). Scaled solar
abundances as in Ryabchikova et al. (1999a) have been assumed for all other chemical elements.
Similar to the case of β CrB, a slightly higher Teff preferable for the model was found with
individual chemical composition, and, in addition, also a slightly lower value for the surface
gravity (see Table 19). A comparison of the fluxes of this new model to the observations of
Adelman et al. (1989) and to the previous model, which was based on a scaled solar metallicity,
is shown in Figure 41. The new model matches the observations remarkably well over most
of the entire wavelength range from near UV to the near IR. Note here that Ryabchikova et
al. (1999a) preferred a slightly different normalisation of the calculated fluxes of their 33 Lib
model atmosphere, which is displayed in their Figure 4. While mag(Fν) = 0 at 5000 Å was
enforced, they have determined the zero point so as to achieve a good match (in the least square
sense) of the neighbouring data points as well. Indeed, the uncertainties of the observed fluxes
prohibit a more accurate determination of the exact normalisation magnitude at 5000Å and
leave some freedom for the determination of the zero point of the calculations (Sect. 14.3.1 and
Fig. 39). If the normalisation of Ryabchikova et al. (1999a) is used instead, a slightly lower value
for Teff of about 100 K would have been preferable for the new model with individual chemical
composition. In any case, the new model predicts the various flux features of 33 Lib in the visual
region considerably better than the model with scaled solar abundance. These conclusions hold
independently of the particular convection model used for the model computations: even for
an atmosphere based on a mixing length treatment of convection with a large value of mixing
length to pressure scale height (α = 1.25), the chosen Teff, log g, and the ∆a obtained would
be the same within the uncertainties of the spectrophotometric data. Because 33 Lib is the
coolest star in the entire sample, this gives some comfort concerning the independence of the
results from the particular treatment of convection in the model atmospheres. This result was
94
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5000Å
λ [Å]
HD 137909 = HR 5747 = β CrB
observations, Adelman
model, individual composition, 8000 K
model, +0.5 dex, 7750 K
(a)
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5000Å
λ [Å]
HD 137949 = 33 Lib = GZ Lib
observations, Adelman
model, individual composition, 7550 K, log(g)= 4.3
model, +0.5 dex, 7350 K, log(g)= 4.4
(b)
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5000Å
λ [Å]
HD 201601 = γ Equ = HR 8097
observations, Adelman
model, individual composition, CM
model, +0.5 dex, CM
model, +0.5 dex, MLT(α=1.25)
(c)
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5000Å
λ [Å]
HD 204411 = HR 8216
observations, Adelman
model, individual composition, log(g)=3.5
model, +0.5 dex, log(g)=3.3
(d)
Figure 41: Upper left panel: spectrophotometric observations of β CrB are compared to fluxes
from a model atmosphere with individual chemical composition and a model with enhanced
metallicity (scaled solar abundances). Upper right panel: the same for 33 Lib. Lower left panel:
the same comparison for γ Equ, but with an additional graph for a model atmosphere with
scaled solar abundance, but a different treatment of convection. Lower right panel: a similar
comparison as for β CrB done for HR 8216. Modelling and comparison details are discussed in
the text.
95
indeed expected from the lower convective efficiency found for model atmospheres with enhanced
metallicity (Piskunov & Kupka, 2001).
For γ Equ the fundamental parameters and element abundances derived by Ryabchikova et
al. (1997) were taken using solar abundances scaled by +0.5 dex for all other elements, except
for C and O, for which redetermined values by Ryabchikova (2017, priv. comm.) have been used,
and N, for which we have taken an estimate based on Roby & Lambert (1990). A summary
of the final abundances is given in Table 17. Even without altering Teff or log g the match of
the observed fluxes of Adelman et al. (1989) to the fluxes from the new model has improved
over its predecessor with scaled solar abundances, as can be seen from Figure 41. This result
is once more essentially independent of the convection model used for our computations. To
illustrate this remark the fluxes from model atmospheres with scaled solar composition based on
both the mixing length theory (no overshooting, α = 1.25) and the convection model of Canuto
& Mazzitelli (1991) were included in Figure 41. Whereas a preference for one or the other
convection model (for the Teff and log g chosen here) cannot be supported from this comparison,
the improvements from using an individual chemical composition in the calculations are much
more obvious. Only in the IR the emergent (normalised) flux is still slightly underestimated by
the new model, though less than by models with scaled solar composition.
The fundamental parameters and the element abundances for the model atmosphere for
HR 8216 were taken from Caliskan & Adelman (1995). For species not included in their Table 2,
solar abundances scaled by +0.5 dex were assumed, as used in their analysis, except for CNO,
for which the estimates for CP2 stars derived by Roby & Lambert (1990) were used. A summary
is shown in Table 17. As can be seen from Fig. 41, already the fluxes of the original model of
Caliskan & Adelman (1995) match the observations of Adelman et al. (1989) very well, except
for the underestimation of the flux in the far red and near IR. However, due to the milder
overabundance of HR 8216 the new model hardly yields any improvements in comparison with
models with a scaled solar abundance. One might argue whether a slightly larger surface gravity
with a log g of 3.5 dex may be taken instead, which was done, as it allows a nearly perfect
match of the observed c1 and Geneva (U − B) indices, which are off by 0.06 and 0.04 mag,
if a log g of 3.3 dex is assumed instead. However, there is no further overall improvement to
spectrophotometry from using a model with individual chemical composition for this star.
In conclusion, the new model atmospheres with individual chemical composition are capable
to reproduce colours and spectrophotometry of each of these four very cool CP2 stars rather
well. Remaining discrepancies are reduced to either the IR and/or to a few parts of some of the
flux features in the visual. But more importantly, the flux depression at 5200Å is represented
much more accurately by these models than by models with a scaled solar composition, as can
easily be seen from Figure 41.
14.4 CP2 stars with 8500 K Teff 10000 K
To complete the sample of cool CP2 stars two objects were chosen which have been assigned the
SrCr subtype, though they are known to have strong Eu features as well: HR 7575 (HD 188041)
and 73 Dra (HD 196502). Both are slightly hotter than the four mCP stars already discussed
and they show some of the largest known ∆a values.
HR 7575 is particularly difficult to analyse with classical model atmospheres. Kato &
Sadakane (1999) performed a thorough spectroscopic study of this star and found it impossible
to achieve ionisation equilibrium for Cr and Fe with model atmospheres having the same
Teff, even when explicitly including Zeeman broadening in their radiative transfer computations.
Remarkably, the same problem was also found for 73 Dra, while it was only of minor
importance in β CrB (see their Table 5; the large magnetic field of β CrB requires to use a
high pseudo–microturbulence, as it is done in the present analysis). For the initial model Teff,
96
Table 20: Element abundances (in dex) from Lyubimkov (1986) for HD 196502 relative to solar
values as in Table 17.
Element Element Element
C −0.50 Cr +1.52 La +0.67
N −0.50 Mn +0.37 Ce +0.77
O −0.50 Fe +0.16 Pr +1.48
Si +0.01 Co +0.44 Eu +2.65
Sc −1.25 Ni +0.58 Gd +1.44
Ti +0.33 Y +0.04
V −0.04 Zr +0.75
pseudo-microturbulence, and element abundances was taken from the work of Kato & Sadakane
(1999). CNO abundances were estimated by reducing the solar abundance value by −0.5 dex.
But emerging spectrophotometric fluxes and model structure differ very little, if the averages
from Roby & Lambert (1990) are used instead. This can be seen from a comparison between the
change in fluxes for HD 204411 and HD 188041, as obtained from a scaled (+0.5 dex) solar CNO
abundance and one based on the individual composition of the two stars (Table 17, Fig. 41 for
HD 204411 and Fig. 42 for HD 188041) Note the carbon feature around 4750Å which was also
discussed in Smalley & Dworetsky (1993). One can conclude that the detailed choice of the CNO
abundances does not significantly affect the overall flux distribution. For all other elements a
solar abundance scaled by +0.5 dex was assumed and thus following Ryabchikova et al. (1999a)
rather than Kato & Sadakane (1999), who had used +1.0 dex. The reason for this choice is
that except for Cr, Mn, and the analysed lanthanides, which had been individually adjusted,
the bulk opacity contributors, including Fe, were found overabundant by less than +1.0 dex in
their own work. The suggested Teff puts the star in the temperature range around the Balmer
maximum, where a self-consistent derivation of both Teff and log g from Balmer lines without
knowing one of them accurately from an independent method is unfortunately unreliable even
for “chemically normal” stars (Smalley et al., 2002). The discrepant ionisation temperatures, on
the other hand, indicate basic shortcomings of chemically homogeneous atmospheres with scaled
solar abundances, when they are used for the analysis of extreme CP stars. It was thus chosen
log g so as to provide spectrophotometric fluxes in best overall agreement with observations.
For the same reason, the model atmosphere with scaled solar abundances used by Ryabchikova
et al. (1999a) was selected as reference. Its basic parameters are given in Table 19. Fluxes from
this model are compared to the data in Figure 42. Even with individual chemical composition
a very high log g is required to match the Balmer jump and 4.5 dex appears to be a lower limit
from this comparison. A Teff of about 8700 K was preferable rather than 8500 K as used for the
scaled solar abundant model atmosphere. Assuming either lower or higher temperatures makes
the fit poorer in various wavelength regions, nor does it resolve the remaining discrepancies
around 4200Å and 5200Å. With a Teff of 8700 K the model based on an individual chemical
composition also matches the observed fluxes in the red and IR region very well. Hence, the
visual region fluxes of HR 7575 cannot be modelled as satisfactorily as those of the four cooler
CP2 stars discussed above, although the predictions for the flux depressions around 4200Å and
around 5200Å are a considerable improvement compared to fluxes from models with a scaled
solar composition.
For 73 Dra, the initial parameters for the model atmospheres for this star were taken from
the work of Ryabchikova et al. (1999a) whenever possible, as the spectroscopic analysis by
Lyubimkov (1986) was based on outdated atomic data and model atmospheres. In particular,
97
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5000Å
λ [Å]
HD 188041 = HR 7575
observations, Adelman
model, individual composition, 8700 K
model, +0.5 dex, 8500 K
(a)
0
0.5
1
1.5
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
mag(Fν)normalisedat5000Å
λ [Å]
HD 196052 = 73 Dra
observations, Adelman
model, individual composition, 8900 K
model, +1.0 dex, 8700 K
(b)
Figure 42: Left panel: spectrophotometric observations of HR 7575 are compared to fluxes
from model atmospheres with an individual chemical composition and a model with enhanced
metallicity (scaled solar abundances). Right panel: a similar comparison done for 73 Dra.
Modelling and comparison details are discussed in the text.
we followed their choice of Teff, log g, pseudo-mircoturbulence, and also assumed a solar element
abundance scaled by +1.0 dex for all elements, for which no other determinations were available
(Tables 16 and 19). Abundances for Cr, Fe, and Eu have been taken from Ryabchikova et al.
(1999a). Otherwise, the abundances published by Lyubimkov (1986, and Table 20) were used,
except for Ca. The very large underabundance he found is based on a single resonance line and
appears unrealistic. Hence this result was substituted with a value of −0.5 dex below the solar
Ca abundance as an indication of a suspected underabundance of Ca (solar abundance or even
overabundance is the common case found for CP2 stars. CNO abundances were chosen as in
the case of HR 7575.
As can be seen from Table 19, it was decided to use a slightly higher log g as well as a Teff
of 8900 K instead of 8700 K, which had been chosen for the model with scaled solar abundance.
The reasons for this new choice are the following: it is possible to match the near IR fluxes with
a model based on individual element abundances and a Teff of 8500 K. However, the match in the
blue and the UV achieved by the 8900 K model is lost in this case, and the remaining mismatch
around the 5200Å feature becomes worse. Similar conclusions hold for the intermediate Teff
of 8700 K. The fundamental parameters thus cannot be adjusted to give a better match than
that one shown in Fig. 42, even if a change in surface gravity is used to optimise the fit, as is
indicated by the slightly higher value chosen for the final model. The mere scaling of a solar
chemical composition does not reproduce the flux depressions in the 4200Å and 4600Å regions
as well as the new model does. The flux predictions are also considerably improved for the
5200Å feature. This becomes evident when comparing the rather mediocre ∆a value of the
scaled solar abundance model with observations (Sect. 14.5). Thus, the new model atmosphere
for 73 Dra is an improvement over its precursor, despite it cannot match the observations within
the uncertainties of the data.
98
14.5 Comparison of the synthetic and observed ∆a photometry for ten CP
stars
In this Section, the synthetic ∆a values with observations for the selected members of the λ
Bootis, the CP1 and the CP2 group are compared. Table 21 lists all observed ∆a indices along
with those calculated from the new model atmospheres. One can conclude that the tendencies of
the observed ∆a values are well reproduced for all programme stars, if the limitations discussed
in Sects 14.5.3 and 14.8 are taken into account. It also has to be emphasised that almost all
magnetic CP stars exhibit photometric variability on the time basis of their rotational period
(Sect. 5). As studies of the variation of element abundances of the target stars over their
rotational period have not been available, it is not possible to give here a quantitative estimate
of this effect. To provide a hint of its magnitude the range of observed ∆a values in Table 21
published for two target stars are included. The same effect is even more prominent among hot
CP2 stars.
14.5.1 λ Bootis stars
Members of the λ Bootis group exhibit significant negative ∆a values (Sect. 11.7). Both
programme stars show extreme underabundances (up to −2 dex) which results in ∆a values of
−13 and −20 mmag for 35 Aql and 29 Cyg, respectively. The synthetic values are about 5 mmag
higher than the observed ones which is a satisfactory agreement. Notice that both objects are δ
Scuti type pulsators (Paunzen et al., 2002a). The ∆a values predicted by models with individual
abundances and by those with an appropriately scaled solar element abundance are essentially
the same for both stars. Heiter et al. (1998, Figure 4) presented a comparison of synthetic fluxes
which includes the wavelength region covered by the ∆a system.
14.5.2 CP1 stars
Only the most extreme CP1 stars have ∆a values up to +14 mmag. In general, members of this
group show only slightly enhanced values (Sect. 11.3). Photometrically, measurements always
suffer from the fact that almost all CP1 stars are within spectroscopic binary systems. The
two programme stars both have observed ∆a values of +3 mmag whereas the synthetic ones are
+8 mmag. Again this is a remarkably good agreement showing that the 5200Å flux depression
is only marginally pronounced in CP1 stars. Model atmospheres with a scaled solar element
abundance increase the synthetic ∆a values to about +10 · · · + 12 mmag. This is essentially
due to the increased microturbulence of 4 km s−1 used in all the model calculations for these
two stars, despite the fact that such a value is even below actual microturbulence velocities
determined for either of them (Table 18 and compare with Table 16). The CP1 stars hence
represent quite the opposite to the case of magnetic CP stars discussed below, because large
values of ξt which are based on abundance analyses lead to an overestimate of ∆a when combined
with scaled solar element abundances. The discrepancy is reduced to an acceptable amount, if
the model atmospheres are based on individual element abundances. For the CP2 stars exactly
the contrary was found, as shown in the following.
14.5.3 CP2 stars
The magnetic CP2 stars are the most investigated within the ∆a photometric systems. The
measured values can go up to +75 mmag and vary over the rotational period. For the four cooler
programme stars (HD 137909, HD 137949, HD 201601, and HD 204411) a good agreement of the
measured (+11 to +26 mmag) and calculated values was found. This is even more remarkable
since these objects have strong surface magnetic fields from 0.5 to 5.7 kG (Table 16). In contrast,
the ∆a values predicted by the best model atmospheres that can be constructed with scaled
99
Table 21: ∆a indices in mmag for the target stars. The values of Teff and (b − y)0 given are
those calculated from the best fitting models from Sect. 14.3 which were also used to determine
the calculated ∆a given in the fifth column. They are compared with observations of ∆a listed
in the fourth column which is based on data taken Section 10. Ranges in ∆a obs. are examples
for variations over the rotational period, ranges in ∆a calc. indicate typical model atmosphere
parameter uncertainties.
HD Teff (b − y)0 ∆a obs. ∆a calc.
[K] [mag] [mmag] [mmag]
108642 8200 0.068 +3 +7 · · · + 8
108651 7900 0.106 +3 +8
137909 7750 0.142 +26 +29 · · · + 33
137949 7550 0.205 +20 · · · + 25 +34 · · · + 40
183324 9300 0.017 −13 −8
188041 8700 0.057 +59 · · · + 90 +22
192640 7800 0.139 −20 −12 · · · − 13
196502 8900 0.010 +72 +32
201601 7700 0.130 +11 +9 · · · + 11
204411 8500 0.036 +19 +10
solar element abundances, as discussed in Sect. 14.3.2 and summarised in Table 19, are only
+12 mmag for HD 137909 and HD 137949 as well as +2 and +3 mmag for HD 201601 and
HD 204411. The flux depression at 5200 Å is hence severely underestimated by these models, in
accordance with the comparison to spectrophotometry in Section 14.3.2. The slightly higher ∆a
values of +12 mmag obtained for model atmospheres for β CrB and 33 Lib with a scaled solar
metallicity are entirely due to an enhanced (pseudo-) microturbulence used in their computation
(Table 16). The beneficial effect of increasing this parameter has already been pointed out by
Adelman & Rayle (2000). However, this increase generally is not sufficient to reproduce the
observed ∆a values and a larger variation would have to be justified by extraordinary magnetic
field strengths. Moreover, in CP1 stars the same values of enhanced microturbulence velocities
are used for a completely different physical reason, yet leading ultimately to the same ∆a value
when using a model atmosphere with scaled solar metallicity. The observed ∆a values of CP1
stars, however, are much lower than those of CP2 stars. On the other hand, combining an
enhanced microturbulence with individual abundances for cool CP2 stars brings the observed
∆a values easily within the range of synthetic calculations through enhancing them even further,
while, as discussed before, those of CP1 stars are reduced in comparison with the case of a scaled
solar abundance. This is confirmed by the results shown in Table 21.
For the two hotter objects, HD 188041 and HD 196502, the synthetic ∆a values are about
+40 mmag too low. Both stars are photometrically variable with a very high amplitude (Catalano
et al., 1998a) which could account for some part of the underestimation of the 5200Å flux
depression when using these models. The models with scaled solar abundance again show a
much poorer performance. A value of +10 mmag is found for HD 188041 only if an enhanced
(pseudo-) microturbulence of 4 km s−1 is used. The model with individual element abundance
assumes a value of 1.75 km s−1 (Table 16) as obtained by the analysis of Kato & Sadakane
(1999). For 73 Dra the comparison is more straightforward, because all model calculations for
this star have been performed with 2 km s−1 (Table 16). In that case, despite an overabundance
of +1.0 dex, the model with scaled solar element abundance only yields a pathetic value of
+6 mmag compared to +32 mmag obtained from the model with individual element abundances,
100
which has to be compared to the +72 mmag found in observations.
Therefore, the two hotter CP2 stars in the present sample demonstrate even more clearly
the improvement obtained from using individual element abundances for modelling the 5200Å
flux depression. Usage of an enhanced (pseudo-) microturbulence could yield an even closer
agreement, but it is also a reminder that a realistic modelling of the magnetic field of these
stars is yet a missing ingredient of even the most recent model atmospheres. To the role of
stratification for these matters is discussed in Section 14.8.
14.5.4 Spectroscopic observations of the 5200Å depression
In this Section, a comparison of observed high resolution spectra with synthetic ones is presented.
It is not intended to check the validity of the abundances used in all detail but show that it
is possible to fit the average line blanketing in the 5200Å depression within acceptable limits
using the described models. This corroborates the direct comparison of synthetic and observed
∆a values as well as synthetic and observed spectrophotometry given in the previous sections.
Observations of all programme stars were made with the coudé spectrograph at the 2-m
RCC telescope of the Bulgarian National Astronomical Observatory Rozhen during 2000 and
2001 by Ilian Kh. Iliev. The Photometrics AT200 camera with back-illuminated SITe SI003AB
(1024 × 1024, 24 µ pixel) CCD chip attached to the Third camera was used. The spectra were
taken with a 632 mm−1 Bausch & Lomb grating resulting in a resolution of about 20000. Due to
the “classical” coudé scheme the entire spectral range between 5000Å and 5400Å was covered
by eight consecutive and fairly overlapping sub-regions. Each of these sub-regions is 100Å large.
A hollow-cathode ThAr lamp was used to produce a reference spectrum with a FWHM of
about 2 pixels for the comparison lines. Flat fields were made by using a tungsten projection
lamp mounted in front of the entrance slit. The spectra were bias-subtracted and flat-fielded
within standard IRAF procedures. The typical signal-to-noise ratio between 200 and 300 in the
continuum was achieved for most of the spectra. Wavelength calibration resulted in an r.m.s.
wavelength error of typically 0.005Å.
Figure 43 shows the difference of the observed and synthetic spectrum for two CP2 stars
(HD 137909 and HD 204411) which have the largest and smallest scatter, respectively. The
other “differential” spectra are very similar and are “in between” the cases shown here. From
this figure it can be concluded that most of the strong lines in the region have been included
in the computations. In many cases the same lines (e.g. around 5170Å) deviate which is quite
likely caused by wrong or incomplete atomic line data. Otherwise, the line blanketing at the
5200Å depression is well reproduced with a scatter of 5 to 10% of the differential spectra around
a (nearly) zero mean.
14.6 Observational constraints
If a model atmosphere would be at hand for which the overall emergent surface flux distribution
matches the observed one at the few percent level, as it is possible for example for Vega (Castelli
& Kurucz, 1994), the ∆a indices derived within both observed and synthetic systems should
agree to within a few mmag (Sect. 14.1.2). This should hold unless flux deviations in the
wavelength range of the ∆a filters were larger than average, for instance due to a peculiarity in
the radiative transfer of the stellar atmosphere which has not been accounted for by the model.
The results of Sections 14.3 and 14.5 show that this is indeed what happens for models of CP1
and CP2 stars, if a scaled solar element abundance is assumed. The comparison of observed
spectrophotometry with calculations from the models with individual abundances, however,
reveals a better agreement not only over most of the visual region, but in particular for the
wavelength range around 5200Å (Figs. 39 to 41). Table 21 shows that observed and synthetic
∆a values obtained from the new models frequently agree to within a few mmag. Even the
101
5295 5310 5325 5340 5355 5370 5385 5400
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5205 5220 5235 5250 5265 5280 5295
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5100 5115 5130 5145 5160 5175 5190
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HD 137909
(a)
5295 5310 5325 5340 5355 5370 5385 5400
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5205 5220 5235 5250 5265 5280 5295
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5100 5115 5130 5145 5160 5175 5190
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HD 204411
(b)
Figure 43: A comparison of high resolution observed and synthetic spectra for HD 137909 and
HD 204411. Note that the noise level of both sets of observations is roughly the same, hence
the larger deviations for HD 137909 are significant. They may indicate missing weaker lines
in the data base, but HD 137909 also has a much stronger magnetic field and is known to be
vertically stratified (see text in Sects. 14.5.4 and 14.8 for further discussion). Fluxes as used
here are relative to local continuum contrary to the much lower resolution spectrophotometry
shown in Figure 41.
two hotter CP2 target stars, HR 7575 and 73 Dra, fit within this framework. However, it is
already obvious from Fig. 42 that despite an overall agreement of observed and synthetic fluxes
in the visual region, the flux depression at 5200Å is underestimated by all models available for
these two stars, and indeed the ∆a values listed in Table 21 agree with this expectation. Hence,
comparing observational and synthetic ∆a values is a reliable method to judge whether a model
atmosphere for an individual CP star is capable to predict the extent of a flux depression at
5200Å or not.
