Bolometric Corrections
and Colors
system throughput
depends on Teff, gravity and Z
June 2005
Lectures on Stellar Populations
Average of Observed Stellar Spectra:
Dwarfs
SpT
T(K)
F c.g.s.
O 50000 3.5e+14
A 10000 5.7e+11
G 6000 7.3e+10
M 3500 8.5e+09
June 2005
Lectures on Stellar Populations
Dwarfs SED & Filters
BC strongly depends on SpT
Cool stars detected in Red
Hot stars detected in Blue
B
V
I
U
COLORS:
are Temperature Indicators
Cool stars are Red
Hot stars are Blue
June 2005
Lectures on Stellar Populations
Effect of gravity
Gravity effects are very
Important for very hot
And very cool stars
B0
M5
B5
M2
A0
June 2005
K5
Lectures on Stellar Populations
COLORS: Empirical
Johnson 1966 ARAA 4 193
B-V colors are good Teff indicators
for late A, F, G and early K stars
For Hot stars SpT is preferred
June 2005
Lectures on Stellar Populations
Bolometric Corrections: Empirical
Hottest and Coolest stars
are 3-4 mags fainter in V
than in Bolometric
Gravity dependence can
amount to 0.5mags
June 2005
Lectures on Stellar Populations
Model Atmospheres:
Kurucz Grid revised by Castelli
Models
June 2005
Empirical
Lectures on Stellar Populations
Model Atmospheres:
dependence on gravity
Models
June 2005
Empirical
Lectures on Stellar Populations
Model Atmospheres:
dependence on
Metallicity
Molecules
Blanketing
June 2005
Lectures on Stellar Populations
Model Atmospheres:
Calibration
• The Models do a good job for the SED of Dwarfs, especially for
intermediate Spectral Types
• Not too bad for Giants and Supergiants also
• Major problems are met al low Temperatures (Opacity, Molecules)
• Anyway, the use of Model Atmospheres becomes a MUST because:
they allow us to compute Colors and BCs for various Metallicities
AND
for whatever filters combinations
To do that we:
Take a grid of Models
Perform calibration
Produce Tables of BC, Col function of (Teff ,Log g, [M/H])
June 2005
Lectures on Stellar Populations
Balmer Jump
Go Back
June 2005
Lectures on Stellar Populations
Colors from Model Atmospheres
Origlia and Leitherer 1998: Bessel, Castelli and Pletz models through Ground Based Filters
June 2005
Lectures on Stellar Populations
Bolometric Correction from Model Atmospheres
Nice and smooth
BUT
Probably off for
Late K and M stars
Have you noticed that lines of different colors
Span different Temperature Range?
THIS IS NOT A SUPERMONGO FALIURE:
June 2005
Lectures on Stellar Populations
Tracks on the Log Teff – Log g Plane
WE LACK LOW GRAVITY MODELS FOR MASSIVE STARS
WE LACK LOW TEMPERATURE AND LOW GRAVITY MODELS
FOR LOW MASS STARS (AT HIGH METALLICITIES)
June 2005
Lectures on Stellar Populations
Go back
M&M: attach empirical calibrations
Montegriffo et al. (1998) traslated
June 2005
Lectures on Stellar Populations
Bessel, Castelli & Pletz
(1998, A&A 333, 231)
Compare Kurucz’s revised models (ATLAS9)+ Gustafsson et al revised (NMARCS) models
for red dwarfs and giants to empirical colors and BCs for stars in the Solar
Neighbourhood (i.e. about solar metallicity).
They show color-temperature, color-color, and BC-color relations.
