The cluster parameters
1. Reddening
2. Distance modulus
3. Age
4. Metallicity
Determination in the order: Reddening, age,
distance modulus simultaneously, metallicity with
possible iterations
Star Clusters – tricky to analyze
NGC
7789
Star Clusters – tricky to analyze
Distance:V0-MV
AV
k.AV
Turn-off
Glushkova et al., 2013, MNRAS, 429, 1102
Color – Magnitude - Diagram
Different CMDs for one open cluster
Grocholski & Sarajedini, 2003, MNRAS, 345, 1015
Different photometric indices
Several different indices et al. are available (very much
incomplete):
• Sensitive to temperature:
1. Johnson: B-V, V-I, R-I, V-K, …
2. Strömgren: b-y, u-b, b
3. Sloan g-r, r-i, …
4. Geneva: B2-V1, X, …
5. Gaia: BP-RP
6. 2MASS: H-K, J-K and H-J
• „Mixture“:
1. Johnson: U-B
2. Strömgren: c1, m1, …
3. Geneva: d, D, m2, …
Photometric calibrations
Mucciarelli & Bellazzini, 2020, Research Notes of the AAS, 4, 52
Be aware of the extinction!
Photometric calibrations
Ruiz-Dern et al., 2018, A&A, 609, A116
Photometric calibrations
Ruiz-Dern et al., 2018, A&A, 609, A116
Final calibration
Photometric calibrations
Ruiz-Dern et al., 2018, A&A, 609, A116
Comparison
with other
calibrations
Photometric calibrations
Martell & Laughlin, 2002, ApJ, 577, L45
Error: +-0.10 dex
How to derive cluster
parameters?
• Use as much as possible available indices
• Check the literature for published values
as least as a starting point
• First try it with a “standard set” of data
• Automatic procedures available, but be
careful
Absorption = Extinction = Reddening
• AV = k1 E(B-V) = k2 E(V-R) = …
• General extinction because of the ISM
characteristics between the observer and
the object
• Differential extinction within one star
cluster because of local environment
• Both types are, in general wavelength
dependent
Reasons for the interstellar
extinction
• Light scatter at the interstellar dust
• Light absorption => Heating of the ISM
• Depending on the composition and
density of the ISM
• Main contribution due to dust
• Simulations and calculations in Cardelli et
al., 1989, ApJ, 345, 245
Cardelli et al., 1989, ApJ, 345, 245
Important parameter:
RV = AV/E(B-V)
Normalization factor
Standard value used
is 3.1
Be careful, different
values used!
Depending on the
line of sight
Cardelli et al., 1989, ApJ, 345, 245
Dependency of
the extinction
from RV
How to derive the reddening?
• Non-Isochrone approach: from photometric
and spectroscopic observations
Classical approach: Neckel &
Klare, 1980, A&AS, 42, 251
Take all available UBV and
Strömgren b photometry
MK classifications
Bailer-Jones,
1996, PhD,
Cambridge
University
Absolute Magnitude
Assume V = 10 mag
and no reddening
O5: -5.6 => 13 000 pc
A0: +1.0 => 630 pc
G0: +4.5 => 125 pc
M0: +8.9 => 15 pc
Assume V = 20 mag
and no reddening
O5: -5.6 => 1.3 Mpc
A0: +1.0 => 63 kpc
G0: +4.5 => 12.5 kpc
M0: +8.9 => 1.5 kpc
Crawford,
1976, AJ,
83, 48
Example
for the b
index
Cut off as you like
Reddening Maps
Piskunov et al., 2006, A&A, 445, 545
http://argonaut.skymaps.info/
http://www.univie.ac.at/p2f
Neckel & Klare, 1980, A&AS, 42, 251
Needed:
Galactic coordinates
Distance from Sun
Haffner 18
Age about 8 Myr
d = 6000 pc
differential
extinction within
the cluster
Yadav & Sagar, 2001, MNRAS, 328, 370
Differential
reddening in young
open clusters
Determination of the reddening -
Isochrones
• From two temperature sensitive
parameters, the determination of the
reddening is not possible
• You need one “other” observational
index
• First choices: (U – B), (u – b), [X], b
• Normally, you only have V, J, H, K, and so
on
Reddening vector
Mean values for
E(B-V) and E(V-I)
You would need a spectral information
The reddening shifts the main sequence
by a value of
E(U-B) = 0.72E(B-V) + 0.05E(B-V)2
Reddening vector
Mean values for
E(B-V) and
E(U-B)
Reddening vector
1
2
1: „early type region“, hotter than A5
2: „late type region“, cooler than A5
Mean values for
E(B-V) and Av
Significant effect
due to reddening
No effect due to reddening
Mean values for
E(B-V) and Av
No stars hotter than A0
Good estimate for the reddening
and distance
Distance modulus
• Apparent DM: (V - MV) which still
includes the reddening
• Absolute DM: (V - MV)0 or (V0 - MV) which
not includes the reddening
• Be careful there is always a mixture in
the literature!