The accuracy of this assertion is based on how well one knows the spectrophotometric flux
distribution of a target star, as this method was chosen to determine the stellar fundamental
parameters. A variation of Teff by ±200 K for 73 Dra changes ∆a by about 2 to 3 mmag, while a
variation of log g by ±0.2 dex changes it by just 1 mmag. To distinguish between these internal
errors of parameter determination and those which can be achieved on an absolute scale would
require a better knowledge of the effects of atmospheric extinction and instrumental calibration
on the spectrophotometric data. As far as atmospheric extinction and instrumental effects are
102
concerned, no alternative but to accept the limitations of the current data is available. Problems
with data normalisation perhaps account for some of the deviations noted in the far red and
IR for most of the target stars in Section 14.3. For that reason less weight is given to those
differences. Notably, the same phenomenon was found for the standard model atmosphere of
Vega published by Castelli & Kurucz (1994). From their Figures 1 and 5 it is clear that fluxes of
ATLAS9 and ATLAS12 models are too low redward of Hα. This problem could also be caused by
the flux calibration of Vega rather than by an intrinsic shortcoming of the model atmospheres.
Hence, a recalibration of our standard sources as well as a new generation of spectrophotometric
flux measurements would be a major step towards tighter error margins in the determination of
fundamental parameters through spectrophotometry.
14.7 Microturbulence, abundances, and atomic data
Although the microturbulent velocity ξt is usually associated with a photospheric velocity field,
it is also used to mimic enhanced line blanketing due to Zeeman splitting in a magnetic field
(Sect. 14.2.1). One of the results of Sect. 14.5 is that an increase of ξt from 2 to 4 km s−1 can
raise synthetic ∆a values by up to +10 mmag. From an enhanced ξt alone it is not possible
to distinguish between CP1 and CP2 stars, because they may be modelled with similar values
of this parameter, but for different physical reasons. Model atmospheres with scaled solar
element abundance leave this distinction between CP1 and CP2 stars unexplained. As shown
in Sect. 14.5, they yield values for ∆a which are too large for CP1 stars, while for many of the
CP2 stars which have a ∆a of +20 mmag or more the increase provided by an already large ξt
of 4 km s−1 is not sufficient. This explains why the previous model atmospheres based on grid
calculations with pretabulated line opacities and fixed, scaled solar element abundances cannot
be used to analyse the contributors to the flux depression in the 5200Å region, although the
latter can sometimes be matched by such models, as noted in Adelman & Rayle (2000). Only
a combination of both individual element abundances and ξt, whether the latter be attributed
to a velocity field as in CP1 stars or to a magnetic one as in CP2 stars, recovers the correct
distinction between the two: mostly marginal ∆a values for CP1 stars and moderate to large
ones for CP2 stars. Consequently, both the effect of magnetic fields (Zeeman splitting) and
the particular abundance pattern are required to understand the large flux depressions around
5200Å found for many CP2 stars. On the same grounds it can be also understood why some
extreme CP1 stars have moderate ∆a values of up to +14 mmag (which are also found in some
CP2 stars), despite the fact that they do not show detectable magnetic fields.
This leaves one with uncertainties in element abundances and thus in the amount of line
opacity contributing to the 5200Å flux depression as a problem to look into for judging the
new models. Derived element abundances depend on the model atmosphere used, and hence on
fundamental parameters assumed, on the atomic data taken as input for model construction and
radiative transfer calculations, and, particularly for the CP2 stars, also on magnetic field and
stratification effects not accounted for in the present models. The accuracy and completeness of
atomic line data affects any approach to construct model atmospheres for CP stars. Examples
relevant for CP2 stars were given by Cowley et al. (2000). They had to artificially increase iron
peak element abundances to compensate for missing line opacities due to lanthanides in their
model atmosphere for the extreme, very cool CP2 star HD 101065, and it was argued (Wahlgren
et al., 2001) that the third spectra of lanthanides may contribute to the flux depression at 5200Å.
However, no major improvement over the present results from just more complete atomic data
alone is expected. The figures in Sect. 14.3 and Table 21 underline the success of the new models
to predict emergent fluxes from the UV to the red and particularly in the 5200Å region. The lines
of Nd iii discussed by Wahlgren et al. (2001) have already been included in the calculations as
they are part of VALD. Note that while it is not possible to exclude the presence of autoionisation
103
lines, the results from Sects. 14.3 and 14.5 indicate that they do not seem likely to play any role
for the 5200Å flux depression for the CP stars with a Teff of less than 10 000 K.
14.8 Stratification and magnetic fields
For the model atmospheres a homogeneous composition was assumed and also a solar abundance
of He. The present studies of stratification effects are based on phenomenological multi-layer
models (Cowley et al., 2009) which differ from the approach used here only by assuming a
different average composition in two or three vertical layers (sometimes with smooth transitions
zones in between) which build up the photosphere. This setup allows a much closer match of
the observed spectral line profiles of cool Ap stars and is supported by their gross agreement
with diffusion calculations. But the latter in turn are not based on a model atmosphere with
a self-consistent treatment of magneto–convection (see below). Further research is still needed
to corroborate the conclusions from these more refined models of atmospheres of magnetic Ap
stars.
Here, an enhanced microturbulence was used to model the effect of line blanketing in strong
magnetic fields on average surface fluxes, because a direct modelling of a global stellar magnetic
field (and ultimately a global, three dimensional stellar model atmosphere) in this context is so
far not possible. The analytical and numerical complexity of a model stellar atmosphere are
considerably increased and suitable (observational) data are required to constrain the topology
and strength of the field. Even with these data at hands, it is not expect that they be sufficient
on their own, as vertical stratification of element abundances may easily influence observed
fluxes by an even larger amount than a strong magnetic field (Alecian & Stift, 2010).
For the cool CP2 stars an additional physical problem is introduced by the convective instability
of the H ionisation zone situated in their lower photosphere. Vertical stratification models
(and diffusion calculations which provide their theoretical justification) have not yet been coupled
to magneto-convection in a self-consistent manner, owing to the complexity of the problem,
despite the unforseeable changes of the results one might expect for that case. For instance,
contrary to common belief, a magnetic field does not always have to suppress convection. One
example for such a scenario is normal solar granulation (as in magnetically quiet regions – not
to be confused with what happens in sunspots) for which, on the basis of more refined measurement
techniques available, quite considerable field strengths are thought to be present (López
Ariste & Sainz Dalda, 2012). These obviously cannot suppress solar convection. For a more
simplified physical problem, Canuto & Hartke (1986) have shown that depending on the field
strength and efficiency of radiative losses even the opposite may occur: at weak to moderate
field strengths the convective flux can be enhanced for a certain range of Rayleigh numbers (and
hence radiative loss rates) because of an extra contribution originating from the transport of
magnetic energy. At larger field strengths the flux may indeed be suppressed for the case of
inefficient convection (with small to moderate Rayleigh numbers), as has already been shown
much earlier for several cases by Gough & Tayler (1966). However, for very efficient convection,
even a strong field rather results in a change of shape and orientation of convective cells. More
accurate predictions could be expected from magneto–hydrodynamical simulations. However, to
obtain quantitative results for individual cool CP2 stars from this technique requires to account
for a magnetic field which changes on the scale of the entire stellar surface and which is coupled
to the local velocity fields that have to be resolved at least on the scale of up- and downflows
by a hydrodynamical simulation. Evidently, such simulations pose a serious, though interesting
computational challenge.
104
14.9 Stellar model atmospheres with magnetic line blanketing
In a series of three papers, Kochukhov et al. (2005); Khan & Shulyak (2006a,b), developed
new model atmospheres of A- and B-type taking into account magnetic line blanketing and
polarized radiative transfer. These calculations are based on the new stellar model atmosphere
code LLMODELS (Sect. 14.9.1) which implements direct treatment of the opacities due to the
bound-bound transitions. The anomalous Zeeman effect is calculated for the field strengths
between 1 and 40 kG and a field vector perpendicular to the line of sight. The model structure,
high-resolution energy distribution, photometric colours, metallic line spectra and the hydrogen
Balmer line profiles were computed for magnetic stars with different metallicities and were
discussed with respect to those of non-magnetic reference models. The magnetically enhanced
line blanketing changes the atmospheric structure and leads to a redistribution of energy in the
stellar spectrum.
They also studied the effects of the magnetic field, varying its strength and orientation, on
the model atmosphere structure, the energy distribution, photometric colours and the hydrogen
Balmer line profiles. A probable explanation of the visual flux depressions (especially at 5200Å)
of the magnetic CP stars in the context of these models was presented. They calculated a grid
of model atmospheres of magnetic A- and B-type stars for different effective temperatures (Teff
= 8000, 11000, and 15000 K), magnetic field strengths (B = 0, 5, 10, 40 kG) and various angles
of the magnetic field (Ω = 0 - 90o).
The models, techniques, and results are presented here because they investigated the behaviour
of the ∆a, (∆V 1−G), and Z (Sect. 4) depending on different metallicities and magnetic
field configurations. This can be seen as supplement and update to the models as well as results
presented in Sections 14.1.2 and 14.2.
14.9.1 The stellar model atmosphere code LLModels
The stellar model atmosphere code LLMODELS developed by Shulyak et al. (2004) uses a direct
method, the so-called line-by-line or LL technique, for the line opacity calculation. Such
an approach allows to account for the anomalous Zeeman splitting of spectral lines in the line
blanketing calculation and, hence, to achieve a qualitatively better level of accuracy in modelling
the influence of the magnetic field on the stellar atmospheric structure. LLMODELS aims to
model early and intermediate type stars taking into account their individual chemical composition
and an inhomogeneous vertical distribution of elemental abundances. The code is based on
the modified ATLAS9 subroutines (Kurucz, 1993) and on the spectrum synthesis code described
by Tsymbal (1996). It uses the following general approximations:
• a plane-parallel geometry is assumed;
• Local Thermodynamic Equilibrium (LTE) is used to calculate the atomic level populations
for all chemical species;
• the stellar atmosphere is assumed to be in a steady state;
• the radiative equilibrium condition is fulfilled.
The main goal of the LL modelling technique is to avoid a simplified or statistical description
of the bound-bound opacity in stellar atmospheres. The temperature distribution for a given
model strongly depends upon the accuracy of the flux integration over the whole spectral range
where the star radiates significantly. Consequently, to ensure an accurate flux integration, the
number of frequency points has to be sufficient to provide a realistic description of individual
spectral lines. In the past, limited computer resources and imperfect numerical techniques
were applied to solve this problem. The Opacity Distribution Function method (ODF, Kurucz,
105
Figure 44: Difference between photometric colour indices of magnetic stars in comparison with
the predictions for the non-magnetic reference models taken from Kochukhov et al. (2005). The
effect of magnetic field on the photometric parameters of the Strömgren system is shown for
(b − y) (solid line), m1 (dotted line), c1 (dashed line) and β (dash-dotted line). The peculiarity
indicators in the Geneva 7-colour system, (∆V 1 − G) and Z, are shown with open circles and
crosses, respectively.
1979) and the Opacity Sampling technique (OS, Gustafsson et al., 1976) are employed. Within
the LL method, no precalculated opacity tables are needed. Furthermore, no approximations
about the line opacity coefficient are made during the model calculation. By using a large
number of wavelength points (up to 500 000), a detailed description of the line absorption for all
atmospheric depths and achieve a higher dynamical range in opacity is provided. This allows to
reach the required accuracy of the resulting model atmosphere structure, especially in the upper
atmospheric layers. The atomic line data provided by Kurucz (1992) and the VALD project
(Kupka et al., 1999) are used.
For the detailed implementation of the Zeeman effect and the magnetic field configuration,
the reader is referred to Kochukhov et al. (2005); Khan & Shulyak (2006a,b).
14.9.2 The behaviour of ∆a, (∆V 1 − G), and Z in correlation with Teff and B
Here, a summary of the results for ∆a, (∆V 1 − G), and Z depending on different metallicities
and magnetic field configurations is given.
Kochukhov et al. (2005); Khan & Shulyak (2006a) studied the influence of magnetic line
blanketing on the different photometric systems, besides ∆a, also Strömgren uvbyβ and the
Geneva 7-colour system. All colours were calculated using modified computer codes by Kurucz
(1993), which take into account transmission curves of individual photometric filters, mirror
reflectivity and a photomultiplier response function. The synthetic colours are computed from
the energy distributions sampled every 0.1Å, so integration errors are expected to be negligible.
106
Figure 45: The magnitude of the a, V 1 − G and Z photometric indices as a function of the
magnetic field strength for Teff = 8000, 11000 and 15000 K taken from Khan & Shulyak (2006a).
Different curves show calculations with metal abundances [M/H] = 0.0 (open circles), [M/H] =
+0.5 (triangles) and [M/H] = +1.0 (filled circles). Open squares illustrate the effect of increasing
Cr overabundance to [Cr] = +2.0 in the Teff = 8000 K, [M/H] = +1.0 models. All curves are
shifted so that for [M/H] = 0.0 and zero magnetic field in each frame the a, V 1 − G and Z
indices equal zero.
Having introduced a more accurate treatment of Zeeman splitting on line blanketing, it is
particular interesting to study specific photometric indices (∆a, (∆V 1 − G), and Z) whose
aim is to identify CP stars. The behaviour of the photometric indices is closely related to the
flux distribution between the visual and UV regions (Sect. 14.3) and the presence of the flux
depression at 5200Å.
A relation between changes of all photometric indices and the intensity of magnetic field
depends strongly on the stellar effective temperature. For low Teff, photometric changes are
very pronounced, whereas for hotter magnetic stars modification of the uvbyβ photometric
observables is fairly small (except c1). The Geneva photometric colours show a similar decrease
of the sensitivity to the magnetic effects with increasing Teff. These effects are shown in Figure
44.
The results of the calculations of the synthetic a, (V 1 − G), and Z parameters by Khan &
Shulyak (2006a) are shown in Figure 45.
The ∆a system is most sensitive to the magnetic field strength, except for model atmospheres
with Teff = 8000 K where the (∆V 1−G) demonstrates the best sensitivity. As already shown in
Sect. 14.2, it is not very sensitive to metallicity (although it does increase with increasing B) for
this temperature range. Khan & Shulyak (2006a) supposes that this phenomena appears due
to some saturation effect of enhanced line blanketing in the narrow region around 5200Å, which
is mainly dominated by the Fe i and low excitation Fe ii lines for low effective temperature. In
contrast to the narrow-band ∆a-system, the sensitivity of medium-band parameters (V 1 − G)
107
and Z does not suffer much from the specific properties of spectral feature in the narrow interval
around 5200Å. This state is well illustrated in flux units (Fig. 46). One can see that the flux
depression in the region longward of 5200Å is clearly affected by additional abundance and
magnetic intensification, while the narrow region centred at 5200Å is not altered much.
To test the influence of an anomalous concentration of an individual species on the photometric
peculiarity parameters, and especially the ∆a value for low effective temperature, Khan
& Shulyak (2006a) increased the Cr overabundance by a factor 100 relative to the Sun and
calculated additional model atmospheres. As illustrated in Figs. 45 and 46, this results in 12 –
15 mmag growth of the ∆a index for Teff = 8000 K, [M/H] = +1.0 model and field strength 5 –
20 kG. For (∆V 1 − G) the increase is smaller and amounts to 8 – 13 mmag while, the Z-index is
almost unaffected (1 – 3 mmag). This behaviour indicates that observable anomalous ∆a values
for low effective temperature may arise not only from the influence of the magnetic field but
also from specific anomalous abundances as well. Nevertheless, even with overabundant Cr, the
∆a system demonstrates the least sensitivity to the magnetic field strength, with only 8 mmag
change from 5 – 20 kG, while the value for Z is 13 mmag and 20 mmag for (∆V 1 − G).
Finally, none of the photometric peculiarity indicators (except a for Teff = 8000 K) show a
linear trend over the whole range of the considered magnetic field strength. Saturation effects
for their changes with the magnetic field intensity appear for B 10 kG. The ∆a index for low
effective temperature (Teff = 8000 K) demonstrates almost linear dependency on B from 5 to
40 kG.
As a conclusion it can be said, that the ∆a photometric system is best suitable to detect not
only magnetic fields but also CP stars of the upper MS.
14.9.3 Effects of the individual abundance patterns
As last part of their detailed investigation of CP stars, Khan & Shulyak (2007) presented the
effects of individual abundance patterns on the model atmospheres of CP stars which is summarized
here. The main purpose was to conduct a systematic homogeneous study to explore
the abundance parameter space occupied by these stars. They calculated a grid of the model
atmospheres for B- and A-type MS stars for Teff values between 20 000 and 8000 K, and chemical
compositions. Using the LLmodels codes (Sect. 14.9.1) to compute model atmospheres with
individual abundance patterns, the following elements were varied: C, Mg, Si, Ca, Ti, Cr, Mn,
Fe, Ni, Sr, Eu, and He. They presented a homogeneous study of model atmosphere temperature
structure, energy distribution, and photometric indices in the Strömgren uvbyβ and ∆a
systems, hydrogen line profiles, and the abundance determination procedure as it applies to CP
stars. The draw several conclusions (summarized in the following) which are important for the
interpretation of the ∆a index for several star groups (Sects. 6 and 7).
The majority of the tested chemical elements (within the limits of abundance values considered)
produce less than 1% variations in the model atmosphere temperature profile and fall into
the small changes group. These elements are He, C, N, O, Mg (deficient), Ca, Sr, Eu, and Hg.
Several elements were assigned to the moderate changes group in accordance with the effects
they produce on the model atmosphere structure (1 – 3%) and the energy distribution. These
elements were Mn, Ni, and Mg (enhanced). The group of elements which produced large changes
in the model atmosphere structure (more than 3%) and energy distribution consisted of Si, Cr,
Fe and scaled abundance patterns.
If they considered changes in the temperature structure produced by the elements Si, Cr,
and Fe in the main line forming region then they found that the sequence of Fe–Si–Cr represents
these elements from the most to the least influential. Model atmospheres peculiar in Cr, Mn,
and Fe demonstrate a very similar, highly organized, temperature behaviour. There were two
distinct cooling and heating regions in the upper and the lower (i.e. the main line forming
108
Figure 46: Energy distribution around 5200Å for Teff = 8000 K, B = 20 kG and two values of
metallicity [M/H] = +0.5 and [M/H] = +1.0; for the second metallicity value, the behaviour
for overabundant [Cr] = +2.0 is also shown. The top frame represents the comparison of
fluxes from Kochukhov et al. (2005), the bottom frame shows the respective data from Khan
& Shulyak (2006a), including polarized radiative transfer. The fluxes are convolved with a
Gaussian profile assuming a resolution R = 150. The curves of photometric filters (dash-dotted
lines) are presented for comparison. The g1, g2, and y are profiles of filters of the ∆a system,
and V 1 and G of the Geneva 7-colour system.
region) atmosphere, respectively. As the abundance value grew, the temperature dropped in the
upper atmosphere and increased in the lower atmosphere. The inflection point which separates
these two regions moves outwards with growing Teff. The magnitude of the heating region
steadily grew with increasing Teff excluding the lowest value of 8000 K. The same effects, except
for the cooling region feature, applied to models with scaled abundances as well. The reason
why Cr, Mn, and Fe demonstrated such a behaviour is likely the similarity of their energy level
configurations (and the corresponding spectral line distribution patterns), and their relatively
high content in the atmosphere.
They concluded that the elements Si and Fe are the main providers of two different types
of the temperature changes to produce the same distinctive temperature structure that model
atmospheres with scaled abundances do. In other words, the temperature structure of a model
atmospheres peculiar only in Si and Fe may be close to the temperature profile of a models
with scaled abundances. The agreement is quite good for low effective temperatures, while for
Teff > 11 000 K the cumulative effect of all other chemical elements was required. They suspected
109
that overabundant C, Mg, and Ca are of the most significance.
They found that Fe is the principal contributor into the 5200Å depression for the whole
range of Teff, while Cr and Si are important primarily for low Teff. The analysis of the diagram
of the peculiarity index a versus (b − y) for the model atmospheres peculiar in Si, Cr, and Fe
revealed regular patterns in the locus of points representing those models. In fact, there were
three separate directions (axes) associated with the growing content of each element on the
diagram. The inclination of the Fe-axis to the normality line (Sect. 3) and the fact that it did
not depend on Teff clearly demonstrated that Fe is indeed the key element to the fundamental
property of the ∆a system.
15 Heuristic observational correlations for CP stars
The CP stars of the upper MS (Sect. 6) were the primarily targets of ∆a observations over the
last four decades in the Galactic field (Sect. 10), open clusters (Sect. 17), and the LMC (Sect.
19). Therefore, an overview of some heuristic observational correlations for CP stars are given.
The theoretical models and synthetic photometry are described in Sects. 8.1, 9, and 14.
Abundances: Netopil (2013) investigated the correlation of ∆a and ∆(V 1−G) (Sect. 4) with
the abundances in more detail. Here, these results are reviewed. Ryabchikova (2005) presented
the observational evidence that the abundances of Fe and Cr are strongly depending on the
Teff which led to the conclusion that these are mainly responsible for the absolute value of ∆a.
Later, Khan & Shulyak (2007) confirmed this result on the basis of stellar atmospheres (Sect.
14.9.3). Netopil (2013) used the abundances listed in Ryabchikova (2005) as a starting point,
and updated it with the recent literature. If more investigations were available for one object,
an average of the abundances have been derived. In total, abundances of the major elements
for 87 magnetic chemically peculiar objects were compiled. If averaged Teff were available in the
lists by Netopil et al. (2008), these were adopted, otherwise the values given in the respective
references were used. From this sample, 50 stars have a measured ∆a value (Sect. 10). The
results are shown in Figure 47. Although due to the different sensitivity of these two peculiarity
indices on specific spectral features (Sect. 14.9.2), a direct comparison is somehow problematic,
an offset of +15 mmag was applied to ∆(V 1 − G) to obtain a comparable peculiar index for
all objects. The upper panel shows the Teff dependency of the photometric indices, whereas
the others the dependency of selected elements. The correlation between the Fe abundance and
the peculiar indices can be easily recognized also in Fig. 48, supporting the conclusion that Fe
is the main contributor to the flux depression at 5200Å and hence for positive ∆a values. Its
“zero point” is located at about 7500 K, coinciding also with solar Fe abundances, whereas the
respective solar reference values were taken from Asplund et al. (2009). The hotter end of the
sample is not optimal covered, but is roughly estimated at about 15 000 K. However, ∆a values
can be designated as significant only at a level of +15 mmag, depending on the scatter of the
normal type stars (Sect. 11.1). Hence, taking into account this significance level, the Teff range
decreases to about 8000 − 14 000 K. Cooler or hotter CP stars will be probably only detected
if large overabundances of Si or Cr are present and/or a strong magnetic field contributes to
enhance ∆a. The overall lower ∆a values at higher Teff can be also noticed in the models by
Khan & Shulyak (2006a). Nevertheless, in this Teff range, all stars of the investigated sample
(Fig. 47) would have been unambiguously detected with ∆a photometry.
Colour: Figure 49 shows the ∆a versus (b − y)0 diagram for all stars (Sect. 10) included in
Renson & Manfroid (2009, RM09) together with the detection limit of CP stars according to
Section 11.1. The red circles mark the objects therein which are well-established CP stars of
all types. These stars seem to be uniformly distributed over the complete colour range with an
apparent gap at 0 < (b − y)0 < +0.05 mag. This is not only the region where the Balmer jump
is at it maximum, but also where the estimation of the reddening is most difficult (Napiwotzki
110
-20
0
20
40
60
80
100
6000 8000 10000 12000 14000 16000
a
(V1 - G)Peculiarityindex[mmag]
-1
0
1
2
3
log(NX
/NH
)-log(NX
/NH
)[dex]
Fe
Si
Cr
6000 8000 10000 12000 14000 16000
0
2
4
6
Eu
Sr
Teff
[K]
Figure 47: The Teff dependency of ∆a (filled circles) and ∆(V 1 − G) (open circles) is shown in
the upper panel. The ∆(V 1 − G) values were shifted by +15 mmag. The solid lines indicate the
zero point of ∆a at 7400 K and the dotted line a ∆a limit of +15 mmag. The lower two panels
show the abundances of some selected elements versus Teff. The data were taken from Netopil
(2013).
