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
Distance:V0-MV
AV
k.AV
Turn-off
Grocholski & Sarajedini, 2003, MNRAS, 345, 1015
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
Reddening Maps
Piskunov et al., 2006, A&A, 445, 545
http://argonaut.skymaps.info/
http://www.univie.ac.at/p2f
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
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
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
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
• [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 - Sun
Asplund et al.
Abundance - Sun
Asplund et al.
Metallicity => different opacity
Isochrones for 10 Myr
Metallicity - isochrones
Schaller et al., 1993, A&AS, 101, 415
Different He abundances – [Z]
constant
Color-Magnitude Diagram
Gaia Collaboration, 2018, A&A, 616, A10
Color-Magnitude Diagram
Color-Magnitude Diagram