How to determine the DM?
• Direct isochrone fitting
• Calibrate MV directly via photometry and
spectroscopy with known reddening and
V magnitude => distance directly
• Advantage: statistical sample
Balaguer-Núñez et al., 2007, A&A, 470, 585
Guerrero et al., 2011, RMxAA, 47, 185
Distance:V0-MV
AV
k.AV
Turn-off
Turn off point
• Where is the turn-off point located?
–Color/temperature
–Absolute/apparent magnitude/luminosity
• Direct correlation with the age
• Difficult to define for young star clusters
• First, classical method, just „to look“ at
color-magnitude-diagram
Mermilliod, 1981, A&A, 97, 235: no newer paper available!
Dereddened indices
„Bluest“ (U – B)0
at main sequence
MV of red giants
Mermilliod, 1981, A&A, 97, 235
No direct error estimation possible
Possible to use for star clusters
between 20 Myr and 800 Myr
Mermilliod, 1981, A&A, 97, 235
Very precise method
Possible to use between
for star clusters between
20 Myr and 300 Myr
(U – B)0 for cooler stars
= older ages
is almost constant
Not very accurate but still useful, never done for 2MASS and NIR
Calculation of Isochrones
The calculation of theoretical isochrone (= lines
of equal age) is done with stellar atmospheres
Free parameter : Metallicity [X, Y, Z]
1. Zero Age Main Sequence [Teff , L]0
2. Chemical and gravitational evolution
3. [Teff , L](t)
4. Adequate stellar atmosphere = PHYSICS
5. Absolute fluxes
6. Folding with filter curves
7. Colors, absolute magnitudes and so on
Which astrophysical “parameters”
are important?
• Equations of state
• Opacities
• Model of convection
• Rotation
• Mass loss
• Magnetic field
• Core Overshooting
• Abundance of helium
• …
Maeder & Mermilliod, 1981, A&A, 93, 136
Maeder & Mermilliod, 1981, A&A, 93, 136
Different treatment
of convection
A comparison of isochrone sets
• Grocholski & Sarajedini (2003, MNRAS,
345, 1015) compared the following
isochrones:
1.“Padova”: Girardi et al., 2002, A&A, 391, 195
2.Baraffe: Baraffe et al., 1998, A&A, 337, 403
3.“Geneva”: Lejeune & Schaerer, 2001, A&A, 366, 538
4.Y2: Yi et al., 2001, ApJS, 136, 417
5.Siess: Siess et al., 2000, A&A, 358, 593
For Pop II
The location of the
Sun with isochrones
of 5 Gyr
Isochrones by
Siess et al. (1997)
seem “to have
a problem”
Comparison of
different masses
for a constant MV
100%
M5
Zero line is the
isochrone of the
Padova group
Comparison of
different color
indices for a
constant MV
Zero line is the
isochrone of the
Padova group
M0
Used
Photometry
Parameters from the literature
log t, E(B-V) and [Fe/H] fixed, only
Distance modulus determined
Value from the
literature
Transformation in distances [pc]
• M35: 1148 [916,1208]; -20% +5%
• M37: 2042 [1905,2239]; -7% +10%
• NGC 1817: 2692 [2344,2884]; -13% +7%
• NGC 2477: 2042 [1698,2089]; -17% +2%
• NGC 2420: 2630 [2399,3090]; -9% +17%
• M67: 912 [776,912]; -15% +0%
• Mean values: -13(5)% +7(6)%, for one free parameter!
In a statistical point-of-view: significant
For a given reddening, metallicity and age, the isochrones
by Baraffe et al. yield significantly brighter and Yi et al.
significantly fainter absolute magnitudes .
In addition, the isochrones by Siess et al. do not reproduce
the location of the Sun correctly.