111
-20 0 20 40 60 80 100
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
a
(V1 - G)
log(NFe
/NH
)-log(NFe
/NH
)[dex]
Peculiarity index [mmag]
Figure 48: The [Fe/H] abundances of CP stars in correlation with ∆a (filled circles) and ∆(V 1−
G) (open circles).
et al., 1993). However, although the estimation of the reddening for the sample has been cross
checked with several methods (Sect. 10.1), there is small chance of an undetected bias because of
an inadequate treatment. If this hypothesis is rejected, one can conclude that all well established
CP stars in this colour range were successfully detected by the ∆a photometric system. The
apparent majority of CP stars with (b − y)0 < −0.05 mag can not be argued by astrophysical
means but is an manifestation of the intrinsic distribution of the observed stars (Fig. 22).
Looking for the most extreme ∆a values larger than +50 mmag, they are found for stars with
(b−y)0 < +0.13 mag (spectral type of about A7). The majority of these objects are B-type stars
which is line with the predictions of the detailed stellar atmospheric models (Sect. 14.9.2). A
detailed analysis of the detection probabilities of the different CP groups is given in Section 11.
Magnetic field strength: the catalogue by Bychkov et al. (2009) was search for all entries of
the complete sample of stars as listed in Section 10. Bychkov et al. (2009) published quadratic
effective magnetic field ⟨Be⟩ on the basis of different methods. For the definition of ⟨Be⟩ and its
correlation with the magnetic field modulus, for example, the reader is referred to Bychkov et al.
(2003). If more than one mean value is available for a star, the following measurement (the flag is
according to the used methods/lines) was used, sorted after the priority “all” ⇒ “met” ⇒ “Hl”.
This is a pure heuristic sequence based on the number of available measurements, Bychkov
et al. (2003, 2009) list neither weights nor a discussion of the quality for the corresponding
methods, for example. In total, 288 objects are included in both catalogues. From these, only
187 stars have a σ (the significance of the found magnetic field) larger than three. Figure 50
shows the results for the latter sample divided according to a (b − y)0 value of −0.05 mag which
corresponds roughly to a spectral type of B9. There is a clear correlation between log⟨Be⟩ and
∆a independent of the colour evident. This result is well in line with the predictions from stellar
112
-150 -100 -50 0 50 100 150 200 250 300 350
-10
0
10
20
30
40
50
60
70
80
90
RM09 (all)
RM09 (*)
a[mmag]
(b - y)
0
[mmag]
Figure 49: The ∆a versus (b − y)0 diagram for all stars included in Renson & Manfroid (2009,
RM09, black circles). The stars marked therein as well-established are denoted with red circles.
The dotted line marks the detection limit of CP stars according to Section 11.1.
model atmospheres (Sect. 14.9.2). From this figure it can be concluded that for all objects with
a ∆a value larger than +30 mmag, a ⟨Be⟩ larger than 200 G was unambiguously detected. This
lower limit for the magnetic field is statistically highly significant because there are 105 stars
with ∆a > +30 mmag in this sample and range. From these, 94 have a measured ⟨Be⟩ larger
than 200 G. From the remaining 11 stars, only one object (HD 74169) has a significant lower
⟨Be⟩ with 130(40) G, five objects (HD 6164, HD 44456, HD 91239, HD 137193, and HD 161277)
have insignificant magnetic field measurements lower than even 100 G, but five objects (HD
37140, HD 136347, HD 150035, HD 164429, and HD 219749) have mean values between 250 and
950 G, respectively. Note that there is, as far as it is known, no contamination of supergiants
(Sect. 11.8) at such large ∆a values. Only Pleione reached during its shell phase, once, an
exceptional ∆a value of +36 mmag (Sect. 11.9). Therefore, the contamination of objects other
than CP ones in this spectral type range is almost zero. This shows the uniqueness of the ∆a
photometric system to trace stellar magnetic fields for stars of the upper MS with a statistically
high probability.
Rotational period: Photometric variability of the CP2 star α2 Canum Venaticorum (ACV)
was first reported by Guthnik & Prager (1914). The light curves of CP stars can be fitted well
by a sine wave and its first harmonic with varying amplitudes depending on the photometric
filter systems (Bernhard et al., 2015a,b). For some CP stars, a double-wave structure of the
photometric light curves depending on the observed wavelength region is detected (Maitzen,
1980b). However, similar magnetic field modulus variations are rather rare exceptions (Mathys
et al., 1997). The variability of CP stars is explained in terms of the oblique rotator model
(Stibbs, 1950), according to which the period of the observed variations is simply the rotational
113
-10 0 10 20 30 40 50 60 70 80
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
(b - y)
0
< -0.05 mag
(b - y)
0
> -0.05 mag
log<Be
>[dex]
a [mmag]
Figure 50: The log⟨Be⟩ (Bychkov et al., 2009) versus ∆a diagram for the 187 stars with a
measured ∆a value (Sect. 10) and a magnetic field detection with σ > 3. The sample was
divided according to a (b − y)0 value of −0.05 mag which corresponds roughly to a spectral type
of B9. The dotted line marks the detection limit of CP stars according to Section 11.1.
period. Accurate knowledge of the rotational period and its evolution in time is a fundamental
step in understanding the complex behaviour of CP2/4 stars, especially as far as it concerns
the phase relation between the magnetic, spectral, and light variations (Mikulášek et al., 2010).
The “AAVSO International Variable Star Index”; (VSX, Watson, 2006) database was consulted
to check for entries for all stars included in RM09 with measured ∆a values as variable. From
this list, all stars not classified as ACV or ROT variables were deleted. These were mainly
pulsating, δ Scuti, γ Doradus, and Slowly Pulsating B-type, stars but also some elliptical variables
as well as eclipsing binaries. The final sample includes 238 stars. Already Kodaira (1973)
speculated if there is an anti-correlation between the rotational period and the degree of the
chemical peculiarity. In the light of the theory of magnetic accretion (Havnes, 1974) this could
be understood by the loss of angular momentum to the local environment and thus enhanced
accretion which leads to a stronger chemical peculiarity. Therefore, slower rotating CP stars
should have stronger pronounced peculiarities. In the light of the diffusion theory (Alecian,
2015), slower rotation means less influence of the meridional circulation (mixing) and a further
stabilisation of the magnetic field which makes the diffusion more efficient. This effect is called
magnetic breaking. Netopil (2013) presented a comprehensive overview of the literature and
made a thoroughly analysis of the available data. He concluded that there seems to be a correlation
between the investigated parameters: equatorial velocity, magnetic field strength, and
iron abundance. But these properties were also influenced by variations with the phase of the
114
-10 0 10 20 30 40 50 60 70 80
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
(b - y)
0
< -0.05 mag
(b - y)
0
> -0.05 mag
logP[dex]
a [mmag]
Figure 51: The log P versus ∆a diagram for 238 stars with a measured ∆a value (Sect. 10) and
a published rotational period from VSX. The sample was divided according to a (b − y)0 value
of −0.05 mag which corresponds roughly to a spectral type of B9. The dotted line marks the
detection limit of CP stars according to Section 11.1.
rotation period. Furthermore, there were strong indications that the magnetic field strength
declines with increasing equatorial velocity, or vice versa the stronger the magnetic field, the
slower the stellar rotation. This would support the theory of magnetic braking, which occurs
probably already during the pre-MS phase. For the Teff range between 9000 and 12 000 K there
were indeed indications that slower rotations implies higher iron abundances (one of the main
contributers to the ∆a index). But the effects were not very pronounced. Figure 51 shows the
log P versus ∆a diagram for the 238 stars with a measured ∆a value (Sect. 10) and a published
rotational period from VSX. The sample was divided according to a (b − y)0 value of −0.05 mag
which corresponds roughly to a spectral type of B9. It has to be emphasized that such a subdivision
is only a first approximation to stellar evolutionary effects. Although it is statistically
significant, no clear trend can be concluded from this sample. There seems no obvious strong
correlation between the rotational period and the strength of the ∆a index which is not in favour
of magnetic braking.
115
Table 22: Parameter space used for the models and the astrophysical parameters of the standard
star Vega and the λ Bootis stars HD 107233 and HD 204041.
Models Vega 107233 204041
Teff [K] 7000 − 9000 9560 6900 8100
log g [cgs] 3.50 − 4.50 4.05 3.80 4.10
vturb [km s−1] 2 2 3 2
Convection Canuto & Mazzitelli (1991)
Table 23: Location of the stars according to Figure 52. A plus sign means that the objects are
located within the area of the spectroscopic binary models. The results for the individual stars
are listed in Table 24.
Diagram ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 )
∆a − − −
∆(V 1 − G)/Z − − +/− +/− +
m1/m2 − − − +
m1 +/−
16 Investigating the λ Bootis spectroscopic binary hypothesis
using ∆a photometry
Here, a spin-off of the ∆a photometric system and its measurements is presented. This shows
its capability not only to detect different non-normal star groups but also to investigate their
characteristics in more detail.
More than 60 years after the first notification of the peculiar nature of λ Bootis (HR 5351)
by Morgan et al. (1943), the origin and even the existence of a homogeneous group of λ Bootis
stars (Sect. 6) is still a matter of debate.
The issue still remains whether the group itself is homogeneously defined as addressed by
Gerbaldi et al. (2003). Their working group has formulated the hypothesis that the tendency
to detect lower abundances for numerous elements in high resolution spectroscopy abundance
analysis might be explained by assuming an unidentified (or unidentifiable) binary system of
two “normal” (solar abundant) stars with similar spectral type. As a consequence they conclude
that the group of λ Bootis stars consists of single type objects and an unknown, but probable
high percentage of undetected spectroscopic binary systems.
In the following this hypothesis was investigate by comparing synthetic photometric indices
of binary systems to those of apparent group members.
16.1 Modelling the spectroscopic binary systems
The working hypothesis is rather simple: a spectroscopic binary system with two solar abundant
components has to simulate the total energy flux distributions and thus the photometric colours
of an apparent single λ Bootis star.
To investigate the chances of λ Bootis stars being disguised binary systems, we modelled
a set of stars spanning the range in fundamental parameters (Table 22) populated by λ Bootis
stars (Paunzen et al., 2002a).
The turbulent velocity was fixed at a value of 2 km s−1, convection was modelled according to
Canuto & Mazzitelli (1991, hereafter CM) since the stars are situated in the region of weak to no
116
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
m1
[mag]
-0.58
-0.56
-0.54
-0.52
-0.50
-0.48
-0.46
m2
[mag]
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
c1
[mag]
-0.04
-0.03
-0.02
-0.01
0.00
0.01
Z[mag]
0.00 0.05 0.10 0.15 0.20 0.25
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
a[mmag]
(b - y) [mmag]
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
(V1-G)[mmag]
(B2 - V1) [mag]
Figure 52: A comparison of the synthetic Strömgren uvbyβ, ∆a (left panels) and the Geneva
7-colour system (right panels) with the observations for the group of λ Bootis stars (full circles).
The open circles are the binary models whereas the grey shaded triangles are the single star
models used to construct them. Vega is marked as asterisk, the two synthetic “standard”
λ Bootis stars are open triangles. The standard lines are from the literature.
convection. To model the atmospheres as well as the energy flux distribution of these stars and
of the photometric anchor Vega, the code LLmodels v.SE/8.0 (Shulyak et al., 2004) was used.
This model atmosphere code supports individual chemical composition, VCS theory (Vidal et
al., 1973; Lemke, 1997) for the treatment of Hydrogen lines and the CM convection treatment.
To represent the atomic line opacities a separate line list for each model was created. The line
parameters where obtained form the Vienna Atomic Line Database (Kupka et al., 1999). All
lines for which lν/αν ≥ 1% (lν and αν are line and continuum absorption coefficient) was realized
for the given model structure were selected. The step size in wavelength of the synthetic spectra
was set to 0.1 Å.
An energy flux distributions of 105 hypothetical binary stars was built by preparing all
possible combinations of always two spectra. On these, synthetic photometry for the Strömgren
uvbyβ, ∆a, and the Geneva 7-colour system was performed. As it is common practice, Vega was
the reference point for the synthetic photometry. This stars atmosphere was modelled according
to the parameters of Hill & Landstreet (1993), the observed photometric indices were inquired
from the SIMBAD/CDS and GCPD astronomical databases.
To show also a comparison to synthesized intrinsic λ Bootis stars, the stars HD 107233 and
HD 204041 were modelled with the parameters and abundances listed in Heiter et al. (2002a).
For the statistical analysis, no reddening was taken into account. Gerbaldi et al. (2003) have
117
Table 24: The results for λ Bootis stars taken from Paunzen et al. (2002a) according to Fig. 52
and Table 23. Only the stars of group ( 5 ) can be considered as being good candidates for
undetected spectroscopic binary systems. No conclusion can be drawn for group ( 6 ), the abbreviations
in ( 7 ) are Passed or Failed. The last row contains the number of objects as part of
the total sample.
( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 )
6870 319 31295 111604 23392 13755 P
11413 7908 35242 156954 110377 15165 P
24472 30422 101108 193256 170680 54272 P
75654 74873 193281 198160 87271 P
81290 91130 90821 F
83041 110411 105759 P
83277 125162 111005 P
84123 130767 120500 F
102541 183324 120896 P
105058 204041 175445 F
106223 221756
107233
109738
125889
142703
142994
149130
153747
154153
168740
168947
184779
192640
210111
216847
44 % 19 % 5 % 7 % 7 % 18 %
extensively discussed the problems using the standard Strömgren uvbyβ dereddening procedures
for the group of λ Bootis stars. Their values were compared with those of Paunzen et al. (2002a)
and a good agreement was found. However, the reddening for most objects is negligible because
they are all located in the solar neighbourhood.
16.2 Results and Conclusions
Figure 52 shows the results of the relevant photometric diagrams. The observational data for
the λ Bootis stars were taken from Paunzen et al. (2002a). The classical metallicity sensitive
diagrams m1 versus (b − y) and m2 versus (B2 − V 1) show that for cooler objects, the λ Bootis
stars are nicely separated from the models on the MS, for example c1 versus (b − y). These
observational facts were also described in Paunzen et al. (1997).
Very interesting are the other three diagrams which include directly metallicity depend
indices (Sect. 4). The most important index is ∆a, for which, unfortunately, the least measurements
are available whereas ∆(V 1 − G) seems less sensitive with a larger scatter. Notice
118
that Vega as metal-deficient object (Hill & Landstreet, 1993; García-Gil et al., 2005) shows, as
expected, a reduced ∆a value. Otherwise, the standard lines and observations of Vega fit the
synthetic values very good. The differences of the synthetic and observed values for the two
λ Bootis stars are only 1 to 2 mmag for ∆a, Z, and ∆(V 1 − G), respectively.
According to Fig. 52, the sample was divided in six different groups numbered from ( 1 ) to
( 6 ) depending if the placement is compatible with the spectroscopic binary models taking an
error of ±5 mmag into account.
The final division is listed in Table 23 whereas Table 24 shows the results for the individual
stars. The first two groups include objects which are not located in the spectroscopic binary area
(SBA hereafter) in any diagram. The third and fourth group include stars which are situated
in the SBA either in the ∆(V 1 − G) or Z diagram, but not in the classical metallicity and the
∆a diagram or do not have an available ∆a measurement (fourth group).
The fifth group comprise good candidates for undetected spectroscopic binaries among the
λ Bootis group because these stars compare well to the synthetic photometry of the binary
models. HD 198160 is already known as close visual binary star whereas inconsistent v sin i
measurements were reported by Heiter (2002) for HD 170680. The four objects of this group
certainly deserve further attention in the future.
The last group includes those stars which could only be tested within the m1 versus (b − y)
diagram which prevents any clear conclusion.
If one compares the list of Table 24 with the results of Faraggiana et al. (2004), only two
stars, HD 11413 and HD 210111, were reported as spectroscopic binary systems on the basis of
radial velocity shifts of two and three spectra, respectively. Both are well investigated δ Scuti
pulsators (Breger et al., 2006) which makes them especially interesting for further investigations.
HD 210111 comprises of two equal (within the estimated errors) underabundant λ Bootis-type
stars (Paunzen et al., 2012). This object is very similar to the systems HD 84948 and HD 171948
investigated by Iliev et al. (2002).
The percentage of undetected spectroscopic binary systems mimicking a single, metal-weak
object seems very low. From 47 well investigated stars, groups ( 1 ) to ( 5 ), only four objects
seem good candidates for a further investigation which is below 10% of the complete sample.
A carefully preselection of λ Bootis stars, using ∆a photometry results in a homogeneous
group of intrinsic λ Bootis stars which can be used to investigate the group properties in more
detail.
17 The ∆a observations of Galactic open clusters
Since the 1970ies, CP stars in open clusters were targets of, first, photoelectric (Maitzen, 1981)
and then CCD (Bayer et al., 2000) observations. Up to now, fifteen parts of photoelectric
(last: Paunzen et al., 2014) and eight parts of CCD (last: Netopil et al., 2007) ∆a photometry of
Galactic open clusters are published by now (Table 25). In addition, there is one paper published
by Netopil et al. (2005) which presented CCD ∆a and BVR photometry of NGC 7296.
Netopil (2013) performed a deep and comprehensive study of the a-priori detected CP stars
and their characteristics in these open clusters. The interested reader is referred to this work.
Here, the focus is set on how to conduct photoelectric and CCD ∆a observations as well as
how to interpret the different diagrams. Still, there are a lot of unpublished photoelectric and
CCD measurements in the archive available which await for reductions and publication.
In addition, the list of already published aggregates with their parameters are given for both
samples. First, a short overview about the advantages of observations of open clusters are listed.
119
Table 25: The list of the fifteen papers including photoelectric (upper panel) and the eight with
CCD (lower panel) ∆a observations of Galactic open clusters.
I Maitzen & Hensberge (1981) IX Maitzen & Pavlovski (1987a)
II Maitzen & Floquet (1981) X Jenkner & Maitzen (1987)
III Maitzen (1982) XI Maitzen & Schneider (1987)
IV Maitzen & Wood (1983) XII Maitzen & Pavlovski (1987b)
V Maitzen & Schneider (1984) XIII Maitzen et al. (1988)
VI Maitzen (1985) XIV Maitzen (1993)
VII Maitzen et al. (1986) XV Paunzen et al. (2014)
VIII Maitzen & Catalano (1986)
I Bayer et al. (2000) V Paunzen et al. (2003a)
II Paunzen & Maitzen (2001) VI Paunzen et al. (2005a)
III Paunzen & Maitzen (2002) VII Paunzen et al. (2006)
IV Paunzen et al. (2002b) VIII Netopil et al. (2007)
17.1 The characteristics of open clusters
Open clusters are physically related groups of stars held together by mutual gravitational attraction.
Therefore, these populate a limited region of space, typically much smaller than their
distance from the Sun, so that the members are all approximately at the same distance (Lata
et al., 2002). They are believed to originate from large cosmic gas and dust clouds (diffuse
nebulae), and to continue to orbit the host galaxy through the disk. In many clouds visible as
bright diffuse nebulae, star formation still takes place, so that one can observe the birth of new
young star clusters (Massi et al., 2015). This process of formation takes only short time (a few
Myrs) compared to the lifetime of the cluster, so that, speaking in terms of stellar evolution, all
member stars are of similar age. Also, as all the stars in a cluster are formed from the same
diffuse nebula, they are all of similar initial chemical composition (Netopil et al., 2016). Hence,
open clusters are of great interest for several fields of astrophysics because:
• The cluster members are all at about the same distance from the Sun.
• Within a few million years cluster members have approximately the same age: a small
range compared to the age of all clusters older than a billion years.
• The chemical composition of the members is quite homogeneous within a cluster, but the
metallicities of the various open clusters range from about −1.0 to +0.6 dex compared to
the Sun.
• The member stars have different masses, ranging from about 120 M⊙ for the most massive
stars in very young clusters to less than about 0.08 M⊙
Distance, age and metallicity are, in general, not straightforward to determine for galactic
field stars. Open clusters, on the other hand, represent samples of stars of constant age and
homogeneous chemical composition, suited for the study of processes linked to stellar structure
and evolution, and to fix lines or loci in several most important astrophysical diagrams such as
the colour-magnitude diagram (CMD), or the Hertzsprung-Russell diagram (HRD). Comparing
the “standard” HRD, derived from nearby stars with sufficiently well known distances, or the
theory of stellar evolution, with the measured CMD of star clusters, provides a considerably good
method to determine the distance of star clusters. Comparing their HRD with stellar theory
120
Table 26: Fundamental parameters of the target clusters taken from Paunzen & Netopil (2006)
and Zejda et al. (2012).
Cluster α(2000) δ(2000) R⊙ E(B − V ) age µα cos δ µδ
[pc] [mag] [Myr] [mas/yr] [mas/yr]
Feinstein 1 C1103−595 11 05 56 −59 49 00 1180 0.41 5 −6.1 +2.9
NGC 2168 C0605+243 06 09 00 +24 21 00 830 0.23 100 +1.5 −2.9
NGC 2323 C0700−082 07 02 42 −08 23 00 895 0.23 100 +0.4 −2.0
NGC 2437 C0739−147 07 41 46 −14 48 36 1495 0.16 235 −5.0 +0.4
provides the best way to estimate the age of star clusters. The fact that all the cluster HRDs
can be explained by the theory of stellar evolution gives convincing evidence for our theories and
models, and moreover for the underlying physics including nuclear and atomic physics, quantum
physics and thermodynamics. In those cases where certain detailed features of cluster HRDs
deviate from theoretical predictions, this gives an incentive to review and improve the parts
of the stellar evolution models which cause the deviations. Observations of open clusters thus
enables to enhance the knowledge about the physics of stellar evolution.
About 2800 open clusters are known in the Milky Way (Kharchenko et al., 2013), and this
is probably only a small percentage of the total population. Most of them are much too distant
and therefore too faint to be observable, or have only a short life as stellar swarms. As they drift
along their orbits, some of their members escape the hosting cluster due to velocity changes in
mutual closer encounters, tidal forces in the galactic gravitational field and encounters with field
stars and interstellar clouds crossing their way (Chumak et al., 2010). A typical open cluster
has lost most of its member stars along its path after several hundred Myrs. Only some of them
reach an age older than a few billion years. The escaped individual stars continue to orbit the
Milky Way on their own as field stars. It is suspected that most or even all field stars in our
and the external galaxies have their origin in clusters.
17.2 Photoelectric ∆a observations of Galactic open clusters
In a series of fifteen papers (Table 25), photoelectric ∆a observations of Galactic open clusters
were published.
Based on the example of four open clusters (Feinstein 1, NGC 2168, NGC 2323, and
NGC 2437), the typical reduction process and detailed analysis is presented.
17.2.1 Observations and reduction
This work was originally initiated by the European working group on CP stars of the upper main
sequence (Mathys et al., 1989). The regular photoelectric observations of this programme were
performed until 1991. Nevertheless, there are no doubts about the accuracy of the photoelectric
measurements.
The fundamental parameters of the target clusters taken from Paunzen & Netopil (2006)
and Zejda et al. (2012) are listed in Table 26. The observations log is listed in Table 27.
Standard stars were usually measured 10 to 20 s per filter, programme stars of 120 s per filter.
In several cases the latter were observed only 20 to 30 s per filter in the corresponding filter
sequences which were repeated several times. This way inhomogeneities of the sky were thought
to be averaged out more effectively. The raw data were corrected for dead-time depending on the
used photomultiplier tube, converted to magnitudes, and corrected for night-to-night variations
and extinction, and averaged over the individual observations.
