From Bolometric to Monochromatic
L
SSP

md
 L ( m) ( m)dm

mi
One isochrone of given (AGE,Z) is {m, L, Te}
{R g Te}
Divide isochrone in small cells with (m,L,Te)
Each cell corresponds to (g,Te)  Fλ(m) either observed stellar spectra or model atmospheres
R
 Lλ(m)
L ( m)  4 ( R ) 2 F ( g, Teff )
Then sum up along the isochrone
Get the Spectral Energy Distribution of the SSP
Compute Colors by convolving with photometric system
Lectures on Stellar Populations
An Alternative
best suited for FCT applications
L
SSP

mTO
 L ( m) ( m)dm   n L

j
M bol  M bol, 0  2.5 LogL / L0
BC  BC , 0  2.5 Log
M   M  , 0  2.5 LogL / L , 0
L / L , 0
L / L0
BC  M bol  M 
SSP
L
 L  9.75  10 b( )  t j L j
MS
10
PMS
L , j
Lj
,j
PMS
mi
L
0.4 ( BC  BC , 0 )
 10
L
10
 LMS
  9.75  10 b( )  F j  10
0.4 ( BC  , j  BC  , 0 )
PMS
The monochromatic contributions of the PMS phases are weighted with the Fuel
Burned in each phase
Lectures on Stellar Populations
Exercise: the Bolometric Correction of an SSP
SSP
BC
SSP
L

LSSP
10
LSSP

 2.5 Log SSP
L

 L ( m) ( m)dm
 L ( m) ( m)dm

0.4 BC SSP



0.4 BC ( m )

 L ( m)  10   ( m)dm
 L ( m) ( m)dm

L ( m )
0.4 BC  ( m )
 ( m )  10
dm
SSP
L
The Bolometric Correction of each portion of the isochrone is weighted by its contribution
to the bolometric light: cells with a small contribution to total L are not important to the
bolometric correction of the SSP
Lectures on Stellar Populations
Contributions of individual phases
At short wavelenghts we see
the MS (turn off, mostly)
In the K band the MS is never
important
Notice the AGB phase transition
and the RGB dominating past
approx 3 Gyr
Lectures on Stellar Populations
Contributions of individual phases: Z dependence
BOL: MS,AGB,RGB
V: MS, RGB
At Low Z HB is important
K: AGB and RGB
Lectures on Stellar Populations
Calibration of AGB
Total Fuel will depend on Z
More important: The C - M share depends on Z
Based on:
dependence of envelope mass
at the first pulse on age;
scaling of Renzini & Voli models
behaviour with metallicity
Lectures on Stellar Populations
SSPs at AGB phase transition
In the optical there’s no difference
In the IR the flux is 3 times higher than
without TP AGB
Notice the strong absorption features
due to C (C2, CN) and M (TiO,H2O) stars
The V-K color jumps by more than 1 mag
Lectures on Stellar Populations
SSPs across AGB phase transition
At higher Zs the O-rich stars
are favoured
At older ages the TP AGB
becomes less important
Lectures on Stellar Populations
SSP: Integrated Colors
Older SSPs are redder
Metal rich SSPs are redder
Past 2-3 Gyr the colors
dependence on age is mild
Frascati vs Padova tracks:
B-V bluer with Padova
Larger TO mass at given age
V-K redder with Padova
Redder RGB at solar Z
The discrepancy between
The various authors is >
than the systematics due to
the use of different tracks
Lectures on Stellar Populations
Integrated Colors: Comparison with Observations
OLD SSPs
Data: MW Globulars from Harris et al.
[Z/H] on Zinn & West scale
Models: Maraston 2004 13 Gyr old SSPs
blue and intermediate HB at [Z/H]<-1
solid Kroupa
dashed; Salpeter
dotted Bruzual & Charlot 2003
Colors are not affected by IMF
Most lum comes from stars within a
small mass range
Agreement is good but for B-V
Likely Color-Temperature transformation
Lectures on Stellar Populations
Integrated Colors: Comparison with Observations
INTERMEDIATE AGE
Filled circles: MC Globulars with SWB
type in 3 – 6 (several authors)
Models: younger than 2 Gyr and with Z=0.5 Zo
solid Maraston 2004
dashed PEGASE
dotted Bruzual & Charlot 2003
Optical – IR colors span
a wide range among these
clusters: a sizeable effect
from the development of the
AGB must be present
Open Triangles: Clusters in
NGC7252, a merger remnant
Lectures on Stellar Populations
SEDs: Comparison with Observations
ACROSS the AGB PHASE TRANSITION
Lectures on Stellar Populations
Mass to Light Ratios
IMF effect
M/L increases with age in every band
Reasonable agreement among authors
But notice the AGB phase transition in K
Notice the Y scale
BC2003 have different tracks
Worthey : possibly too much light on RGB
Vazdekis ?
M/L increases with Z
But notice the small span in the K band
Lectures on Stellar Populations
What have we learnt
•
•
•
•
0.4 BC
Each isochrone portion contributes to the total BC factor 10 
weighted by its contribution to the total bolometric light of the SSP
Short wavelenghts (U,B,V) best sample the MS Turn off
Long wavelenghts (IR) best sample RGB and AGB
The contribution of the various phases in the various bands depend on Z
at low Z the HB becomes important in optical light
at high Z the MS always dominates the optical
•
The treatment of the TP AGB is very critical for SSPs between 0.2 – 2 Gyr
still a lot of work to do, but a sizeable contribution from this phase IS needed
•
Considerable discrepancies still in the integrated colors from different
authors
because of (a) different tracks (b) different atmospheres (c) different codes
• M/L ranges from about unity to about tens from young to old SSPs
• In the K band the M/L ratio is almost independent of metallicity
Lectures on Stellar Populations