Grocholski & Sarajedini, 2003, MNRAS, 345, 1015
Age determination ONLY
based on these three
stars
Isochrones for [Z] = 0.040
and log t = 8.0, 8.1 und 8.2
Result: t = 130+40
-30 Myr
E(B-V) = 0.75(5) mag
V – MV = 14.00(25) mag
log t = 7.0
Automatic Methods
Jorgensen & Lindegren, 2005, A&A, 436, 127
Definition of different
„important“ areas (Box)
in the CMD. Do this
allocation as you like.
Turn-off point, location
of the red giant clump,
and so on.
Count the number of stars
in each box.
Warning: you always
„lose“ stars because of
discrete boxes.
Only for t > 300 Myr
1 Gyr
Other methods
• https://github.com/hektor-monteiro/OCFit
• https://asteca.readthedocs.io/en/latest/
• An et al., 2007, ApJ, 655, 233
• Buckner & Froebrich, 2013, MNRAS, 436, 1465
• Fernandes et al., 2012, A&A, 541, A95
• Frayn & Gilmore, 2003, MNRAS, 339, 887
• Kharchenko et al., 2005, A&A, 438, 1136
• Monteiro et al., 2010, A&A, 516, A2
• Oliveira et al., 2013, A&A, 557, A14
• Pinsonneault et al., 2003, ApJ, 598, 588
Metallicity - Basics
• Metallicity as [X:Y:Z]
• X = Hydrogen
• Y = Helium
• Z = „the rest“
𝑋 ≡
𝑚 𝐻
𝑀
Y ≡
𝑚 𝐻𝑒
𝑀
Z = σ𝑖>𝐻𝑒
𝑚𝑖
𝑀
= 1 – X – Y
Metallicity - designations
• In the literature you will find
– [Z]
– [Fe/H]
– [M/H]
– [Element 1 / Element 2]
• Relations for the transformation are necessary
Metallicity – designations
Metallicity - designations
• [dex], e.g. [Fe/H] = -0,5 dex
dex factor dex factor
-2 0,01 0,1 1,26
-1,5 0,03 0,2 1,58
-1 0,10 0,3 2,00
-0,9 0,13 0,4 2,51
-0,8 0,16 0,5 3,16
-0,7 0,20 0,6 3,98
-0,6 0,25 0,7 5,01
-0,5 0,32 0,8 6,31
-0,4 0,40 0,9 7,94
-0,3 0,50 1 10,00
-0,2 0,63 1,5 31,62
-0,1 0,79 2 100,00
The Sun as standard star
• „Our“ standard star for the normalisation of
the metallicity is the Sun
• We define:
– Mass
– Luminosity = absolute (bolometric) magnitude
– Temperature = spectral type = color
– Age
– Chemical composition
– Internal structure (rotation, magnetic field,
convection, diffusion, pulsation, …)
Abundance analysis - Sun
• Review article: Asplund et al., 2009, Annual
Review of Astronomy & Astrophysics, 47, 481
• Ingredients:
– Stellar atmosphere
– Atomic line data
– High resolution spectra
– Analysis method
– Starting parameter
• Gray, 2005, The Observation and Analysis of
Stellar Photospheres, Cambridge University Press
Stellar atmospheres
• ATLAS, http://atmos.obspm.fr/
• MARCS, http://marcs.astro.uu.se/
• NEMO, http://www.univie.ac.at/nemo
• PHOENIX, http://www.hs.uni-
hamburg.de/EN/For/ThA/phoenix/index.html
• TLUSTY, http://nova.astro.umd.edu/
• Stellar Atmospheres Software,
http://www.arm.ac.uk/~csj/software_store/
• Workshop:
http://astro.physics.muni.cz/events/spec_ws_2017/
Stellar atmospheres
Different synthesized
stellar spectra “for
the same star“
Abundance - Sun
• Problems with
–Hydrogen
–Helium
–Elements with only a few lines
–Elements with only weak lines
• LTE versus NLTE (Local Thermodynamic
Equilibrium )
Abundance - Sun
Asplund et al.
Abundance - Sun
Asplund et al.
Abundance - Sun
PhD thesis – U. Heiter
Abundance - Sun
Asplund et al.
Determination of the metallicity
• The determination of the metallicity can be
done in three ways:
1. Spectroscopic abundance analysis
2. Fitting of isochrones
3. Photometric calibrations
• ESO- Gaia survey:
https://www.gaia-eso.eu/
„Metalls“ in stars
Metallicity => different opacity
Isochrones for 10 Myr
Metallicity - isochrones
Schaller et al., 1993, A&AS, 101, 415
Different He abundances – [Z]
constant