121
Table 27: Observations log, the description of the used equipment can be found in the last
column.
Cluster Observatory Telescope Time Reference
Feinstein 1 ESO Bochum 0.61 m 89/04 Maitzen (1993)
NGC 2168 Hvar 0.65 m 89/01, 89/02 Maitzen & Pavlovski (1987b)
NGC 2323 ESO 0.5 m 85/02, 85/03 Maitzen & Schneider (1987)
NGC 2437 ESO 1.0 m 84/02 Maitzen (1993)
To deredden the programme stars, use was made of photometric data in the Johnson, Geneva,
and Strömgren systems, compiled from the open cluster database WEBDA1. For the first two
systems, the well-known calibrations based on the X/Y parameters (Cramer, 1999) and Q-index
(Gutierrez-Moreno, 1975), respectively, applicable for O/B-type stars were applied. Objects with
available Strömgren data were treated with the routines by Napiwotzki et al. (1993), allowing
the dereddening of cooler type stars. For member stars without sufficient photometry, the mean
cluster reddening was adopted. There are only a few non-member stars (fifteen in total), for
which it was not possible to derive individual reddening values; these were therefore rejected in
the subsequent analysis. If several estimates for a particular object are available, a mean value
was calculated. Since all clusters are rather near to the Sun, a strong reddening especially for
cool-type stars is hardly expected.
Because of the reddening, the normality line is shifted by E(B −V ) to the red and by a small
amount E(a) to higher a-values (Sect. 3). The mean ratio of these shifts f = E(a)/E(B − V )
was determined as f ≈ 0.035. The final values were calculated as acorr = a(obs) − fE(B − V ).
For the subsequent analysis, the dereddened diagnostic acorr versus (B −V )0 diagrams (Fig. 53)
were used. The mean (B − V ) values have been calculated from the data included in WEBDA.
The normality line for each cluster was determined using the photometric data of member
and non-member stars, which is justified because of the use of individually dereddened colours.
Objects deviating more than 3 σ were rejected in an iterative process. The final coefficients of
acorr = b+c(B −V )0 together with their errors are listed in Table 28. An object is considered as
positively (or negatively) detected if its ∆a value, taking into account the observational error,
lies above (or below) the 3 σ limit of the corresponding normality line. In the following, the
numbering system from WEBDA (W no.) is used.
For the membership probabilities of the individual stars, the method given in Balaguer-Núnez
et al. (1998) was employed. In addition, the results were compared with those of the algorithm
published by Javakhishvili et al. (2006), yielding excellent agreement. The first method takes
both the errors of the mean cluster and the stellar proper motions into account. The mean
proper motions of the target clusters were taken from Zejda et al. (2012) and are listed in Table
26. The proper motions of the individual stars were taken from the following sources, sorted by
the priority:
• TYCHO-2 (Høg et al., 2000);
• UCAC4 (Zacharias et al., 2013);
• PPMXL (Röser et al., 2010).
For the complete sample, kinematic data are available. A comparison with the results published
by Baumgardt et al. (2000) yields an excellent agreement.
1
http://webda.physics.muni.cz
122
Table 28: Final results, all photometric values are given in mmag. For Feinstein 1 W17 it was
not possible to derive reliable astrophysical parameters (see text). The errors in the final digits
of the corresponding quantity are given in parenthesis.
Feinstein 1 NGC 2168 NGC 2323 NGC 2437
acorr = b + c(B − V )0, N 17(2)/55(6)/24 29(2)/47(17)/21 −34(4)/35(17)/17 123(1)/61(6)/37
3 σ ±8 ±9 ±14 ±12
N(> 50%)/N(< 50%) 22/6 19/8 9/9 36/12
#CP/∆a/Prob W16/+16/99 W244/+16/93 W171/+51/82 W172/+34/80
W17/+15/59 W336/+17/37 W457/+26/76
W364/+23/69 W469/+38/63
W476/+19/50
log Teff / log L/L⊙ 4.350/3.36 4.126/2.32 4.105/2.07 3.993/1.67
−/− 4.060/2.25 4.018/1.82
4.086/2.77 3.978/1.98
3.985/1.72
The effective temperature calibrations and bolometric corrections for CP stars by Netopil et
al. (2008) were applied on the available photometric data in the Johnson, Geneva, and Strömgren
systems. The luminosities were derived using the cluster parameters listed in Table 26 regardless
of the kinematic non-membership in order to obtain an additional membership criterion. In
general, an uncertainty for the derived temperatures of 500 K and 700 K for CP2 and CP4 stars
were adopted, respectively (Netopil et al., 2008). The errors in luminosity were derived using a
standard error in distance of 10 %, 0.1 mag for bolometric correction, and 0.02 mag for brightness
and interstellar reddening.
By comparing the derived absolute magnitudes and temperatures with available spectral
types, it was concluded that all kinematic non-members can be also considered cluster nonmembers
from the photometric point-of-view.
One exceptional case is Feinstein 1 W17 which is a kinematical member, but from photometry
it seems the contrary. A detailed analysis for it is given in Section 17.2.2.
From the final acorr versus (B − V )0 diagrams (Fig. 53), ten stars were found that deviate
significantly from the corresponding normality lines. Only two of them seem not to be a member
of their associated star cluster. However, since each star was dereddened individually, these stars
are still very good candidates for being true CP stars. In the following, the results for the open
clusters are discussed in more detail.
17.2.2 Feinstein 1
This aggregate is an accumulation of brighter stars around the β Cephei variable and helium
star HD 96446 (W20). If this is indeed a true star cluster, it is very young and all A- and F-type
stars should still be in their Pre-MS phase (Feinstein, 1964). Since its initial discovery, it has
hardly been studied.
Two stars, HD 305941 (W16) and HD 306034 (W17), were found significantly above the
normality line. Garcia (1993) classified W16 as B2 IV/V (v sin i of 80 km s−1) and W17 as Am
(kA2 IV, mF6 III/IV). The projected rotational velocity of W16 is exceptionally low for an early
B-type star which already points to a CP nature. They also noted that “He ii at 4009Å presents
intensity variations”. From the classification of W17 it is already clear that this is a very extreme
CP1 star.
From the kinematic data, the membership probabilities of 99% and 59% were derived, respectively.
Therefore, these stars were calibrated using the reddening and distance of Feinstein 1
123
-0.20 -0.15 -0.10 -0.05 0.00
0.00
0.01
0.02
0.03
0.04
0.05
0.06
W336
W364
NGC 2168
W244
-0.15 -0.10 -0.05 0.00
-0.06
-0.04
-0.02
0.00
0.02
W171
NGC 2323
(B - V)
0
[mag]
acorr
[mag]
-0.2 -0.1 0.0 0.1 0.2 0.3
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
(B - V)
0
[mag]
W457
W469
W476
W172
NGC 2437
-0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00
-0.01
0.00
0.01
0.02
0.03 Feinstein 1
W16
acorr
[mag]
W17
Figure 53: acorr versus (B −V )0 diagrams for the target clusters listed in Table 26. Filled circles
denote stars with a kinematical membership probability of more than 50%, open circles less than
50%. Stars with a statistical significant ∆a value, are denoted with their WEBDA numbers (W
no.). The solid line is the normality line.
(Table 26). This resulted in Teff and MBol of [22 400 K, −3.7 mag] and [10 300 K, −1.6 mag] for
W16 and W17. While the values for W16 are perfectly in line with the spectral type, they
are not compatible for W17 even if a pre-main-sequence status is assumed. For W17, a different
approach on the basis of Johnson UBV photometry was chosen. Taking the standard
relation for (B − V ) versus (U − B) from Schmidt-Kaler (1982) and the observed values, the
reddening was estimated assuming that the object follows the standard relation. As a result,
E(B − V ) = 0.15 mag was calculated. With this reddening value, the Teff was calibrated as
7800 K. This value is well in line with the spectral type of Am (kA2 IV, mF6 III/IV). As a last
step, the Teff value was kept fixed and the distances were calculated which place the star either at
the zero- or terminal-age-main-sequence within the evolutionary grids by Schaller et al. (1992).
The derived values are between 300 pc and 850 pc which establishes it as being a foreground
star. Recalculating the ∆a value using the reddening given above and the relation from Table
28 yields +10 mmag. However, this peculiar object is worthwhile for follow-up spectroscopic observations.
One can conclude that W17 is not associated with Feinstein 1, although its kinematic
characteristic is, to a certain degree, compatible with the mean cluster proper motion.
From its stellar parameters, it can be inferred that W16 is a CP4 (He-strong) star with
about 7.7 M⊙. This star is the most massive and most luminous star among the CP candidates.
Cidale et al. (2007) presented a similar diagram for a sample of CP4 stars (see Fig. 7 therein).
From this diagram, it was found that this star is among the youngest CP4 objects known so far.
124
17.2.3 NGC 2168
For this open cluster, two CP star candidates are listed in the literature (Niedzielski & Muciek,
1988): W364 (HD 252405) and W547 (HD 252459). The source of the corresponding information
is unknown. Both stars are classified in Hoag & Applequist (1965) as B6 III: and A3 V,
respectively. The star W364 has a measured ∆a value of +23 mmag which confirms its peculiar
nature. For W547, +17 mmag is measured, but the error of the mean is too large to make it
statistically significant. One could argue that this is caused by an apparent photometric variability
due to spots and rotation. However, according to the kinematical data, W547 is not a
member (1% probability) of NGC 2168. On the other hand, W364 is a member of the cluster.
It is close to the Terminal-Age-MS with a mass of about 4.1 M⊙. This would correspond to a
probable B7 Si-type star.
In addition, two other stars from our sample are significantly above the normality line,
namely W244 (TYC 1877−356−1, +16) and W336 (HD 252427, +17). For neither of these
objects spectral classifications are available (Skiff, 2016). The kinematical data supports the
membership of W244 (93%), but not for W336 (37%). They both have masses between 3 M⊙
and 4 M⊙ and would be therefore classified as late B-type Si stars. Note that HD 252427 is
incorrectly identified as W335 in SIMBAD/CDS. For W336, the star HD 252458 is listed.
The only known emission-type object in the cluster area (Kohoutek & Wehmeyer, 1999),
HD 41995 (W781), was not measured.
17.2.4 NGC 2323
The known CP candidate stars within NGC 2323 are HD 52965 (W3) and BD−08 1708 (W51).
Bychkov et al. (2009) listed upper limits of the magnetic fields for these objects of 89 G and 49 G,
respectively. They list a spectral classification of B8 Si, taken from Renson & Manfroid (2009),
for HD 52965 which is probably wrong. The only found reference in this respect is from Young
& Martin (1973) who list “B9 p: Si ii (4128/4130) slightly enhanced”. A ∆a value of +3 mmag
was measured. This value together with the non-detection of a magnetic field suggests that this
object is not a CP star. Young & Martin (1973) published the spectral type of “B9p:: Hg ii
3984Å weak” for BD−08 1708. A classification which is not typical for a CP3 object. However,
this star was not measured.
For the star CD−08 1704 (W171) a significant positive ∆a value of +51 mmag was found.
Its membership probability is 82%. The are some investigations of NGC 2323 that include
photometric but no spectroscopic data (Clariá et al., 1998; Sharma et al., 2006; Frolov et al.,
2012). Clariá et al. (1998) list E(B − V ) = 0.23 mag for W171 which corresponds to the mean
value of the cluster (Table 26). The star W171 is a 100 Myr old, 3.4 M⊙ (late B-type), probable
Si, star.
17.2.5 NGC 2437
The open cluster NGC 2437 has been studied photometrically several times because it might
host a planetary nebula (Majaess et al., 2007). However, there is no detailed spectroscopic
analysis available in the literature. Neither CP nor Be stars within the cluster area have been
detected so far.
Four stars were detected that lie above the normality line, namely W172 (TYC 5422−967−1,
∆a = +34 mmag), W457 (TYC 5422−2127−1, +26), W469 (BD−14 2133, +38), and W476
(TYC 5422−305−1, +19). For none of these objects are spectral classifications available in
the literature. All stars are, within the errors, well represented by the isochrone for NGC 2437
with a distance of 1500 pc and an age of 235 Myr. The derived masses range from 2.4 M⊙ to
2.9 M⊙ which corresponds to early A-types.
125
17.3 CCD ∆a observations of Galactic open clusters
The large photoelectric survey in the ∆a system was mainly dedicated to clusters no more distant
than 1000 pc from the Sun (Sect. 17.5). Nevertheless, these results still serve as an important
basis for new CCD observations in order to provide photometric standards, for example. With
the CCD technique, it is possible to observe open clusters much more distant than that providing
a more general representation of the Galactic field.
Nowadays, one can hardly find any photomultiplier tubes (PMT) in operation at international
observatories. The CCD technique has developed very rapidly over the last twenty years.
But even early comparisons between PMTs and CCDs were in favour of the latter, both in
accuracy and efficiency (Abbott & Kleinman, 1994).
However, the CCD technology not only has advantages but also has pitfalls. Here a short
list of things are listed, the user of CCD ∆a observations has to keep in mind.
• Because the normality line is deduced from the apparent normal type stars of the same
frame where the apparent peculiar objects are located, photometry can also be performed
in non-photometric conditions. The only assumption is that the absorption due to clouds,
for example, is homogeneous over the whole frame and the exposure time (Croom et al.,
1999).
• The observation of bright and faint stars with the same exposure time is very critical.
Normally, each CCD chip has a limited linearity range. Therefore, for a given exposure
time, bright stars in the field are saturated and faint ones are underexposed. To overcome
this problem, one has to use at least two different exposure times and then merge the
frames accordingly.
• Normally, the field of view of modern instruments with CCD is limited to about 25’,
except of CCD arrays. This means that if one wants to observe near and large clusters,
the mosaicing technique has to be applied. It is a well known technique but care has to
be taken that enough common stars on the fields are available or in other words, there is
a sufficient overlap.
In a series of eight papers (Table 25), CCD ∆a observations of Galactic open clusters were
published. In addition, there is one paper published by Netopil et al. (2005) which presents
CCD ∆a and BVR photometry for NGC 7296.
The reduction of the individual photometric CCD frames of the different filters follow the
common ways of such a framework. There are many books, recipes, and guides available in the
literature (Howell, 2006). Here only the very basic and common steps are mentioned (see also
Sect. 18.1).
• Subtract dark from all images, but bias frames
• Combine all bias files
• Subtract bias from all images
• Combine flats for a mean flat field
• Apply mean flat field to all scientific images
• Get photometric values using aperture and/or point spread function fitting for all objects
• Search for possible zero point offsets and/or trends between the photometric values of the
individual frames and correct for them
126
17
16
15
14
13
12
11
10
16
15
14
13
12
11
NGC 6451
-0.75 -0.60 -0.45 -0.30 -0.15 0.00 0.15
0.60
0.63
0.66
0.69
0.72
0.75
0.78
0.81
0.84
0.87
a
0
= 0.798 + 0.343 (g
1
- y)
(g
1
- y) [mag]
17
16
15
14
13
12
11
10
NGC 6192
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
0.80
a
0
= 0.786 + 0.251 (g
1
- y)
(g
1
- y) [mag]
NGC 6134
V[mag]
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
a
0
= 0.809 + 0.279 (g
1
- y)
a[mag]
(g
1
- y) [mag]
Figure 54: Typical diagnostic diagrams within the ∆a photometric system. Here, three open
clusters (NGC 6134, NGC 6192, and NGC 6451) observed with the CCD technology are shown.
The solid line is the normality line whereas the dotted lines are the confidence intervals corresponding
to 99.9 %.
• Get mean photometric values for all objects
• Generate the different photometric plots
The analysis of the observational material is in general identical as listed in Section 17.2. In
Fig. 54, three typical examples of diagnostic diagrams within the ∆a photometric system for
three open clusters (NGC 6134, NGC 6192, and NGC 6451) are shown. Their cluster parameters
are listed in Table 30. From this figure several conclusions can be drawn which are very important
when working with the ∆a photometric system. The individual cluster diagrams are described
in more detail in the following.
• NGC 6134: There is a well defined MS, turn-off point, and the giant population for this
cluster. Several Blue Stragglers (BS, Ahumada & Lapasset, 2007) and one very bright nonmember
are visible. Neither of these stars exhibit a significant deviating a value which is
line with the investigation listed in Section 11.8.
• NGC 6192: Again, the MS and three giants are clearly visible, but no BS are present. One
CP star was detected in this cluster.
• NGC 6451: Here, a typical, more general case for distant open cluster is shown. There
are two bright non-members which are probable foreground stars. Notice that the bluer
of these objects show a significant positive ∆a value. But with the help of the CMD,
this object can be unambiguously identified as non-member and not as cluster CP star
127
candidate. In addition, several more reddened background stars are present. None of them
show a deviating a value because this diagram is almost insensitive to reddening (Sect. 3).
These examples illustrate the variety of possible characteristics of the diagnostic diagrams.
However, normally, the true nature (membership, fore- and background as well as bona-fide CP
stars) of the deviating cases can be solved with the help of these diagrams, alone without the
help of additional information such as astrometric or spectroscopic data.
17.4 The observation of Blue Stragglers in open clusters
As described in Sect. 7.1, Blue Stragglers (BS) were discovered as members of open and globular
clusters which are hotter (bluer) than the turn-off point of the corresponding cluster (Mermilliod,
1982).
Pendl & Seggewiss (1975) were among the first who investigated the spectra of these stars in
more detail. Moreover, they were testing the hypothesis if BS are CP stars which would explain
their bluer colour. This “blueing” effect is typical for some magnetic CP objects due to stronger
UV absorption than in normal type stars (Adelman, 1980). They investigated BS which are
true members of IC 4756. They found a percentage of up to 58% of CP stars among BS. Later
on, Abt (1985) found even a higher incidence of 62%. These numbers are much higher than the
normal incidence of CP stars among all MS objects (a maximum of 15%) of the same spectral
type (Sect. 6). However, these findings were somehow contradicted by a series of papers by
Schönberner et al. (2001) who derived detailed elemental abundances for BS of open clusters.
Although they found several He peculiar objects, the iron and titanium abundances agreed with
those of the normal cluster members. The projected rotational velocities of the confirmed BS
were significantly lower than the mean values typical for their spectral types. This would give a
hint that diffusion might play a significant role in their atmospheres. Up to now, no detectable
(strong) magnetic fields of BS have been found yet (Mathys, 1988).
Maitzen et al. (1981) studied 27 BS within nine open clusters via photoelectric ∆a measurements
in order to derive the CP incidence among this sample. This was, until now, the only
dedicated investigation of this star group.
Their target clusters were all older than 100 Myr which corresponds to a BS population of
a spectral type between B3 and F0. The targets were selected on the basis of their location
in the HRD as well as radial velocity and proper motion data to guarantee a high membership
probability. They found two stars (8.3% of the total sample) with strong and another four
(17%) with a mild photometric variability on the basis of the dereddened normality line (Sect.
3). This number is very much in line with the “normal overall” incidence of CP stars (see
discussion above). But one has to keep in mind that this conclusion is based on somehow poor
number statistics.
17.5 Statistics of the observed open clusters
In this section, an overview of all, up-to-now, observed Galactic open clusters is given. This
includes all photoelectric and CCD observations. The cluster parameters were taken from
DAML02, version 3.5 (Dias et al., 2002) whereas the metallicity ([Fe/H]) is from Netopil et
al. (2016). The Cartesian [XY Z] coordinates are defined as
• X: radially outwards away from Galactic Centre
• Y : in direction of Sun’s rotation around the Milky Way
• Z: out of Galactic plane, positive towards North Galactic Pole
128
Table 29: All observed aggregates with the references listed in Table 25.
Cluster α (2000) δ (2000) l b X Y Z peo CCD
[h] [o
] [o
] [o
] [pc] [pc] [pc]
Berkeley 11 04 20 36 +44 55 00 157.0815 −03.6421 −2022 +855 −140 VII
Berkeley 94 22 22 42 +55 51 00 103.0946 −01.1844 −596 +2561 −54 VII
Collinder 121 06 56 20 −24 43 46 235.7016 −09.9906 −610 −895 −191 IV
Collinder 132 07 15 20 −30 41 00 242.9893 −08.8024 −212 −416 −72 XIV
Collinder 140 07 24 27 −31 51 00 244.9298 −07.5912 −170 −364 −54 X
Collinder 272 13 30 26 −61 19 00 307.5947 +01.2016 +1278 −1660 +44 IV
Feinstein 1 11 05 56 −59 49 00 290.0251 +00.3847 +397 −1089 +8 XV
Haffner 15 07 45 32 −32 51 00 247.9516 −04.1576 −1310 −3235 −254 VII
IC 2391 08 40 32 −53 02 00 270.3622 −06.8387 +1 −174 −21 VIII
IC 2602 10 42 58 −64 24 00 289.6014 −04.9061 +54 −151 −14 XIII
IC 4665 17 46 18 +05 43 00 30.6191 +17.0820 +290 +171 +103 V
IC 4725 18 31 47 −19 07 00 13.7023 −04.4335 +601 +146 −48 VI
King 21 23 49 54 +62 43 00 115.9465 +00.6827 −920 +1891 +25 VIII
Lynga 1 14 00 02 −62 09 00 310.8494 −00.3373 +1243 −1437 −11 VII
Lynga 14 16 55 04 −45 14 00 340.9189 −01.0885 +832 −288 −17 IV
Melotte 20 03 24 19 +49 51 42 146.5676 −05.8625 −154 +101 −19 XII
Melotte 22 03 47 00 +24 07 00 166.5707 −23.5211 −119 +28 −53 IX
Melotte 105 11 19 42 −63 29 00 292.9039 −02.4119 +667 −1578 −72 I
Melotte 111 12 25 06 +26 06 00 221.3538 +84.0248 −8 −7 +95 IX
NGC 1039 02 42 05 +42 45 42 143.6580 −15.6132 −387 +285 −134 VII
NGC 1502 04 07 50 +62 19 54 143.6724 +07.6577 −798 +587 +133 VI
NGC 1662 04 48 27 +10 56 12 187.6950 −21.1142 −404 −55 −157 I, IV
NGC 1901 05 18 11 −68 27 00 279.0397 −33.6065 +60 −378 −255 XIV
NGC 2099 05 52 18 +32 33 12 177.6354 +03.0915 −1380 +57 +75 V
NGC 2168 06 08 54 +24 20 00 186.5910 +02.1913 −905 −105 +35 XV
NGC 2169 06 08 24 +13 57 54 195.6076 −02.9345 −1012 −283 −54 XIV I
NGC 2232 06 27 15 −04 45 30 214.4324 −07.5422 −294 −201 −47 X
NGC 2287 06 46 01 −20 45 24 231.0196 −10.4446 −439 −543 −129 IV
NGC 2323 07 02 42 −08 23 00 221.6722 −01.3311 −709 −631 −22 XV
NGC 2343 07 08 06 −10 37 00 224.2681 −01.1728 −756 −737 −22 X, XIV
NGC 2362 07 18 41 −24 57 18 238.1789 −05.5482 −777 −1252 −143 III
NGC 2422 07 36 35 −14 29 00 230.9582 +03.1303 −308 −380 +27 IV
NGC 2423 07 37 06 −13 52 18 230.4836 +03.5369 −486 −590 +47 XIV
NGC 2437 07 41 46 −14 48 36 231.8576 +04.0644 −930 −1185 +107 XV
NGC 2439 07 40 45 −31 41 36 246.4425 −04.4666 −518 −1188 −101 III
NGC 2447 07 44 30 −23 51 24 240.0387 +00.1346 −518 −898 +2 XIV
NGC 2451A 07 43 12 −38 24 00 252.5754 −07.2986 −56 −179 −24 VIII
NGC 2451B 07 44 27 −37 40 00 252.0509 −06.7264 −92 −285 −35 VIII
NGC 2489 07 56 15 −30 03 48 246.7128 −00.7731 −1564 −3634 −53 II
NGC 2516 07 58 04 −60 45 12 273.8158 −15.8558 +26 −393 −112 I, IV
NGC 2546 08 12 15 −37 35 42 254.8552 −01.9859 −240 −887 −32 III
NGC 2547 08 10 09 −49 12 54 264.4649 −08.5975 −34 −355 −54 XV
NGC 2567 08 18 32 −30 38 24 249.7951 +02.9610 −578 −1572 +87 II
NGC 2632 08 40 24 +19 40 00 205.9196 +32.4843 −142 −69 +100 XII
NGC 2658 08 43 27 −32 39 30 254.5554 +06.0698 −535 −1937 +214 II
NGC 3105 10 00 39 −54 47 18 279.9147 +00.2636 +1469 −8403 +39 VI
NGC 3114 10 02 36 −60 07 12 283.3317 −03.8395 +210 −884 −61 XIII V
NGC 3228 10 21 22 −51 43 42 280.6971 +04.5453 +101 −533 +43 III
NGC 3293 10 35 51 −58 13 48 285.8562 +00.0736 +636 −2238 +3 VIII
129
Table 29: continued.
Cluster α (2000) δ (2000) l b X Y Z peo CCD
[h] [o
] [o
] [o
] [pc] [pc] [pc]
NGC 3532 11 05 39 −58 45 12 289.5708 +01.3468 +165 −463 +12 XI
NGC 3960 11 50 33 −55 40 24 294.3672 +06.1826 +759 −1675 +199 III
NGC 4103 12 06 40 −61 15 00 297.5736 +01.1551 +755 −1446 +33 XV
NGC 5281 13 46 35 −62 55 00 309.1610 −00.7137 +700 −859 −14 II
NGC 5460 14 07 27 −48 20 36 315.7462 +12.6281 +489 −477 +153 VI
NGC 5662 14 35 37 −56 37 06 316.9370 +03.3939 +486 −454 +39 XI
NGC 5999 15 52 08 −56 28 24 326.0082 −01.9249 +1699 −1145 −69 VIII
NGC 6025 16 03 17 −60 25 54 324.5508 −05.8840 +613 −436 −78 XV
NGC 6031 16 07 35 −54 00 54 329.2813 −01.4981 +1567 −931 −48 VII
NGC 6087 16 18 50 −57 56 06 327.7258 −05.4256 +750 −474 −84 VI
NGC 6134 16 27 46 −49 09 06 334.9170 −00.1976 +1141 −534 −4 III
NGC 6192 16 40 23 −43 22 00 340.6473 +02.1223 +1459 −512 +57 III
NGC 6204 16 46 09 −47 01 00 338.5597 −01.0395 +1117 −439 −22 V
NGC 6208 16 49 28 −53 43 42 333.7545 −05.7648 +838 −413 −94 II
NGC 6250 16 57 56 −45 56 12 340.6832 −01.9196 +816 −286 −29 I
NGC 6268 17 02 10 −39 43 42 346.0486 +01.2998 +1048 −260 +24 VI
NGC 6281 17 04 41 −37 59 06 347.7306 +01.9725 +468 −102 +16 V
NGC 6396 17 37 36 −35 01 36 353.9299 −01.7737 +1185 −126 −37 IV
NGC 6405 17 40 20 −32 15 12 356.5802 −00.7766 +486 −29 −7 V VII
NGC 6451 17 50 41 −30 12 36 359.4775 −01.6005 +2079 −19 −58 III
NGC 6475 17 53 51 −34 47 36 355.8606 −04.5005 +299 −22 −24 II
NGC 6611 18 18 48 −13 48 24 16.9540 +00.7935 +1722 +525 +25 IV
NGC 6633 18 27 15 +06 30 30 36.0112 +08.3278 +301 +219 +54 XV
NGC 6705 18 51 05 −06 16 12 27.3070 −02.7759 +1666 +860 −91 V
NGC 6756 19 08 42 +04 42 18 39.0884 −01.6813 +1169 +950 −44 V
NGC 6802 19 30 35 +20 15 42 55.3256 +00.9167 +1011 +1462 +28 VIII
NGC 6830 19 50 59 +23 06 00 60.1353 −01.7997 +816 +1421 −51 VIII
NGC 6834 19 52 12 +29 24 30 65.6981 +01.1890 +850 +1883 +43 VII
NGC 7092 21 31 48 +48 26 00 92.4027 −02.2418 −14 +325 −13 VII
NGC 7235 22 12 25 +57 16 12 102.7011 +00.7822 −732 +3248 +45 VI
NGC 7243 22 15 08 +49 53 54 98.8568 −05.5237 −124 +795 −78 XII
NGC 7296 22 28 01 +52 19 22 101.8831 −04.5880 −503 +2390 −196
NGC 7510 23 11 03 +60 34 12 110.9026 +00.0645 −1242 +3251 +4 VI
Pismis 20 15 15 23 −59 04 00 320.5164 −01.2002 +2525 −2080 −69 IV
Ruprecht 44 07 58 51 −28 35 00 245.7456 +00.4823 −1943 −4312 +40 VIII
Ruprecht 115 16 12 52 −52 24 00 330.9588 −00.8493 +1888 −1048 −32 VIII
Ruprecht 120 16 35 10 −48 17 00 336.3854 −00.4932 +1832 −801 −17 VIII
Ruprecht 130 17 47 32 −30 06 00 359.2214 −00.9600 +2100 −29 −35 VII
Stock 2 02 14 43 +59 29 06 133.3339 −01.6942 −208 +220 −9 XV
Stock 16 13 19 29 −62 38 00 306.1486 +00.0631 +1068 −1462 +2 VI
Trumpler 2 02 36 53 +55 54 54 137.3765 −03.9710 −532 +490 −50 XV
Trumpler 10 08 47 54 −42 27 00 262.7907 +00.6740 −53 −421 +5 X
130
Table 30: The cluster parameters of all observed aggregates (Table 29). The apparent diameter
(d), distance from the Sun (R⊙), colour excess E(B − V ) in (B − V ), and age (log t) were taken
from DAML02, version 3.5 (Dias et al., 2002) whereas the metallicity ([Fe/H]) is from Netopil
et al. (2016).
Cluster d R⊙ E(B − V ) log t [Fe/H] Cluster d R⊙ E(B − V ) log t [Fe/H]
[’] [pc] [mag] [dex] [dex] [’] [pc] [mag] [dex] [dex]
Berkeley 11 5 2200 0.950 8.041 −0.01 NGC 3114 35 911 0.069 8.093 +0.05
Berkeley 94 3 2630 0.608 6.996 NGC 3228 5 544 0.028 7.932 +0.01
Collinder 121 60 1100 0.040 7.080 NGC 3293 6 2327 0.263 7.014
Collinder 132 80 472 0.037 7.080 NGC 3532 50 492 0.028 8.477 0
Collinder 140 60 405 0.030 7.548 +0.01 NGC 3960 5 1850 0.290 9.100 −0.04
Collinder 272 10 2095 0.604 7.020 +0.03 NGC 4103 6 1632 0.294 7.393
Feinstein 1 25 1159 0.400 7.000 NGC 5281 7 1108 0.225 7.146 −0.02
Haffner 15 4 3500 1.050 7.300 NGC 5460 35 700 0.092 8.200 +0.03
IC 2391 60 175 0.008 7.661 −0.01 NGC 5662 29 666 0.311 7.968 +0.04
IC 2602 100 161 0.024 7.507 −0.02 NGC 5999 3 2050 0.450 8.600 −0.03
IC 4665 70 352 0.174 7.634 −0.03 NGC 6025 14 756 0.159 7.889
IC 4725 29 620 0.476 7.965 0 NGC 6031 3 1823 0.371 8.069 0
King 21 4 2103 0.886 7.163 +0.03 NGC 6087 14 891 0.175 7.976 +0.21
Lynga 1 3 1900 0.450 8.000 +0.02 NGC 6134 6 1260 0.350 8.950 +0.11
Lynga 14 3 881 1.428 6.712 NGC 6192 9 1547 0.637 8.130 +0.12
Melotte 20 300 185 0.090 7.854 +0.14 NGC 6204 5 1200 0.460 7.900 +0.02
Melotte 22 120 133 0.030 8.131 −0.01 NGC 6208 18 939 0.210 9.069 −0.01
Melotte 105 5 1715 0.830 8.550 +0.06 NGC 6250 10 865 0.350 7.415
Melotte 111 120 96 0.013 8.652 0 NGC 6268 6 1080 0.400 7.600 +0.14
NGC 1039 35 499 0.070 8.249 +0.02 NGC 6281 8 479 0.148 8.497 +0.06
NGC 1502 8 1000 0.700 7.000 NGC 6396 3 1192 0.926 7.506
NGC 1662 20 437 0.304 8.625 −0.11 NGC 6405 20 487 0.144 7.974 +0.07
NGC 1901 10 460 0.030 8.780 −0.08 NGC 6451 7 2080 0.672 8.134 +0.01
NGC 2099 14 1383 0.302 8.540 +0.02 NGC 6475 80 301 0.103 8.475 +0.02
NGC 2168 40 912 0.200 8.250 −0.21 NGC 6611 6 1800 0.800 6.110
NGC 2169 5 1052 0.199 7.067 NGC 6633 20 376 0.182 8.629 −0.08
NGC 2232 53 359 0.030 7.727 +0.11 NGC 6705 32 1877 0.428 8.400 +0.12
NGC 2287 39 710 0.010 8.400 −0.11 NGC 6756 4 1507 1.180 7.790 +0.08
NGC 2323 14 950 0.200 8.000 NGC 6802 5 1778 0.840 8.980 +0.01
NGC 2343 5 1056 0.118 7.104 +0.03 NGC 6830 5 1639 0.501 7.572 +0.22
NGC 2362 5 1480 0.100 6.700 NGC 6834 5 2067 0.708 7.883
NGC 2422 25 490 0.070 7.861 +0.09 NGC 7092 29 326 0.013 8.445 0
NGC 2423 12 766 0.097 8.867 +0.08 NGC 7235 5 3330 0.900 6.900
NGC 2437 20 1510 0.100 8.400 −0.07 NGC 7243 29 808 0.220 8.058 +0.03
NGC 2439 9 1300 0.370 7.000 NGC 7296 8 2450 0.240 8.450 −0.02
NGC 2447 10 1037 0.046 8.588 −0.05 NGC 7510 6 3480 0.900 7.350
NGC 2451 A 108 302 0.055 7.648 0 Pismis 20 4 3272 1.280 6.864
NGC 2451 B 120 189 0.010 7.780 −0.08 Ruprecht 44 10 4730 0.619 6.941
NGC 2489 6 3957 0.374 7.264 +0.05 Ruprecht 115 5 2160 0.650 8.780 +0.01
NGC 2516 30 409 0.101 8.052 +0.05 Ruprecht 120 3 2000 0.700 8.180
NGC 2546 70 919 0.134 7.874 +0.01 Ruprecht 130 3 2100 1.200 7.700 0
NGC 2547 25 361 0.186 7.585 −0.14 Stock 2 60 303 0.380 8.230 +0.17
NGC 2567 7 1677 0.128 8.469 −0.04 Stock 16 3 1810 0.520 6.900
NGC 2632 70 187 0.009 8.863 +0.16 Trumpler 2 17 725 0.400 7.950
NGC 2658 6 2021 0.043 9.152 −0.01 Trumpler 10 29 424 0.034 7.542 −0.12
NGC 3105 2 8530 0.950 7.300
131
0 40 80 120 160 200 240 280
0
10
20
30
40
50
Numberofclusters
Diameter [']
0 1200 2400 3600 4800 6000 7200 8400
0
2
4
6
8
10
12
Distance from the Sun [pc]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
2
4
6
8
10
12
14
16
18
20
22
24
26
Reddening [mag]
6 7 8 9
0
2
4
6
8
10
12
Numberofclusters
Age [dex]
-0.2 -0.1 0.0 0.1 0.2
0
2
4
6
8
10
12
14
16
18
20
[Fe/H] [dex]
Figure 55: The histograms of the cluster parameters taken from Table 30.
All values are listed in Tables 29 and 30. The histograms of the cluster parameters are shown
in Figure 55. From this figure, the following conclusions can be drawn
• d: because the apparent diameters of open clusters are directly connected to the distance
(the absolute diameters do not exceed 20 pc), the peak at less than 10’ is due to the clusters
observed via the CCD technology.
• R⊙: most clusters are located within 2 kpc around the Sun. Only a few are more distant
than that. Clearly, more distant clusters are needed to be observed to complete a
statistically significant sample.
• E(B − V ): clusters with reddening values of up to 1.5 mag were observed and also CP
stars have been detected. This shows the capability of the ∆a to function even within
such highly reddened environments.
• log t: clearly, there is a lack of very young (younger than 10 Myr) investigated clusters. This
is mainly because there are almost no close and young clusters in the solar neighbourhood
(photoelectric survey) existing. With the CCD technology, already several very young
aggregates have been observed.
• [Fe/H]: only clusters with ±0.2 dex have been observed so far. For further observations,
the metallicity range has to be significantly increased.
Figure 56 shows the Galactic location of the sample projected to the Galactic plane together
with the spiral arm model published by Bobylev & Bajkova (2014). The spiral arms from the
inner to the outer area are Scutum-Crux, Carina-Sagittarius, Perseus, and Cygnus. The regions
132
-8
-6
-4
-2
0
2
4
6
8
4 6 8 10 12 14
-1
0
1
7 8 9
photoelectric
CCD
both
l = 90
l = 180
l = 270
X [kpc]
Y[kpc]
l = 0
Figure 56: Galactic location of the published open clusters observed via ∆a photometry projected
to the Galactic plane. The Galactic centre is located at (X/Y ) = (0/0) kpc and the Sun at
(X/Y ) = (8/0) kpc. Galactic longitudes in degrees are indicated for better orientation. Furthermore,
the spiral arm model by Bobylev & Bajkova (2014) is shown as solid lines. The spiral arms
from the inner to the outer area are Scutum-Crux, Carina-Sagittarius, Perseus, and Cygnus.
with the highest reddening (Neckel et al., 1980) around l = [90,270] are still not investigated
in more detail because the lack of observable star clusters. However, the solar neighbourhood
around 1 kpc is already well analysed. One also have to keep in mind the survey of Galactic
field stars (Sect. 10) within this region.
18 The first ∆a observations of three Galactic globular clusters
Globular clusters are main astrophysical laboratories to test and modify evolutionary models.
They are extensively used to place constraints on key ingredients of canonical stellar evolution
models, such as the mixing length parameter of convective energy transport theory (Ferraro
et al., 2006). They are also rather “simple” stellar systems consisting of a distinct population,
which is in dynamic equilibrium. Therefore, they are used for extensive N-body simulation in
order to understand the formation and evolution of the Milky Way (Sippel et al., 2012). There
are about 160 Globular clusters known in the Milky Way (Harris, 1996, 2010 edition).
It is well known that several globular clusters have at least two main sequences (MS), which
are explained by a different helium content (Piotto et al., 2007). In addition, different red giant
(RGB) and sub-giant branches (SGB) were also found (Piotto et al., 2012). A similar characteristic
of the horizontal-branch (HB), namely at least two different populations, was detected
by Grundahl et al. (1998). There are different “jumps” in the blue HB (BHB) distribution in
the V versus (u − y) colour-magnitude diagram (CMD), which could be used to select apparent
133
Table 31: The basic cluster parameters of the targets taken from Harris (1996, 2010 edition).
NGC Name α(2000) δ(2000) l b R⊙ RGC E(B − V ) [Fe/H]
[o
] [o
] [o
] [o
] [kpc] [kpc] [mag] [dex]
104 47 Tuc 00 24 05.67 −72 04 52.6 305.89 −44.89 4.5 7.4 0.04 −0.72
6205 M13 16 41 41.24 +36 27 35.5 59.01 +40.91 7.1 8.4 0.02 −1.53
7099 M30 21 40 22.12 −23 10 47.5 27.18 −46.84 8.1 7.1 0.03 −2.27
Table 32: Observing log for the programme clusters. The clusters were observed by I.Kh. Iliev
(II) and O.I. Pintado (OP).
Cluster Site Date Obs. #g1 #g2 #y tg1 tg2 ty
[s] [s] [s]
NGC 104 CASLEO 08.2001 OP 6 10 10 5x60, 1x120 5x60, 5x120 5x120, 5x300
NGC 6205 BNAO 07.2003 II 12 12 13 12x100 12x100 13x100
NGC 7099 CASLEO 08.2001 OP 15 16 15 10x60, 6x120 10x60, 5x120 10x60, 5x180
peculiar objects (Grundahl et al., 1999). Also, peculiar HB extensions, like the blue-hook were
found (Brown et al., 2001). However, the cause of these phenomena is still not clear, but it is
probable connected to the complex star formation history of the individual clusters (Valcarce et
al., 2012). In Sect. 7.5 an overview of the interesting stellar groups are given.
Here, as a pioneer study, the first photometric ∆a observations of three, widely different,
globular clusters NGC 104, NGC 6205, and NGC 7099 are presented. It is a vital test, if the
∆a system is able to detect peculiar stars both at the HB and RGB, G- as well as K-type MS
stars. While it is not expected to find traces of the different star sequences due to the fact that
helium does not contribute in the 5200Å region at all.
In total, photometry of 2266 stars from 109 individual frames are presented. According to
the 3σ detection limit of each globular cluster, 61 objects with positive and 29 with negative
∆a values were detected. This corresponds to an upper limit of about 3% of apparent peculiar
objects.
For NGC 6205, it was possible to compare the results with abundance determinations from
the literature. The ∆a values of three HB stars, one without chemical peculiarities, listed in
Behr (2003a), are in perfect agreement. The peculiar objects were clearly detected with +57
and +60 mmag, whereas the non-peculiar object does not stand out. In addition, 10 RGB stars
with [Mg/Fe] values from −0.15 to +0.30 dex, published by Johnson et al. (2005) were analysed.
None of them exhibit a significant ∆a value, which means that the elemental peculiarity of
magnesium has to be much larger to be detected.
18.1 Target selection, observations and reduction
For this first case study, three globular clusters with widely different overall metallicities, namely
NGC 104, NGC 6205, and NGC 7099, were selected. Such a criterion guarantees to detect
possible peculiar stars for various local environments. Table 31 lists the basic cluster parameters
of the targets, taken from Harris (1996, 2010 edition).
The observations of the three globular clusters were performed at two different sites:
• 2 m RCC telescope RCC telescope of the Bulgarian National Astronomical Observatory
(BNAO, Rozhen), direct imaging, SITe SI003AB 1024 × 1024 pixel CCD, 5’ field of view,
1 pixel = 0.32”,
134
Figure 57: The photometric diagrams of the three globular clusters. The dotted lines are the
3σ upper and lower limits of the ∆a detection sensitivity according to Table 33. The vertical
lines are the locus of (B − V )0 = 1.0 mag.
135
Table 33: Summary of results. The errors in the final digits of the corresponding quantity are
given in parenthesis.
NGC 104 NGC 6205 NGC 7099
V = a + b · (y) −3.23(21)/0.909(22) −2.82(16)/0.965(9) −5.10(19)/1.009(17)
Reference Hesser et al. (1987) Grundahl et al. (1998) Alcaino et al. (1998)
a0 = a + b · (g1 − y) 0.922(3)/0.194(4) 0.373(1)/0.217(9) 0.946(2)/0.248(3)
3σ [mag] 0.033 0.042 0.028
n(obj) 1107 365 794
n(positive) 21 28 12
n(negative) 16 5 8
n(frames) 26 37 46
• 2.15 m telescope of the El Complejo Astronómico El Leoncito (CASLEO, San Juan), direct
imaging with focal reducer, TEK-1024 CCD, 9.5’ field of view, 1 pixel = 0.813”.
The observing log with the number of frames in each filter and the integration times is listed in
Table 32. The typical seeing conditions were between one and two arc seconds. The observations
were performed with two different filter sets, both having the following characteristics: g1
(λc = 5007 Å, FWHM = 126 Å, TP = 78%), g2 (5199, 95, 68) and y (5466, 108, 70).
The CCD reductions were performed with standard IRAF v2.12.2a routines. All images were
corrected for bias, dark, and flat-field. The photometry is based on point spread function fitting
(PSF). For each image, at least 20 isolated stars were selected to calculate the individual PSFs.
A Moffat15 function fitted the observations best. In the following, only stars were used which
are detected on all frames. Because of instrumentally induced offsets and different air-masses
between the single frames, photometric reduction of each frame was performed separately and
the measurements were then averaged and weighted by their individual photometric error. The
used photometric errors are based on the photon noise and the goodness of the PSF fit as
described in Stetson (1987).
For NGC 6205 three different, overlapping, fields around the centre were observed. No
significant photometric offsets between the fields were detected. The most inner parts (radius
of about 1.5’) of NGC 104 and NGC 7099 were not used for the further analysis because of the
severe crowding and the unresolved single star content.
There is no significant reddening towards the targets (see Table 31). Assuming that all
stars exhibit the same interstellar reddening and metallicity, peculiar objects deviate from the
normality line more than 3σ (Sect. 3).
For the transformation of the instrumental y to V magnitudes, the following references were
used: Hesser et al. (1987, NGC 104), Grundahl et al. (1998, NGC 6205), and Alcaino et al. (1998,
NGC 7099). Note that the zero-points for the measurements taken at BNAO and CASLEO are
not the same due to different CCD gain and bias levels as well as extinction coefficients.
All results are summarized in Table 33. In total, 2266 stars on 109 frames are finally analysed.
The complete photometric data together with the coordinates are available in electronic form.
18.2 Discussion
The tool of ∆a photometry measures any flux/spectral abnormalities in the 5200Å region (Sect.
8). Employing the ∆a photometric system on globular clusters aims primarily towards two
widely different star groups (Sect. 7.5).
136
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
V > 16
N = 576
3 = 0.028
a[mag]
V < 16
N = 218
3 = 0.026
NGC 7099
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
a[mag]
(g1
- y) [mag]
Figure 58: The a versus (g1 − y) diagram of NGC 7099. The sample was divided into stars
which are brighter (upper panel) and fainter (lower panel) than 16th magnitude.
1. Photospheric chemically peculiar HB stars
2. Peculiar RGB, G- and K-type MS stars
The first group shows enhancements of iron peak elements of up to three times solar, or 2 dex
compared to the mean metallicity, whereas the latter could be detected by peculiarities of Mg i
lines as well as MgH features around 5200Å. In addition, cool type dwarfs and giants can be
sorted out by the different equivalent widths of their Mg features. However, such a distinction
can also be easily done in the classical CMD.
In Fig. 57, the results of the photometric observations are presented. For each globular
cluster, the V versus (g1 − y) and a versus (g1 − y) diagrams are shown. As expected, the
CMDs, especially the characteristics of the HB, of the three aggregates are widely different.
The slopes of the normality lines range from 0.194 to 0.248 (Table 33), which is perfectly in
line with values found for Galactic open clusters (Sect. 17). Notice that there seems to be a
correlation with [Fe/H], i.e. NGC 104 with the highest metallicity exhibits the shallowest slope.
However, with only three aggregates, one has to be careful with such a conclusion. Further
observations are clearly needed to prove this apparent correlation.
Due to the photon noise, fainter stars have, in general, larger photometric errors. Inspecting
the a versus (g1−y) diagrams in Fig. 57, no correlation of the 3σ detection limit with the a values
is visible. For NGC 7099, the detailed analysis is shown in Figure 58. The complete sample was
divided in stars brighter and fainter than 16th magnitude. Both samples are rather different in
terms of the number of stars and the range of (g1 − y). In comparison with the overall solution,
137
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
11 - 12 mag
12 - 13 mag
13 - 14 mag
14 - 15 mag
15 - 16 mag
16 - 17 mag
NGC 104
1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
11 - 12 mag
12 - 13 mag
13 - 14 mag
14 - 15 mag
15 - 16 mag
16 - 17 mag
17 - 18 mag
18 - 19 mag
NGC 7099
Fractionrecovered
Distance from cluster centre [arc min]
Figure 59: Results of the artificial-star tests for NGC 104 and NGC 7099. The inner most core
parts with a radius of about 1.5’ were not used for the analysis.
only one object would not be detected as peculiar in the second sample with ∆a = +0.027 mag
which is just one mmag below the detection limit. In addition, the other samples were divided
in different V subsamples and the 3σ detection limit were calculated anew. All values agree
within 1.5 mmag. Those tests justify using the sample as a whole for the analysis. This strong
advantage of the ∆a photometric system was already noticed before and is because for a given
(g1 − y) value, a wide range of V values are sampled.
Also an artificial-star test to determine the completeness level of our sample was performed
which is very important when analysing crowded field photometry (Anderson et al., 2008).
Normally, faint stars in very crowded regions are either lost in the saturated cores or have be
detected against the high background of these bright star aureoles. Thus, the magnitude limits
for the detection of faint stars and the undercount correction estimates are functions of both the
stellar magnitude and the distance of the objects from the most crowded and therefore bright
cluster centre. As mentioned before, the inner-most core parts with a radius of about 1.5’ were
not used for the analysis. For this purpose, artificial stars were added with the IRAF task
“addstar” to frames of each filter with the longest integration times. About 100 independent
experiments, each consisting of 1000 artificial stars within a 1 mag interval randomly scattered
throughout the image, were performed. These frames were then photometrically analysed the
same way as the original ones. The detected fraction of artificial stars was determined in
concentric annuli of 0.5’ width. Finally, a weighted average of the recovery fraction at each radius
and magnitude interval was computed. For NGC 6205, we got almost a 99% completeness level
for all bins because we observed fields quite far off the centre. Figure 59 shows the artificial-star
138
11 12 13 14 15 16 17 18 19 20
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
a[mag]
V [mag]
NGC 7099
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
a[mag]
Distance from cluster centre [arc min]
Figure 60: The differences of the a values from the artificial-star test and the observed ones
(σa) versus the V magnitude (upper panel) and the distance from the centre (lower panel) for
NGC 7099. The peculiar candidates (Fig. 57) are marked as filled circles.
tests for NGC 104 and NGC 7099. The band width of the individual curves is about ±3%. Since
almost all regions and magnitude ranges are well above 90%, one can be confident that the effect
of undetected binary stars do not play a significant role for the analysis. As a further test, the
differences of the a values from the artificial-star test and the observed ones were calculated.
Figure 60 shows these differences versus the V magnitude and the distance from the centre for
the data of NGC 7099. Again, the distribution of the outliers does not significantly alter from
the apparent normal type objects.
In total, photometric ∆a values for 2266 stars were secured. According to the well established
3σ detection limit, 61 stars fall above, and 29 objects below the normality line. The latter can
be also due to higher reddened background stars, which would shift these objects below the
normality line. The only reliable distinction could be done via membership probabilities based
on proper motions. However, such kinematic data are not available for our target sample. Indeed,
such field stars are present in globular cluster areas (Sariya et al., 2012). Those field stars are
clearly visible in the right most upper panel of Fig. 5 in Sariya et al. (2012) where they exhibit
redder (V − I) colours than the cluster members. In the ∆a photometric diagram, such stars
could lie below the normality line, but not above it. The possibility of the influence of undetected
visual companions for the outliers was also checked. In general, applying point-spread-functionfitting,
already accounts for such cases. A comparison of “visual binaries” among normal type
objects and outliers shows no significant accumulation among the latter.
To estimate the a versus (g1 − y) diagram of background/foreground stars in the field of
139
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2
0.65
0.70
0.75
0.80
0.85
0.90
a[mag]
Observed
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2
0.65
0.70
0.75
0.80
0.85
0.90
Simulated field
a[mag]
(g1
- y) [mag]
Figure 61: The simulated fore- and background population using the theoretical Galactic model,
TRILEGAL (lower panel) and the observed one for NGC 104.
view of our targets, the theoretical Galactic model, TRILEGAL 1.62 described by Girardi et al.
(2005) was used. It includes the populations of the thin and thick disc as well as the Galactic
halo but it is not able to simulate star clusters, yet. Fields of 12’x12’ with the central coordinates
as listed in Table 31 were simulated. The synthetic ∆a photometry taken from the Vienna New
Model Grid of Stellar Atmospheres, NEMO3 (Heiter et al., 2002b) was used. The TRILEGAL
output includes Teff, log g, [Fe/H], and V for each object. First of all, the sample to the V
magnitudes was restricted as deduced from Figure 57. Then, for each star, the closest model
from the NEMO data base was searched for and the corresponding ∆a photometry was taken.
Figure 61 shows the observed and synthesized field of NGC 104. The situation for the other two
fields is similar. The slope for the normality line of the observational data is 0.194(4) whereas
it is 0.196(5) for the synthetic data. There are a few stars below (see discussion above) but
none above the normality line. Therefore, one can be confident that fore- and background stars
cannot mimic a statistically significant number of peculiar globular cluster members in the a
versus (g1 − y) diagram. However, some negative outliers of NGC 104 and NGC 7099 (Fig. 57)
can be caused by field stars.
NGC 104: no significant deviating ∆a values for HB stars were found. About 10 outstanding
objects are probable non-members and can be easily identified in the V versus (g1 −y) diagram.
NGC 6205: this is the most detailed investigated globular cluster among the targets. Three
HB stars listed in Behr (2003a) were measured, namely, WF2-820 (No. 147), WF-2692 (No.
2
http://stev.oapd.inaf.it/trilegal
3
http://www.univie.ac.at/nemo
140
227), and WF2-3035 (No. 74). The latter shows no chemical peculiarities, whereas the other
two have large overabundances of almost all iron peak elements from 1 to 1.5 dex compared
to the cluster metallicity. The ∆a values are perfectly in line with the abundances. For WF2-
3035 an insignificant value of +8 mmag was found, whereas the other two stars were detected
with +57 and +60 mmag. This lends to confidence that the ∆a photometric system is indeed
capable to detect chemically peculiar HB stars. However, further observations of such objects
have to prove this conclusion. There are also several BHB stars which are below the normality
line. For none of these objects, membership probabilities are available in the literature (Johnson
& Pilachowski, 2012). One may speculate that this behaviour could be due to photometric
variations. Such a behaviour is a common phenomenon for CP stars (Sect. 5), but was never
investigated for members of globular clusters, yet.
As next step, the RGB stars published by Johnson et al. (2005) among the sample were
investigated. In total, 10 stars were found in common. The [Mg/Fe] values for those objects
range from −0.15 to +0.30 dex. None of them exhibit a significant ∆a value, probably because
the effect of the Mg lines compared to Fe for such rather low peculiarities is too small in the
5200Å region.
NGC 7099: there are no detailed elemental abundances for members in the literature available.
There are three HB stars with a ∆a detection, from which one object lies significantly
above the HB in the V versus (g1 − y) diagram. If it is a member then this is probably a
very interesting object for follow-up observations. The reasons why several fainter stars deviate
from the normality line (as also seen for NGC 104), are not straightforward to determine
without any additional observations. However, from the previous considerations one can think
of non-members or very strong peculiarities of magnesium.
19 The ∆a observations within the Large Magellanic Cloud
Our Galaxy’s brightest satellite systems are the Large and Small Magellanic Clouds (LMC and
SMC), which are only visible from the southern hemisphere. They are both classified as irregular
dwarf galaxies and have been greatly distorted by tidal interaction with the Milky Way as they
move close to it. It is even possible to observe streams of neutral hydrogen connecting them
to the Milky Way and to each other. The significant astrophysical differences between the
Magellanic Clouds and the Milky Way are (Choudhury et al., 2016)
• Different global structure including rotational/kinematical properties and magnetic field
strength
• A factor of ten lower total mass
• Gas-rich
• Their overall metallicity is by a factor of two to four lower
Therefore, the formation and evolution of the Magellanic Clouds is significantly different to
our Milky Way. It is possible to study the most important astrophysical mechanisms (convection,
diffusion, accretion, rotation, and pulsation) in a completely different global environment. Since
the construction of several major observatories in Chile was mainly argued with the exploration
of the Magellanic Clouds, our knowledge about these galaxies was significantly enhanced in the
last 40 years.
There are several important issues which can be answered from the observational side by
establishing the incidence of CP stars in the LMC. Most important is the question if there is an
influence of metallicity on the (non-)presence of peculiarities since metallicity seems to distinctly
141
Table 34: Characteristics of the used filters.
Filter λC Bandwidth Transmission
[Å] [Å] [%]
g1 5027 222 66
g2 5205 107 50
y 5509 120 54
Table 35: Observing log
α(2000) δ(2000) Date #N
Field 1 04 45 20 −69 12 00 11/1998 25
08/2001 32
NGC 1866 05 13 40 −65 27 49 11/1998 76
NGC 1711 04 50 37 −69 59 01 01/2003 45
NGC 2136/7 05 53 07 −69 29 15 04/1995 12
08/2001 29
01/2003 28
influence the star formation scenario in the sense that the formation of larger clusters is only
possible in low metallicity media. It seems worthwhile to investigate whether the formation of
magnetic peculiar and (non-magnetic) λ Bootis stars occurs in the same proportion to “normal”
stars for all degrees of metallicity. Furthermore, one should ask whether different general magnetic
field strengths in the surrounding area of star formation will lead to the same frequency
of magnetic stars. While one could try to find a relationship concerning metallicity also in our
own Galactic disc, the Magellanic Clouds offer a scenario with distinctly lower metallicity and
lower magnetic field strength. In order to explain the characteristics of CP stars, stellar models
(Sect. 14) are needed which take into account different metallicities, ages and magnetic field
strengths.
Here, ∆a observations of four fields including four star clusters (NGC 1711, NGC 1866, and
NGC 2136/7) within the LMC are presented. In addition, the incidence of CP stars is estimated.
19.1 Target fields and observations
The observations were done on several nights at two different telescopes with the identical ∆a
filter set (Table 34):
• CASLEO: 215 cm telescope, TEK-1024 CCD, field of view of about 9.5’, November 1998,
August 2001 and January 2003, observer: O.I. Pintado
• ESO-LaSilla: Bochum 61 cm telescope, Thompson 7882 CCD, 384x576 pixels, 3’x4’, April
1995, observers: H.M. Maitzen and E. Paunzen
In the following, a brief description of the observed bulge field and star clusters (Table 35)
are given. Furthermore, comments are given for the surrounding field of NGC 1711.
142
Field 1: is located in the bulge of the LMC on its eastern edge (Cioni et al., 2000) centred at
α = 04:45:20 and δ = −69:12:00 (2000.0). There are no prominent clusters or Hii regions within
this field in order to ensure that only the field population of the LMC is observed.
Field 2: it consists of a MS similar to that of NGC 1711 and an older population with a
vertical extension of the red clump. Such a characteristics was observed in several areas of the
LMC (Dolphin, 2000). It seems that stellar evolution was rather uniform throughout the LMC
until 200 Myr ago. Since then, a significant increase can be inferred from observational data.
The different populations are also seen in Fig. 62 especially for the surrounding of NGC 1711.
NGC 1866: this is one of the most massive young clusters of the LMC in the age range 100
– 200 Myr (Marconi et al., 2013) and has been the subject of many studies. It is located in the
outskirts of the LMC, so that field star contamination is not severe. This cluster contains many
Cepheids which were used to determine the distance (Molinaro et al., 2012). The metallicity,
[Fe/H] = −0.55 dex is typical for the LMC, the reddening E(B − V ) = +0.07 mag is a little bit
less than the mean value of the LMC.
NGC 1711: the only recent detailed investigation of this cluster was done by Dirsch et
al. (2000) who derived the following parameters within the Strömgren photometric system:
log t = 7.70(5), [Fe/H] = −0.57(17) dex. However, these data are neither available in electronic
form nor upon request from the authors. Therefore, it was not possible to testify their results.
Kubiak (1990) lists an age of log t = 7.3 on the basis of solar abundant isochrones and Johnson
BV I photometry. Mateo (1988), on the other hand, derived an age between log t = 7.3 and 7.7,
respectively. This is in line with the results by Popescu et al. (2012) of log t = 7.3 and 7.61 based
on previously published broadband photometry and a stellar cluster analysis package.
NGC 2136/7: Dirsch et al. (2000) concluded that NGC 2136 and NGC 2137 are a physical
binary (possibly triple) cluster system of same age (log t = 8.0) and metallicity ([Fe/H] =
−0.55 dex). The estimated reddening of E(B − V ) = 0.1 mag is typical for other clusters in the
LMC. As for NGC 1711, it was not possible to use the Strömgren photometry from Dirsch et
al. (2000) for the calibration of the photometric values and the identification of objects because
it has been available neither in electronic form nor upon request from the authors of the given
reference. Furthermore, no printed tables are available. Mucciarelli et al. (2012) used a sample
of high-resolution spectra to derive the kinematical and chemical properties of NGC 2136 and
NGC 2137. They found that the two clusters share very similar systemic radial velocities, and
have also indistinguishable abundance patterns. They suggest that the two clusters are gravitationally
bound and that they formed from the fragmentation of the same molecular cloud that
was chemically homogeneous.
19.2 Reduction and calibration
Here, a brief summary about the reduction and calibration process for NGC 1711 and its surrounding
field is listed. It can be immediately compared with those for Galactic open (Sects.
17.2.1 and 17.3) and Globular clusters (Sect. 18.1).
For both fields, the results of the extensive UBV R CCD survey conducted by Massey (2002)
were used to calibrate and check the data. He presented accurate measurements for approximately
250 000 objects brighter than 18th magnitude in the SMC and LMC. Although there are
several other sources of photometric data available, only data of Massey (2002) were included
in the analysis in order to guarantee a sample free of bias on the basis of one widely accepted
photometric standard system.
As mentioned before, it was tried to obtain the Strömgren uvbyβ photometry from Dirsch et
al. (2000) published for NGC 1711 and five other clusters in the LMC. But it is neither available
in electronic form nor upon request from the authors.
For the calibration of the y and (g1 −y) to standard Johnson V as well as (B −V ) values, all
143
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.60
0.64
0.68
0.72
0.76
0.80
0.84
0.88
0.92
0.96
a[mag]
(B - V)
0
[mag]
a
0
= 0.729(1) + 0.162(1) (B - V)
0
-4.50 -3.75 -3.00 -2.25 -1.50 -0.75 0.00 0.75 1.50
0
-1
-2
-3
-4
-5
-6
LMC field stars
non-members
CP candidates
MV
[mag]
(B - V)
0
[mag]
(a)
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8
0.60
0.64
0.68
0.72
0.76
0.80
0.84
0.88
0.92
0.96
(B - V)
0
[mag]
a
0
= 0.733(1) + 0.181(1) (B - V)
0
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
0
-1
-2
-3
-4
-5
-6
field members
CP field candidates
members of NGC 1711
CP candidates of NGC 1711
(B - V)
0
[mag]
(b)
Figure 62: Observed diagrams for two program fields in the LMC. The solid line is the normality
line whereas the dotted lines are the confidence intervals corresponding to 99.9%. The error bars
for each individual object are the mean errors. The measurement errors of MV are much smaller
than the symbols and have been omitted. The scales for the upper and lower diagrams are
different because the relevant range for peculiar objects in the a versus (B − V )0 diagrams
seemed worthwhile to be shown. The MV and (B − V )0values were calculated using a distance
modulus of 18.5 and a reddening E(B − V ) = 0.1 mag.
stars in common with Massey (2002) were chosen. This procedure gives a sample of 372 objects.
A linear least square fit resulted in:
V = −2.67(9) + 0.88(2) · y
(B − V ) = 1.24(6) + 1.44(8) · (g1 − y)
In parentheses are the errors in the final digits of the corresponding quantity.
A distance modulus of 18.5 mag for the LMC was published by Alves (2004) who reviewed
and summarized all relevant measurements as well as their methods. Pietrzyński et al. (2013)
derived a distance modulus (m − M) = 18.49(5) mag and AV = 0.25 mag as mean values for the
LMC .
For the estimation of the reddening towards the observed fields, the maps of Oestreicher et al.
(1995) were taken. Both fields are located in areas with 0.05 < E(B − V ) <0.12 mag. This is in
line with the results for NGC 1711 by Dirsch et al. (2000) who derived E(B − V ) = 0.09(5) mag
on the basis of Strömgren uvby photometry. Therefore E(B − V ) = 0.1 mag was adopted for
both fields.
144
The adopted reddening value and distance modulus were checked by applying appropriate
isochrones (Sect. 13) to the photometric measurements. The results for NGC 1711 are in good
agreement with those from Kubiak (1990) and Dirsch et al. (2000).
For the normality lines, the (g1 − y) measurements were converted into (B − V ) values and
dereddened. For the field of NGC 1711 and its surrounding, the following correlations were
found, respectively:
a0 = 0.716(1) + 0.162(1) · (B − V )0
a0 = 0.733(1) + 0.181(1) · (B − V )0
The results are shown graphically in Figure 62. The 3σ limit for both fields is at ±0.012 mag.
The non-members in the surrounding field of NGC 1711 are objects which are much too blue
in respect to the MS. One can only speculate about their nature since no independent (B − V )
values are available in the literature. The most probable explanation is emission in the g1 filter
which would yield such a blue colour index. Some of these object might also be very distant
galaxies.
Because the observations were performed in the years 1998, 2001 and 2003, the behaviour of
the detector and the intrinsic transformations of all data were checked and no significant trends
or deviations from one year to the other were found.
19.3 The incidence of the apparent peculiar objects
A summary of the results from the CCD ∆a photometric measurements in the LMC is given in
Table 36. In total, 2742 objects of which 35 exhibit significant positive whereas 16 have negative
∆a values (Table 36). The latter are either Be/shell or metal-weak objects and have, in general,
no strong magnetic fields.
It has to be emphasized that in Sect. 14.1 it was shown on the basis of a synthetic ∆a
photometric system that only a shift of the normality line by about −3 mmag assuming an
average metallicity of [Fe/H] = −0.5 dex relative to those in the solar neighbourhood occurs.
The absolute ∆a values for CP stars are not affected.
Objects with significant negative ∆a values: this group consists of either classical emission
line or metal-weak objects (like λ Bootis stars). In total, 16 of such objects were detected.
For one object, the Be nature was spectroscopically confirmed (Sect. 19.4). Without any
further photometric or spectroscopic data, no clear decision about the true nature can be drawn.
However, it is not surprising to find a rather significant amount of these objects in NGC 1711
since it is a very young cluster still connected with stellar activity and emission of all kinds.
Metal-weak MS stars in the relevant spectral range are very scarce (compared to metal-strong
objects) in the field population of the solar neighbourhood (only a maximum of 2% of all stars,
Sect. 6) and almost absent in open clusters older than log t = 7.30 in our Milky Way (Gray &
Corbally, 2002). This might be caused by accretion from a diffuse interstellar cloud together with
diffusion as most probable mechanism for the λ Bootis phenomenon (Kamp & Paunzen, 2002).
This scenario works at any stage of stellar evolution as soon as the star passes a diffuse interstellar
cloud. Its dust grains are blown away by the stellar radiation pressure, while the depleted cloud
gas is accreted onto the star. This would naturally generate an abundance pattern as found
for the λ Bootis group, namely surface underabundances of most Fe-peak elements and solar
abundances of lighter elements (C, N, O, and S). Since denser clouds within clusters dissipate
on time scales of about 50 Myr, no λ Bootis stars are expected in older associations which make
their appearance in clusters of the LMC rather unlikely.
The incidence of Be/Ae/shell and metal-weak stars in the LMC: these are the only groups
which exhibit significant negative ∆a values (Sect. 11) . The Be/shell population in the LMC
is well studied (Keller et al., 1999). They found a fraction of MS stars that are Be objects
145
Table 36: Statistics of observed stars in the spectral range up to F2 divided into NGC 1711,
NGC 1866, NGC 2136/7, Field 1 (centred at α = 04:45:20 and δ = −69:12:0; 2000.0), Field 2
(surrounding field population of NGC 1711), Field 3 (surrounding field population of NGC
1866), and Field 4 (surrounding field population of NGC 2136/7). Nall is the total number of
measured objects within the spectral range up to F2 or (B − V )0 = 0.3 mag, N+ and N− are
the numbers with significant positive as well as negative ∆a values, N1: 100 · N+
Nall
,N2: 100 · N−
Nall
.
Name Nall N+ N− N1 N2
NGC 1711 109 3 5 2.8 4.6
NGC 1866 261 4 3 1.5 1.1
NGC 2136/7 73 3 3 4.1 4.1
Field 1 331 4 2 1.2 0.6
Field 2 622 15 2 2.4 0.3
Field 3 1239 4 − 0.3 −
Field 4 107 2 1 1.9 0.9
between 0.1 and 0.34 (mean value of the Milky Way is about 0.17) varying for six very young
clusters and their field population in the LMC. No correlation of the incidence with the age or
metallicity was detected. Gray & Corbally (2002) concluded that the frequency of λ Bootis stars
in the Galactic field among main sequence A to F objects is about 2% (no investigation for the
LMC is available up to now). The age distribution of both groups are rather different. Whereas
Be/Ae/shell stars are preferably found at young ages with log t < 7.5, the members of the λ
Bootis group in the Milky Way are evolved with a peak at log t = 9.0 (Paunzen et al., 2002a).
The detection capability of the ∆a photometric system for a 3σ limit of 0.012 mag is at 50%
as well as 10% for the λ Bootis and Be/shell group, respectively (Sects. 11.7 and 11.9). This
means that 5% of the complete Be/Ae/shell as well as 60% of the λ Bootis population can still
be detected with a high statistical significance at a limit of 0.012 mag. If one takes the maximum
percentage of the relevant group members from Keller et al. (1999) and Gray & Corbally (2002),
an upper frequency of 2.8% of objects with negative ∆a values (1.7% Be/Ae/shell as well as 1.1%
λ Bootis) among all main sequence B- to F-type stars should occur in the LMC for the derived
detection limit of 0.012 mag. The mean and median value for all detected stars (Table 36) is 1.9
and 1.0%, respectively. These numbers are in excellent agreement with each other. The presence
of these stars is, in general, depending on denser interstellar clouds (λ Bootis group) as well as
stellar activity which is closely correlated with the age. However, it shows that ∆a photometry,
taking into account a certain detection limit, is able to find essentially the same frequency of
Be/Ae/shell and metal-weak stars as other photometric as well as spectroscopic surveys.
The incidence of magnetic CP stars in the Milky Way: the detected 35 objects are most
certainly magnetic CP (CP2 and/or CP4) stars (Sect. 6). Only for the four objects cooler than
A0, (B − V )0 > 0 mag, i.e. one can assume a membership to the CP2 group. Two aspects have
to be taken into account when comparing the number of CP stars in the Milky Way and the
LMC. First of all, the metallicities in the solar neighbourhood and the galactic open clusters
are significantly higher than in the young associations in the LMC which hardly reach −0.5 dex.
The second issue is about the evolutionary effect on the incidence of magnetic CP stars. The
Hipparcos data suggest that the CP group behave just like apparently normal stars in the same
range of spectral types occupying the whole width of the main sequence with kinematic characteristics
typical of thin disk stars younger than about 1 Gyr (Gómez et al., 1998). This finding
146
was supported by Pöhnl et al. (2003) who investigated four young open clusters (ages between
10 and 140 Myr) with known CP2 members establishing the occurrence of such objects at very
early stages of the stellar evolution. However, Hubrig et al. (2000) challenged these results and
claim that the distribution of the magnetic CP stars of masses below 3 M⊙ in the HRD differs
from that of the normal stars in the same temperature range at a high level of significance,
magnetic stars being concentrated toward the centre of the main sequence band. In particular,
they argue that magnetic fields are detected only in stars which have already completed at least
approximately 30% of their main sequence life time. This somewhat discrepant result might be
understood by the detectability of resolved Zeeman patterns which requires a specifically slow
rotation. This gives preference to finding such objects in advanced phases on the main sequence
band where rotational velocities have been decreased by the growth of stellar radii.
Abt (1979) investigated the dependence of the percentage of CP members in open clusters on
their age. His sample, divided into magnetic Ap (Si) and Ap (Sr,Cr) stars, includes data for 14
galactic open clusters as well as associations, a rather small number if one takes into account
that at least 2500 open clusters are known in our Milky Way (Dias et al., 2002). The frequency
of Ap (Si) objects with −1.3 < MV <1.4 mag increases from 4% to 8% during log t = 7.0 and 8.0,
respectively, whereas the youngest Ap (Sr,Cr) stars are found at log t = 7.5 (3% at log t = 8.0).
For, at that time, known peculiar stars (Osawa, 1965) of the Bright Star Catalogue, Abt (1979)
gives a number of 6.5% for the same magnitude and declination range as the investigated members
of open clusters. No value for the CP4 group is listed in Abt (1979). Another source for a
statistically analysis of galactic CP field stars is the conference paper by Schneider (1993) who
considered also the Supplement to the Bright Star Catalogue and the CP stars listed in Renson
(1991). He lists for the magnitude range V < 7.1 mag a lower limit of 16% (CP2 and CP4) and
5% (CP2 only) for stars hotter and cooler than A0, respectively. These numbers should be
taken with care since Schneider (1993) quotes that “the single values should not be taken too
serious because the MK classification influences the single values strongly”. From the mentioned
sources we conclude that one would expect an incidence for magnetic CP stars of at least 6%
over the relevant spectral range up to F2 main sequence objects. This number has to be treated
as statistically lower limit for the percentage of magnetic CP stars for any test sample of main
sequence objects in the Milky Way. The only limitation might be very young open clusters and
associations (log t < 7.0) where the incidence seems slightly less than 6% (Borra et al., 1982).
The incidence of magnetic CP stars in the LMC: first of all, one has to correct the observed
ratio of CP stars for loss of objects because of the detection limit. In Sect. 11, a detection rate
of 90% for CP2 and 65% for CP4 objects for a limit of 0.012 mag was estimated. However, there
a factor of ten more CP2 than CP4 stars known in the solar neighbourhood known (Table 10).
This ratio has to be assumed also valid for the LMC because no other sound measurement is
available. Incorporating these facts for the values listed in Table 36, a mean and median value
of about 2.7% for the incidence of magnetic CP stars in the whole spectral range up to F2 is
inferred. This number is based on the measurements of 2742 individual objects. The occurrence
of magnetic CP stars in the LMC is therefore only about half the value as in the Milky Way.
19.4 The spectroscopic verification of one CP and Be star
Let’s recall that in Sect. 19, the results of the ∆a system for fields in the LMC are presented.
Furthermore, the incidence of CP stars in the LMC with that of the Milky Way is analysed
(Sect. 19.3). However, all these investigations are based on one important assumption: classical
CP stars do exist in the LMC and are unambiguously detected by ∆a photometry.
It is therefore vital, to confirm these photometric results on the basis of spectroscopy. Here,
spectroscopic observations made at Las Campanas Observatory are presented. They confirm
one classical B8 Si star among the photometric sample, as well as one early B-type emission-line
147
Table 37: Targets for the spectroscopic verification. X = Y = 0 corresponds to
α(2000) = 05h13m40s and δ(2000) = −65o27’49”. Notation for stars sorted after X and Y , respectively
and according to Testa et al. (1999). σ1 is the σ-value outside the corresponding
confidence interval of the normality line. In parentheses are the errors in the final digits of the
corresponding quantity.
No1 No2 X Y (g1 − y) a ∆a σ1 y V N
257 −153.15 −184.67 −0.716(3) 0.367(4) −0.058 10.7 21.606(8) 17.059 76
687 4986 −44.75 −38.01 −0.804(8) 0.488(6) +0.044 4.9 21.459(15) 16.908 60
1005 9527 +33.49 −47.05 −0.864(6) 0.477(3) +0.045 9.6 22.308(4) 17.780 71
1093 9448 +52.65 +28.10 −0.932(8) 0.467(6) +0.048 5.7 22.763(7) 18.248 71
star which was also initially detected by its significantly deviating ∆a value.
19.4.1 Target selection, observations, and reductions
From the stars with significant positive ∆a values, detected as described in Sect. 19.1, the CP
candidates #687, #1005, and #1093 were chosen. In addition, the metal-weak/Ae/Be/shell
candidate #257 was selected for this study. The basic information for these stars are listed in
Table 37. The V magnitudes of the targets, all located in the field of NGC 1866, are between 16.9
and 18.2 mag, near the limiting brightness for achieving usable spectra in moderate exposure
times with the instrumentation available.
The observations were performed with the Magellan Inamori Kyocera Echelle (MIKE), a
high-throughput, double echelle spectrograph (Bernstein et al., 2003) on the 6.5-m Magellan
telescope (Clay) at Las Campanas (Chile) on the nights of 18-20 November 2004 by Don J.
Bord. The spectrograph employs a dichroic filter with separate blue and red fibres to provide
simultaneous coverage of wavelengths spanning the range from 3200 to 10 000Å with a typical
one-pixel resolution of 0.04 to 0.05Å. The spectra were binned 2x2 to produce a resolution of
about 0.08 Å in the blue. This value comports well with the measured half-widths of sharp,
unblended comparison lines in the ThAr spectrum near 4000Å which yields on the average
0.12Å. Integration times between 30 and 60 minutes were chosen to control the intensity of the
night sky lines and to limit spectral contamination from neighbouring stars in crowded fields
caused by rotation of the slit on the sky.
All reductions were performed with standard IRAF routines. After the bias, dark, and flat
field corrections, the spectra were wavelength calibrated (including a heliocentric correction)
using two ThAr standard spectra observed before and after the corresponding target. As a final
step, the spectra were co-added to increase the signal-to-noise ratio.
19.4.2 Results and conclusions
Due to the faintness and the high spectral resolution of the instrument, the signal-to-noise ratios
of the final spectra are very low, typically around 15. For the bluest and reddest regions of the
spectra, no signal at all was observed because of the drop of the quantum efficiency of the CCDs.
For all stars, the hydrogen lines are the most prominent features in the spectra. The photometric
candidates are thus clearly in the expected effective temperature range for classical CP
stars and not contaminated by any late-type fore- or background objects.
One of the most prominent features of early-type CP stars is the Si ii doublet at 4128/4131Å
which is very much stronger than comparable lines in normal stars (Sect. 6). The enhancement
148
4125 4130 4135 4140 4145
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
4850 4860 4870 4880
Normalizedflux
Wavelength [Å]
NGC 1866: #1005
Si II doublet 4128/4131Å
Wavelength [Å]
NGC 1866: #257
Figure 63: The Si ii doublet detected in star #1005 (left panel) and the emission structure of
Hβ in star #257 which exhibits a significant negative ∆a value (right panel). The spectra have
been shifted to the rest frame of the Sun. To within the measurement uncertainties (∼15%),
the equivalent width of each Si-line is the same, viz. 0.30Å.
of this doublet is an unambiguous characteristic of magnetic CP stars in general, and so it was
primarily searched for this feature in the spectra.
For targets #687 and #1093 it was not possible to detect any features beside the hydrogen
lines due to the low signal-to-noise ratio of the spectra and moderate rotational velocities of
the stars. Applying several smoothing techniques (boxcar, FFT, and median) still revealed no
additional features above 5σ of the mean noise level. Unfortunately, it was not possible to
reliably analyse the 5200Å region because the depths of the flux depressions for the measured
∆a values for these stars are too shallow for the low signal-to-noise ratio (Sect. 14.5.3).
The rotational speeds of these two stars can be estimated, however, from comparisons of the
observed hydrogen line profiles with synthetic spectra. Establishing a credible continuum level
for the hydrogen lines in the echelle spectra is neither easy nor unambiguous, and normalization
was carried out using the shape of the flat field function of the corresponding aperture. From
different numerical experiments using a range of stellar parameters, it was found that the most
probable v sin i values for #687 and #1093 fall within the range of 100 to 150 km s−1.
Figure 63 shows the Si ii doublet observed for #1005 with the most significant ∆a value
detected, 10.8σ above the normality line. The separation of the two lines was measured which
is, within the errors, identical with the theoretical one. The spectral feature is so strong that
one immediately classifies this object as a typical silicon star of the CP2 group. The equivalent
widths of the doublet were measured to be 0.30 Å for each line with an error of about 15%.
For normal late B-type stars (dwarfs and giants), the corresponding value is 0.19 Å (Jaschek &
Jaschek, 1995). Notice that the equivalent width of the Si ii doublet for dwarfs is at a maximum
149
for spectral type B8 and drops to 0.15 and 0.11 Å for B7 and B9, respectively. The corresponding
equivalent widths for late B-type CP stars range from 0.2 to 0.4 Å, depending on the rotational
phase and the strength of the stellar magnetic field (López-García & Adelman, 1999). These
values are in agreement with the measurements of #1005.
Testa et al. (1999) published V = 17.797(5) and (B −V ) = 0.014(13) mag for this star. Using
the distance modulus of 18.33 and AV = 0.25 mag for NGC 1866 and its surrounding taken from
Salaris et al. (2003), one derives an absolute magnitude of −0.8 mag which coincides with a main
sequence late B-type star. Within the given errors one can classify #1005 as B8 Si star. From
the original as well as a smoothed spectrum, the upper limit of v sin i as 50 km s−1 from the
hydrogen lines and Si ii doublet was determined.
The emission characteristics of Hβ for star #257, which exhibits a significant negative ∆a
value at a 10.7σ significance level, is shown in Figure 63. This object is about 0.7 mag brighter
that #1005 which suggests an early B-type. Again, this result is in agreement with the findings
for similar stars in the Milky Way.
From the wavelength calibrated spectra (Fig. 63), using the hydrogen lines, it was also
possible to obtain estimates of the heliocentric radial velocities for each target star. The final
values are between 280 and 320 km s−1 with errors of about 20 km s−1. This clearly establishes
them as true members of the LMC and not Galactic foreground objects (Prevot et al., 1985).
These two examples show that the ∆a photometric system is indeed able to distinguish
CP and Be from normal type objects via the classical tools (Sect. 3). However, a certain
contamination from other objects, for example Galactic foreground stars, can not be excluded.
To investigate this possible effect, more spectroscopic observations of the bona-fide photometric
candidates are needed. For this, at least 8 meter class telescopes are needed, even employing
classification resolution spectroscopy.
19.5 The (non-)variability of magnetic CP candidates in the LMC
The variability of magnetic CP (mCP) stars is explained in terms of the oblique rotator model
(Sect. 6), according to which the period of the observed light, spectrum, and magnetic field
variations is the rotational period. The photometric changes are due to variations of global flux
redistribution caused by the phase-dependent line blanketing and continuum opacity namely in
ultraviolet part of stellar spectra (Krtička et al., 2012).
The amplitude of the photometric variability is a combination of the characteristics of the
degree of nonuniformity of the surface brightness (spots), the used pass band, and the line of
sight. The observed amplitudes are up to a few tenths of magnitudes. However, for some stars
one also fails to find any rotational induced variability at all. The locations of spots used to
have connection with the dipole-like magnetic field geometry (Krtička et al., 2009).
Besides the confirmation by spectroscopic data (Sect. 19.4.2), it is important to analyse if the
bona-fide CP candidates (Table 36) also show the same variations as their Galactic counterparts
which would be a direct indicator for the presence of a stellar magnetic field.
The list of mCP candidate stars were compared with the OGLE database for corresponding
measurements on the basis of equatorial coordinates and V magnitudes. After a first query, the
positions in the original images and those of OGLE were inspected by eye. In total, fourteen
matches in both sources were found. The final list of stars is given in Table 38.
A further analysis revealed that the sample of mCP candidates is contaminated by two
late-type stars. The first, 135.3 4273, was recognised as the short-period Cepheid OGLE-LMCCEP-0327
pulsating in its first overtone with the period P = 0.8821659(13) d (Soszyński et al.,
2008). The second, 135.3 30107, is a normal, non-variable K-type giant. These objects were
adopted as control stars and their photometric data were analysed together with other stars of
the sample. The HRD of all studied stars constructed from data given in Table 38 is shown in
150
Table 38: The basic photometric parameters and the photometric characteristics of CP candidates
in the V and I bands. V is the mean magnitude in V filter, M0 the V absolute magnitude
assuming the distance modulus m − M = 18.49(5) and AV = 0.25 mag (Sect. 19.2), (V − I)
the mean colour index, the mean ∆a index, NV and NI the numbers of V and I observations,
δmV and δmI the typical uncertainties of particular measurements, 1/P the frequency of the
maximum effective amplitude of Am or S/N, while Am and Ams are the observed maximum
modified amplitude and expected maximum modified amplitude. S/N and S/Ns are the maximum
signal-to-noise value and its expected value; “prob” means the probability of the reality
of designate frequency of periodic variations.
No. OGLE V M0 (V − I) ∆a NV δmV NI δmI
LMC + [mag] [mag] [mag] [mag] [mag] [mag]
1 135.3 4273* 17.80 −0.95 +0.85 (0.089) 67 0.013 370 0.013
2 135.3 30107* 17.76 −0.98 +1.36 (0.094) 65 0.011 466 0.010
3 136.7 861 17.60 −1.14 −0.04 0.078 28 0.010 301 0.018
4 136.7 16501 19.16 +0.41 +0.03 0.087 24 0.024 266 0.058
5 136.8 678 17.84 −0.90 +0.01 0.095 45 0.011 435 0.021
6 136.8 1801 18.79 +0.05 +0.11 0.085 45 0.019 437 0.041
7 136.8 1873 18.64 −0.10 +0.02 0.056 45 0.017 437 0.039
8 136.8 2002 18.67 −0.08 +0.10 0.054 45 0.018 434 0.038
9 136.8 3694 19.10 +0.35 +0.05 0.052 44 0.023 421 0.056
10 136.8 3875 18.98 +0.24 +0.04 0.087 43 0.022 434 0.052
11 190.1 1445 18.08 −0.65 −0.03 0.095 52 0.013 454 0.037
12 190.1 1581 17.89 −0.85 +0.01 0.044 51 0.012 454 0.031
13 190.1 2822 18.68 −0.06 +0.02 0.060 53 0.018 454 0.056
14 190.1 15527 17.16 −1.57 +0.01 0.041 53 0.008 453 0.019
1/P Am Ams S/N S/Ns prob
[d−1
] [mag] [mag] %
1 135.3 4273* 1.1336 0.175 0.041 51 4.8 100
2 135.3 30107* 0.6522 0.005 0.006 4.5 4.5 16
3 136.7 861 1.0088 0.014 0.013 5.1 4.5 29
4 136.7 16501 0.2286 0.044 0.040 5.1 4.6 28
5 136.8 678 1.4388 0.013 0.013 4.7 4.6 18
6 136.8 1801 1.1811 0.027 0.023 5.3 4.3 30
7 136.8 1873 0.6549 0.021 0.022 4.2 4.3 20
8 136.8 2002 0.4372 0.020 0.022 4.1 4.5 13
9 136.8 3694 0.9838 0.031 0.033 4.4 4.7 23
10 136.8 3875 1.8641 0.031 0.032 4.6 4.7 10
11 190.1 1445 0.9183 0.017 0.016 5.6 5.3 26
12 190.1 1581 0.8075 0.019 0.015 7.1 5.3 49
13 190.1 2822 1.6884 0.022 0.024 4.6 5.1 11
14 190.1 15527 2.0260 0.011 0.009 6.7 5.5 32
*The control stars: the first is a short-periodic Cepheid, the second a non-variable K giant.
Figure 64.
The data of the mCP candidates contain the JDhel date of measurement, ti, the measured
V and I magnitudes mi, and the estimate of its internal uncertainty δmi. It was found that the
last quantity represents the real uncertainty of the magnitude determination quite well and that
is why it was used to weight the individual measurements according to the relation wi ∼ δm−2
i .
The mean V magnitudes of mCP candidates (stars 3 to 14) span the interval from 17.16 to
19.16 mag, respectively This corresponds to an interval of absolute V magnitudes from −1.4 to
+0.6 mag. It corresponds mainly to Si-type of mCP stars (Sect. 6) and matches the results
given in Section 19.4.2.
The median of the amplitude of light variations of mCP stars in V is about 0.032 mag
(Bernhard et al., 2015a). The typical error of the determination of one I measurement of the
151
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
14
12
2
M0
[mag]
(V - I)
0
[mag]
1
Figure 64: The HRD of all analysed stars. M0 is the mean V absolute magnitude corrected for
extinction AV = 0.25 mag assuming the distance modulus m−M = 18.49; (V −I)0 is the colour
index corrected for the corresponding interstellar reddening by 0.1 mag. Open circles clustering
towards the MS indicate mCP candidates, the filled circle denoted by 1 is the mean position of
star 1 (135.3 4273), which is a short-period Cepheid. Star 2 (135.30107) is a normal non-variable
K giant. Stars 12 and 14 are mCP candidates suspected for their rotationally modulated light
variations.
mCP candidate set is σIt ∼ 0.038 mag and the typical number of measurements is NIt ∼ 440
(Table 38). Consequently, the expected uncertainty of δIt of the amplitude determination of
periodic variations can be estimated as δIt =
√
8/NIt σIt ∼ 0.005 mag. The same quantities for
V measurements are σVt ∼ 0.015 mag and NVt ∼ 45, δVt =
√
8/NVt σVt ∼ 0.006 mag.
Before starting the analysis of V and I photometric data, the expected relationship between
infrared and visual variations of mCP stars were investigated in more detail.
19.5.1 I light variability of mCP stars
The search for periodic rotationally modulated variations in the sample of 12 LMC mCP candidates
is based mainly on the analysis of the variability of these stars in the near infrared, while
the Galactic mCP star variability is studied mainly in the visual region (Sect. 6). Unfortunately,
the information about the infrared variability of Galactic mCP stars is very scarce. From the
few observations available (Musielok et al., 1980; Catalano et al., 1998b; Wraight et al., 2012)
one can conclude, that the amplitude of the light variations in the near infrared filters is similar
but not identical to that in visual filters. This can be easily understood from the theoretical
model of the light variability of mCP stars (Molnar, 1975; Krtička et al., 2007; Shulyak et al.,
2010), which is based on the light redistribution from the shorter wavelength region (typically
152
the far ultraviolet) to the longer wavelength region (typically the visual and infrared) because
of enhanced opacity in the regions with overabundant elements. The infrared continuum lies in
the Rayleigh-Jeans part of the flux distribution function, where the ratio of the two different
fluxes is independent of wavelength.
To derive a quantitative prediction for the mCP star light variability in the near infrared,
the successful models of the visual light variability of HD 37776 were employed (Teff = 22 000 K,
Krtička et al., 2007), HR 7224 (Teff = 14 500 K, Krtička et al., 2009), and CU Vir (Teff = 13 000 K,
Krtička et al., 2012) and predicted the light curves in the I filter. The light curves are calculated
from the surface abundance maps of these stars (Kuschnig et al., 1999; Khokhlova et al., 2000;
Lehmann et al., 2007) using TLUSTY model atmospheres and the SYNSPEC spectrum synthesis
code (Lanz & Hubeny, 2003, 2007). For these stars, no observations in I are available.
The light curves are predicted using specific intensities filtered by appropriate transmission
curve. The OGLE transmission curve were fitted by a suitable formula with a precision better
than 3% in the form of
M(λ) =
{
exp (a1x + a2x2), λ < λ0,
exp (a4x + a5x2 + a6x3), λ > λ0,
(29)
where the variable x is connected with the wavelength λ in Å as
x =
(
λ − λ0
σ
)2
, (30)
and
λ0 = 8111 , σ = 733 , (31a)
a1 = −0.501, a2 = −0.329, (31b)
a4 = −0.400, a5 = +0.452, a6 = −1.03. (31c)
The resulting light curves are shown in Figure 65. From this plot one can conclude that if the
LMC mCP stars have the same amplitude as their Galactic counterparts, their light variations
should be detectable by OGLE (Table 38).
The detection of photometric variations of LMC mCP candidates is not straightforward
because of their faintness. That is why their light behaviour was approximated by the simplest
possible model assuming that light curves in all filters are simple sinusoidal with the same
amplitude. Whenever a signal of this kind is detected, it is possible to improve the model even
more.
19.5.2 Periodograms
The periods of variable stars are usually inferred by means of various kinds of periodograms.
Two versions of periodograms were chosen based on the fitting of detrended measurements
yi with uncertainties σi done in the moments ti by an ordinary sine-cosine model, f(ω, t) =
b1 cos(ω t) + b2 sin(ω t), where ω = 2π/P is an angular frequency and P the period, using the
standard χ2 least-squares method. If the sum χ2(ω) is for the given ω minimum the so-called
modified amplitude Am(ω) has to be maximum,
N∑
i=1
y2
i
σ2
i
− χ2
(ω) =
N∑
i=1
[
f(ω, ti)
σi
]2
= A2
m
N∑
i=1
1
8 σ2
i
, ⇒ (32)
Am(ω) =
8
∑
σ−2
j
N∑
i=1
[
b1(ω) cos(ωti) + b2(ω) sin(ωti)
σi
]2
, (33)
153
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Magnitude[mag]
Phase ϕ
HD 37776
HR 7224
CU Vir
Figure 65: The predicted light curves in the I band of selected Galactic mCP stars.
where b1(ω) and b2(ω) are coefficients of the fit. When there is a uniform phase coverage, the
modified amplitude is equal to the amplitude of sinusoidal signal. The best phase sorting of
the observed light variations corresponds to the angular frequency ωm with the maximum of
modified amplitude Am(ω).
The second LSM type of periodogram uses for the significance of individual peaks a robust
signal-to-noise (S/N) criterion, which is defined as
S/N(ω) =
Q(ω)
δQ(ω)
=
b2
1(ω) + b2
2(ω)
δ
[
b2
1(ω) + b2
2(ω)
], (34)
where δQ(ω) is an estimate of the uncertainty of the quantity Q(ω) for a particular angular
frequency.
The properties of the S/N(ω) criterion were tested using thousand samples with sine signals
scattered by randomly distributed noise. It was found that if there is no periodic signal in this
data, the median of the maximum S/N(ω) value in a periodogram is 4.52; in 95% of cases, a
S/N value between 4.2 and 5.4 was found. The occurrence of peaks definitely higher than 6
indicates possible periodic variations.
During the treatment of OGLE-III time series, it was concluded that both types of periodograms
correlate very well with other time-proven estimates, the Lomb-Scargle (Horne &
Baliunas, 1986) periodogram, for example. So one can consider them as generally interchange-
able.
All frequencies from 0 to 2.1 d−1 were tested. The upper limit is slightly above the frequency
of the fastest rotating CP star known to date (HD 98000, with the period of P = 0.466 d−1, see
Hümmerich et al., 2017).
154
0 0.5 1 1.5 2
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
1/P [d
−1
]
Am
[mag]
136.7 16501
Figure 66: A typical periodogram of a mCP candidate, star 4 (136.7.16501); all peaks are
inconspicuous.
19.5.3 Discussion of periodograms
The periodograms for all stars of the sample were constructed and frequencies f = 1/P of
their maximum peaks, modified amplitudes Am, and S/Ns for these peaks calculated. These
quantities are given in Table 38. The periodograms of the LMC mCP candidates were compared
with those of the control stars, where the variability of OGLE-LMC-CEP-0327 and its aliases
conjugated with the period of a sidereal day (Fig. 67) were clearly detected. The results exactly
agree with the previous determination of the period and other characteristics of the star. This
lends confidence to the applied time series analysis method.
The periodograms of the known Cepheid and the mCP candidates plus the second control
star apparently differ: the peaks here have only a very narrow margin to the body of a pure
scatter (compare Fig. 66 with Fig. 67). There are additional arguments to explain why all
periods except those found for the stars 12 and probably star 14, listed in Table 38, are very
likely only coincidences:
• The distribution of the maximum amplitude frequencies is shallow and the found frequencies
cover the studied interval 0 to 2.1 d−1 more or less evenly. This is a sign that observed
peaks are most likely mere coincidences.
• The amplitudes of light changes of Galactic mCP stars show no correlation with the colour
index, spectral type, or absolute magnitude. It is in sharp contrast with observations
of LMC mCP candidates whose observed maximum amplitudes exhibit strict monotonic
dependence on the mean magnitude (see circles in Fig. 68). It suggests that the nature of
observed variability of LMC objects might be different.
• It is conspicuous that the median of S/N ratios of the highest peaks in periodograms
of individual CP candidates is only 4.7, corresponding to the median of maxima peaks
155
0 0.5 1 1.5 2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
1/P [d−1
]
A
m
[mag]
135.3 4273
Figure 67: The basic period of the overtone-Cepheid OGLE-LMC-CEP-0327 (135.3 4273) plus
its aliases conjugated with the period of a sidereal day.
S/N = 4.52 in the case of pure scatter. It indicates the lack of detectable periodic signal
in the majority of inspected mCP candidates, with two exceptions (stars 12 and 14) which
are discussed in the following.
Therefore, the hypothesis was tested that the distribution of the data is random via a heuristic
shuffling method. The data of each mCP candidate was re-analysed in the same way as
described above, only all the individual observations (magnitudes and their uncertainties) were
randomly shuffled, the times of the observations remained the same. This should extinguish any
periodic signal. As next step, Ams and S/Ns for each shuffled version of data were calculated.
The median of the both shuffled quantities is given in Table 38 and Figure 68. It is apparent
that the results are nearly the same as in the case of the original, unshuffled data with two
exceptions (stars 12 and 14).
As an added and independent test, we applied two different time series analysis methods,
namely the modified Lafler-Kinman method (Renson, 1978) and the Phase-Dispersion-Method
(Stellingwerf, 1978). All computations were done within the programme package Peranso (Paunzen
& Vanmunster, 2016). Using these utilities only upper limits for variability were found, but
no statistically significant detection except for the case of star 1. The frequencies discussed in
the following for stars 12 and 14, are detected on a 3.4 and 3.9 σ level, respectively.
19.5.4 The mCP candidates suspected of periodic light variations
Both objects suspected of periodic light variations, star 12 (190.1 1581) and star 14 (190.1 15527),
display relatively low amplitude light variation which are only slightly above the detectability
by OGLE-III V and I photometry. Therefore, a very simple model of their behaviour assuming
the linear ephemeris and the sine form of the V and I variations with different amplitudes was
156
17 17.5 18 18.5 19 19.5
0
0.01
0.02
0.03
0.04
0.05
I [mag]
Am
,Ams
[mag]
observed
predicted
Figure 68: The dependence of the maximum modified amplitudes of the observed (Am – circles)
and the shuffled data (Ams – squares) on the mean I magnitude of mCP candidates. The largest
positive relative deviation is found for the star 12 (190.1 1581) and is denoted by an arrow.
used. The following model of light changes were obtained
ϑ(t) =
t − M0
P
, mc(ϑ) = mc −
ac
2
cos(2 π ϑ), (35)
where ϑ(t) is a phase function, M0 is the moment of the basic maximum, P is the period in
days, mc(t) is a predicted magnitude in filter c (c = V, I) at the time t, mc is a mean value of
the magnitude in the filter c, and ac is an amplitude in the filter c. The values for both stars
derived by standard least-squares minimization regression are given in Table 39.
Star 12 (190.1 1581) is one of the brighter stars in the sample. Its mean absolute magnitude
M0 = −0.85 mag and negative dereddened index (V − I)0 = −0.09 mag indicates that this
object belongs among the late B-type stars. If it is a true mCP star, it is most likely a Si- or
He-weak type object (Sect. 6).
In its periodogram one finds a dominant peak at the frequency f = 0.8075 d−1 corresponding
to the period P = 1.2433 d−1. The second peak of nearly the same height consists of two peaks at
the frequencies f = 1.8075 d−1 and f = 1.81025 d−1. Their distance of 0.00275 d−1 corresponds
to the reciprocal value of the sidereal year in days. The internal structure indicates that it is an
alias of the basic period. The bootstrap test of the reality of the found period gives 49%, which
is the absolute maximum among the mCP candidates in the sample. The V and I phased light
curves of star 12 (190.1 1581) are shown in Figure 69.
A careful inspection of CCD images of this star reveals that it is a visual binary with a
companion that is about 1.5 magnitude fainter than the target. The OGLE-III photometry was
apparently done for both components. Future photometric observations and treatments of them
should take this into account. On the other hand, the modest ratio of amplitudes of variations
in V and I filters completely fulfils the theoretical expectation.
Star 14 (190.1 15527) is the brightest and one of the hottest mCP candidates in the sample.
With M0 = −1.57 mag and (V − I)0 = −0.09 mag it is a late Bp star with Si or He-weak
157
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
Phase
Magnitude[mag]
V
I
190.1 1581
Figure 69: The V and I light curves of star 12 (190.1 1581) plotted according to the ephemeris
given in Table 39.
chemical peculiarity (Sect. 6). The most striking result of its analysis is the found period of
P = 0.494 d−1, which is rather short. If it is confirmed, it would be one of the fastest rotating
mCP stars detected so far.
Unfortunately, the found period shorter than 12 hours is not as firmly established as in the
case of the previous mCP candidate with larger light changes. It results in the relatively low
appreciation of the reality probability of the found period only 30%. The rather small variations
in the I filter (Fig. 70) are also not in favour of variability, nor are the simulations with randomly
distributed magnitudes that also constitute periodogramme peaks slightly larger than 2 and 1.
That is why one suspects the feature to be an artefact caused by the specifically distributed
observations.
In conclusion, it is suggest that the periodic variations of star 14 (190.1 15527) remains an
open question.
19.5.5 Conclusions
The OGLE-III photometry for fourteen stars of which twelve are mCP candidates from Sect.
19.3 were analysed. In total, 6476 individual photometric measurements in V and I were used
to perform a time series analysis. For this purpose, periodograms were calculated including a
bootstrap-based probability of the statistical significance. Although the median of the ampli-
158
Table 39: The derived parameters of the light variation model given in Equation 35.
LMC 190.1 1581 LMC 190.1 15527
M0 − 2 450 000 3710.895(36) 3710.245(12)
P [d] 1.23836(5) 0.493570(8)
mV [mag] 17.8917(16) 17.1698(10)
aV [mag] 0.022(4) 0.017(3)
mI [mag] 17.8814(13) 17.1508(8)
aI [mag] 0.016(4) 0.008(2)
tudes of maximum peaks, median Am = 0.02 mag in the periodograms of the mCP candidates,
does not contradict the expectation for Galactic mCP stars, other circumstances suggest that
the prevailing majority of these peaks might not be statistically significant. Periodic variations
in only two of the mCP candidates were found, of which one is doubtful.
It seems that the rotationally modulated variability of the studied mCP candidates in the V
and I bands is very weak (if present at all). It is very likely that the true amplitudes are much
lower than 0.01 mag, which is the limit derived from the time series analysis of the brightest
mCP candidate.
From this finding one is able to conclude that the spots on the stellar surfaces of these objects
are not as contrasting as those of their Galactic counterparts; in other words, the overabundant
elements (Si, Fe, Cr, and so on) are more evenly distributed over the surface or the maximum
abundance is lower. This phenomenon has also been observed for non-magnetic Galactic Am or
weakly magnetic HgMn stars.
The low contrast of LMC mCP photometric spots could be explained by their lower global
magnetic fields strengths compared to those of their Galactic counterparts. It may relate with
the lower level of interstellar magnetic field in the LMC if compared with the Galactic field,
which results in the overall lower percentage of mCP star appearance compared to the Milky
Way (Sect. 19.3).
As future steps, retrieving time series of the remaining published mCP candidate stars is
suggested and getting more accurate measurements of the presented stars. In addition, spectroscopic
observations would shed more light on the surface characteristics.
20 A case study of using Gunn g data to improve ∆a
A case study was conducted for improving the existing ∆a photometric system. It has been
shown (Sect. 9) that the currently used filters are already optimized to measure the typical flux
depression of magnetic CP stars.
The fundamental idea is to employ a broader band filter which measures the 5200Å region
and the continuum blue- and redwards of it. The paradigm is the β index which consists of a
narrow and wide filter centred at Hβ (Crawford, 1958). However, the β index alone is not able
to give any unique astrophysical information. It always has to be used with an additional index
like c1 or m1 (Strömgren, 1966). This strategy is also valid for this analysis.
The corresponding filter to upgrade the ∆a photometric system has to fulfil the following
characteristics
• The bandwidth should be not wider than 1000Å to avoid blurring the effect of the 5200Å
region
• The central wavelength should be close to 5200Å
159
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Phase
Magnitude[mag]
I
V
190.1 15527
Figure 70: The V and I light curves of star 14 (190.1 15527) plotted according to the ephemeris
given in Table 39.
• It should measure the continuum blue- and redwards of the 5200Å region
• The contrast of CP and normal stars should be significant or at least larger than +15
mmag
• The effect of the luminosity should be minimized
• It should be widely available, well established, and tested
One of the choices would be the Z filter (λc = 5160 Å, FWHM = 210 Å) of the Vilnius
UPXY ZV S photometric system (Straižys & Sviderskiene, 1972). More details of this system
and its peculiarity indices are given in Section 4. There are two disadvantages: it does not
measure the continuum redwards of 5200Å and it is hardly available at international observa-
tories.
Finally, the g filter (Fig. 71) of the photometric system by Thuan & Gunn (1976) was chosen
for a more thoroughly investigation. Its adopted version was used also for the Sloan Digital Sky
Surveys (SDSS). This means that the filter is widely available at international observatories.
The synthetic ∆a and g photometric grids were taken from the Vienna New Model Grid
of Stellar Atmospheres, NEMO (Heiter et al., 2002b). The following parameter ranges were
used: 6000 < Teff < 20 000 K (step size of 200 K for Teff < 10 000 K, and 500 K for models hotter
than that), 2.0 < log g <5 dex (step size of 0.2 dex) for [Fe/H] = [−2,0,+1], and microturbulent
160
4200 4400 4600 4800 5000 5200 5400 5600 5800
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Flux
Wavelength [Å]
Gunn g
g1
g2
g3/y
Z
A3 V
A2 Cr Eu Sr
Figure 71: A comparison of the Gunn - g (green line), ∆a (blue), and Vilnius Z (magenta)
filters together with spectrophotometric data of HD 102647 (A3 V; black) and HD 118022 (A2
Cr Eu Sr; red) taken from Section 9.
velocities ξt = [0,1,2,4,8]. This should cover giants and MS stars cooler than a spectral type of
about B2. As next step, several combinations of the filters were investigated. The (g/g2) versus
(g1 − y) diagram gives a null result, or in other words, the contrast of normal and peculiar
objects is only ±3 mmag. From all different combinations, two parameters are worthy for a
further consideration
a1 = g2 − g (36)
a2 = (g1 − y)/(g − g2) (37)
Figures 72 and 73 show the results for three different metallicities [Fe/H] =[−2,0,+1], and
a microturbulent velocities ξt of 2 km s−1. The left panels show the MS whereas the right ones
also include the effect of luminosity. The blue asterisks denote the corresponding Teff values in
steps of 1000 K starting with 6000 K at the red end of (g1 − y).
One has to keep in mind that only distinct models have been calculated. Looking, for
example at Fig. 72 in the upper left panels, for cool type models, “vertical points” are visible.
This means that the models cover the whole area and overlap for the coolest temperatures.
First of all, no significant influence of different ξt values on these diagrams was detected.
Notice that in Sect. 14.7, it was concluded that an increase of ξt from 2 to 4 km s−1 can raise
synthetic ∆a values by up to +10 mmag. This is caused by an decrease of the flux in g2. For
sure, this effect also plays a role for the a1 and a2 parameters, but the overall separation of
normal and peculiar objects is much larger than +10 mmag (Figs. 72 and 73). In addition, also
161
0.08
0.12
0.16
0.20
0.24
0.28
-0.32 -0.28 -0.24 -0.20 -0.16 -0.12 -0.08
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.32 -0.28 -0.24 -0.20 -0.16 -0.12 -0.08
a1
=g2
-g[mag]
log g > 4.0 dex
[Fe/H] = 0
[Fe/H] = -2
[Fe/H] = +1
2.0 < log g < 5.0 dex
a2
=(g1
-y)/(g-g2
)[mag]
g1
- y [mag] g1
- y [mag]
Figure 72: Two combinations of the Gunn g and g1g2y filters which would enhance the nowadays
used ∆a photometric system. The synthetic colours are for three different metallicities
[Fe/H] =[−2,0,+1], and a microturbulent velocities ξt of 2 km s−1. The left panels show the
MS whereas the right ones also include the effect of luminosity. The blue asterisks denote the
corresponding Teff values in steps of 1000 K starting with 6000 K at the red end of (g1 − y).
the g is, to a certain amount, affected by this decrease. Both parameters include the difference
between g2 and g which results in a certain diminishment.
For both parameters, a strong effect of the luminosity (or log g) is apparent. One has to
recall, that normally, giants can be well sorted out on the basis of a V or y versus (g1 − y)
diagram for star clusters (Sects. 17.3 and 18.2).
The Teff range of interest was divided in three parts for the further discussion. One has
to recall that the 3σ limit for the classical ∆a index for stars (V brighter than 19.0 mag) in
the LMC (in one distinct field) is at ±12 mmag (Sect. 19.2). For Galactic open clusters (Sect.
17.2.1) it can even reach half this value.
• Teff < 8000 K: The underabundant models for the MS deviate from the solar abundant ones
between 20 and 50 mmag for a1 as well as between 100 and 800 mmag for a2. Even taking
all log g values up to 2.0 dex, there are separated for the a2 parameter.The overabundant
models deviate by up to 10 mmag for a1 and 100 mmag for a2, respectively. Such a strong
effect for cool type stars is not observed when looking at spectrophotometry (Sect. 9).
Here, both parameters are much more superior than the a index alone.
• 8000 < Teff < 13000 K: The underabundant models overlap with the solar abundant ones for
both parameters, even taking only the MS values. However, in overall, the underabundant
models tend to show lower values, or in other words, they represent the lower envelope.
The overabundant models, are distinct by a constant value of about and 50 and 10 mmag,
162
0.14
0.16
0.18
0.20
0.22
0.24
0.26
-0.31 -0.30 -0.29 -0.28 -0.27 -0.26 -0.25 -0.24
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-0.31 -0.30 -0.29 -0.28 -0.27 -0.26 -0.25 -0.24
a1
=g2
-g[mag]
log g > 4.0 dex
[Fe/H] = 0
[Fe/H] = -2
[Fe/H] = +1
2.0 < log g < 5.0 dex
a2
=(g1
-y)/(g-g2
)[mag]
g1
- y [mag] g1
- y [mag]
Figure 73: The same as Fig. 72, but for Teff hotter than 9000 K.
respectively. As a conclusion it can be said that both parameters do not supersede the
capabilities of the classical ∆a photometric system.
• Teff > 13000 K: Let’s recall that this is the Teff range for which the classical ∆a photometric
system is most sensitive (Sect. 11). This region comprises the (magnetic) CP2 and CP4
stars (Sect. 6). From Fig. 73, one can see that the underabundant models are not
separated from the solar abundant ones. However, the overabundant ones are between
10 and 100 mmag, respectively. Furthermore, there is no overlap for higher luminosities
models. This means that overabundant stars can be unambiguously detected with both
parameters.
It can be concluded that additional observations, or available archival data, with the Gunn g
would gain a significant improvement of the currently used ∆a photometric system.
21 The ALHAMBRA and COSMOS surveys
In Sect. 8.4, spectral templates of different galaxy types without a redshift were presented. It
was shown that the region from 4900 to 5700Å is well suited to study galaxies which would break
new ground. This will be the next logical step in the evolution of the ∆a photometric system
after studying stars, star clusters, and the Magellanic Clouds. However, studying galaxies in a
narrow-band photometric system, large telescopes are needed. Normally, it is not possible to
use other filter sets than those provided by the corresponding observatory. Thus, using a g2
filter at the VLT, for example, seems very unrealistic in the future.
Therefore, another approach was chosen in order to investigate galaxies (and also stars as it
turned out) within this spectral region. The current available photometric surveys were searched
163
4300 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Flux
Wavelength [Å]
AH 457nm
AH 522nm
IA527
g2
A3 V
A2 Cr Eu Sr
Figure 74: A comparison of the ALHAMBRA AH 457nm and AH 522nm (black dashed-dotted),
Subaru Telescope Intermediate Band Filter IA527 (green), and g2 (blue) filters together with
spectrophotometric data of HD 102647 (A3 V; black) and HD 118022 (A2 Cr Eu Sr; red) taken
from Section 9.
for filters which correspond to the genuine g2 one. Two surveys, namely ALHAMBRA and
COSMOS, were found to include one filter fulfilling, within acceptable limits, the requirements.
Both surveys are aimed at studying galaxies at high galactic latitudes (|b| > 40o). Although the
stellar densities at such high galactic latitudes is already quite low, also stars of all types are
observed simultaneously with the galaxies. So it is possible to investigate galaxies and stars
within the same homogeneous photometric system. This is an unique opportunity on the basis
of high quality public available data sets.
The Advanced Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA)
survey (Moles et al., 2008) employs 20 contiguous, equal-width, medium-band filters
covering from 3500Å to 9700Å, plus the standard JHKs near-infrared (NIR) bands. A total
area of four square degrees on the sky will be observed. In Fig. 74, the corresponding filters
centred at 4570 and 5220Å are shown. The latter filter samples the 5200Å very well whereas the
bluer one samples the continuum between Hγ and Hβ. The consecutive filter centred at 5510Å
(not shown in this figure) samples the continuum redwards of the 5200Å without the influence
of the Hα line. Molino et al. (2014) presented the public data release of this survey including
about 100 000 galaxies, 20 000 stars in the galactic halo, and 1000 AGN candidates. The stars
were identified according to their apparent geometry (PSF) on the image, F814W magnitude,
as well as a combination of the optical (F489W − F814W) and NIR (J − Ks) colours (Troncoso
Iribarren et al., 2016), respectively. However, up to now, no comprehensive analysis of the stellar
sample was published. In a forthcoming project, the photometric data will be used to find faint
and most distant CP stars on the basis of a system similar to the “classical” ∆a one (Sect. 3).
164
In addition, the galaxies observed by this survey will be also analysed in the same way as the
stars.
The Cosmic Evolution Survey (COSMOS, Scoville et al., 2007) is designed to probe the
formation and evolution of galaxies as a function of both cosmic time (redshift) and the local
galaxy environment. The survey covers a two square degree equatorial field with imaging
by most of the major space-based telescopes and a number of large ground based telescopes,
with many ongoing surveys. The COSMOS survey is centred at (J2000): α = 10:00:28.6 and
δ = +02:12:21. Objects as faint as 26th magnitude in the optical region are observed. Laigle
et al. (2016) presented the “COSMOS2015 Catalog” which contains precise PSF-matched photometry,
photometric redshifts and stellar masses for more than half a million of sources on the
COSMOS field. It includes photometry in 36 different bands from the NUV (2314Å) to the FIR
(79595Å). Among the whole variety of filters, it includes the “Subaru Telescope Intermediate
Band Filter” IA527 which is centred at 5261Å with a FWHM of 242Å (Fig. 74). This filter
is very useful in the context of studying the 5200Å region. From the huge amount of available
filters, the most efficient ones will be chosen in order to establish an aGal index (Sect. 8.4), for
example. This catalogue is already public available and will serve as a starting point for a pilot
study of galaxies in the near future.
Although the observed fields of both surveys do not overlap, the final results will be compared
and used to analyse the sample of galaxies.
22 Conclusions and Outlook
In this work it was shown how the ∆a photometric system successfully produced countless
scientific output and how it developed from a tool to detect CP stars to an universal tool to
investigate even extragalactic systems. This enormous evolution was done within the last 40
years since its first appearance on the astronomical scene by Maitzen (1976a).
It has to be said that in the 1980ies and 1990ies, the system had its first period of prosperity
because of the huge efforts by the the European working group on chemically peculiar stars of
the upper main sequence (Mathys et al., 1989). Dedicated observing campaigns not only at the
European Southern Observatory, but also at northern observatories such as at Hvar (Croatia)
and Mt. Schöpfl (Austria) led to an active community and many publications. Other than, for
example the Geneva 7-colour system, the characteristics of the ∆a filter system slightly changed
during time evolving to an almost perfect tool for detecting magnetic CP stars. At this time,
the observations were devoted to Galactic field stars and open clusters, only. Joint efforts to
shed more light on the CP phenomenon, to study magnetic fields, and the first important steps
of asteroseismology made these research fields very vibrant.
However, at the end of the 1980ies, the highly developed photomultiplier technology, slowly
but surely, was replaced by the CCD technology. It took a few years until CCDs reached the
same accuracy as photomultipliers for the same exposure time and target brightness.
The second period of prosperity began with the first CCD ∆a observations which were
performed 1995 with the same telescope, the 61 cm Bochum telescope at La Silla, by the same
person, Hans-Michael Maitzen, who initiated in 1971 the observations of CS Vir in g1 and g2. The
results of the first CCD observations, data for 25 Galactic field stars with known spectroscopic
peculiarity types, were published by Maitzen et al. (1997). After that, CCD observations of
open clusters, the LMC and Globular clusters were successfully secured.
Other than in the photomultiplier era, no large international working group was conducting
the observations and their analysis.
Nevertheless, this work has shown that the ∆a photometric system and the study of its
corresponding spectral region from 4900 to 5700Å is able to contribute significant new insights
at many fields of astrophysics. The list of objects which are potential targets is long: cool-type
165
Population I and Population II objects, supergiants, emission type objects, all type of galaxies,
quasars, and so on.
These research fields can be investigated by 1) new observations; 2) archival data not used
so far, for example cool-type objects in star cluster fields and 3) data from other surveys which
employ similar filters. For sure, all three approaches will be extensively utilized in the future.
Several projects have already started or will soon be conducted. Here is a short list of these
projects.
• Reduction of unpublished photoelectric and CCD observations of Galactic open as well as
Globular clusters
• Execution of a complete survey of the Small and Large Magellanic Cloud
• Re-analysis of cool-type stars in star cluster fields
• Analysis of the public available data from the ALHAMBRA and COSMOS surveys in
order to investigate galaxies and stars
• Observations of bona-fide Galactic field CP stars
• Observations of bright Abell galaxy clusters
• Observations of bright quasars
• Observations within the Gunn g filter and/or search for archival data to extend/upgrade
the current ∆a photometric system
• Spectroscopic observations of bona-fide photometric CP stars in the LMC and Globular
clusters
• Comprehensive analysis of more sophisticated galaxy models taking into account redshifts
These projects will guarantee that the classical ∆a photometric system will further evolve
and become even more successful and important as it already currently is.
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