Conclude that :
1. There is a general good agreement for most of the parameter space
2. B-V predicted too blue for late type stars, likely due to missing atomic and molecular
opacity
3. NMARCS to be preferred to ATLAS9 below 4000 K
June 2005
Lectures on Stellar Populations
The models are shown as curves
The data are shown as points
The ptype encodes the literature source
Hot Dwarfs
A-K Dwarfs
GKM Giants
June 2005
Lectures on Stellar Populations
Dwarfs
NM
K
Giants
June 2005
Lectures on Stellar Populations
Dwarfs
Dwarfs
June 2005
Lectures on Stellar Populations
Giants
BaSeL Grid
(Lejeune, Cuisinier and Buser 1997 +)
• Collect Model Atmospheres from Kurucz
+Bessel + Fluks (for RGs) + Allard (for M dwarfs)
• Correct the model spectra so as to match empirical
calibration
• Put the corrected models on the net
June 2005
Lectures on Stellar Populations
Lejeune Models: Z dependence
Check with Globulars’ Ridge Lines
BaSeL 2.2 : Corrected Models at solar Z
& Z theoretical dependence
BaSeL 3.1: Corrected models at various Z
based on GCs Ridge Lines
5 GGs with [Fe/H]=-2.2 to -0.7 in UBVRIJHKL
For each get Te from V-K (using BaSel 2.2)
 BCs vs (Te,g)
BaSeL 3.1 Padova 2000: Correction at various Z
made to match GCs Ridge Lines with
Padova 2000 isochrones
”It is virtually impossible to establish a unique calibration
In terms of Z which is consistent with both color –temperature
Relations AND GCs ridge lines (with existing isochrones)”
Westera et al. 2002
June 2005
Lectures on Stellar Populations
Libraries with high Spectral resolution
Recently developed for Population Synthesis Studies, Stellar spectroscopy, Automatic Classification of Stellar
and Galaxy Spectra … not so important for Broad Band Colors
Observational Libraries
take a sample of well observed stars with known parameters Log Te, Log g, [Fe/H]
and derive their spectra
STELIB – Le Borgne et al. 2003
249 spectra between 3200 and 9500 A,
sp.res. ~ 3 A
June 2005
INDO-US – Valdes et al. 2004
885 spectra between 3460 and 9464 A
+ 400 with smaller wavelength range
sp. res. ~ 1 A
Lectures on Stellar Populations
Libraries with high Spectral resolution
THEORETICAL MODELS
Usually constructed on top of a model atmosphere (Kurucz) +
Code for synthetic spectrum which solves monochromatic radiative transport with a large list of lines
not very important for broad band colors, but could suggest diagnostic tools
Martins et al. 2005: 1654 spectra between 3000 and 7000 A
with sp. res. ~0.3 A
Special care to describe non-LTE and sphericity effects
June 2005
Lectures on Stellar Populations
Check versus STELIB stars
Check versus INDO-US stars
Martins et al. 2005
30000
4.5
0.02
30262 4.18 0.02
14000
4.5
0.02
13622 3.80 0.05
7000
4.0
0.02
7031 4.04 0.01
3500
1.0
0.01
4000
1.0
0.02
3500
0.0
0.02
4540 0.88 0.02
4500
0.0
0.01
June 2005
Lectures on Stellar Populations
3700 1.3 0.01
3910 1.6 0.01
3540 0 0.02
Other Models:
Munari et al. : 67800 spectra between 2500 and 10500 A with res of ~1 A
cover Te from 3500 to 47500 K, Log g from 0 to 5
[M/H] from -2.5 to +0.5 and [A/Fe]=0,+0.4
Bertone et al. : 2500 spectra with resolution of ~ 0.3 A
UV grid
Optical grid
between 850 and 4750 A
3500 and 7000 A
Te from 3000 to 50000 K
4000 to 50000 K
Log g from
1 to 5
0 to 5
[M/H] from
-2.5 to +0.5
-3 to +0.3
Coelho et al. : spectra between 3000 and 1800 A with res of ~0.02 A
cover Te from 3500 to 7000 K, Log g from 0 to 5
[M/H] from -2.5 to +0.5 and [A/Fe]=0,+0.4
June 2005
Lectures on Stellar Populations
Converted Tracks: B and V
June 2005
Lectures on Stellar Populations
Converted Tracks: V and I
June 2005
Lectures on Stellar Populations
What have we learnt
When passing from the theoretical HRD to the theoretical CMD we
should remember that:
• At Zo the model atmospheres are adequate for most TSp
• There are substantial problems for cool stars, especially at low
gravities
• The theoretical trend with Z is not well tested
• The tracks on the CMD reflect these uncertainties
The transformed tracks make it difficult to sample well the upper MS
(large BC); the intermediate MS merges with the blue part
of the loops; the colors (and the luminosities) of the Red giants and
Supergiants are particularly uncertain.
June 2005
Lectures on Stellar Populations
Uncertainty of Stellar Models
Gallart, Zoccali and Aparicio 2005 compare various sets of models (isochrones) to
gauge the theoretical uncertainty when computing simulations with one set.
June 2005
Lectures on Stellar Populations
Age-dating from Turn-off Magnitude
In general the turn-off magnitude
at given age agrees
Teramo models fit the turn off
Magnitude with older ages
(at intermediate ages)
Notice some difference in
isochrone shapes , and SGB
for old isochrones
June 2005
Lectures on Stellar Populations
Deriving metallicity from RGB
The RGBs can be very different
especially at high Z
The difference is already substantial
at MI=1.5 where the BCs can still
be trusted (Te ~ 4500)
The comparison to Saviane’s lines
Seem to favour Teramo at high Z,
but the models do not bend
enough at the bright end.
June 2005
Lectures on Stellar Populations
Deriving distance from RGB Tip
The RGB Tip is an effective distance indicator in the I band and at low Zs
The theoretical location depends on the bolometric magnitude and on
The BC in the I band.
There is a trend of Padova models
to yield relatively faint TRGB at
all metallicities.
Observations are not decisive,
But undersampling at TRGB should
lead to systematically faint
observed TRGB.
June 2005
Lectures on Stellar Populations
Magnitude location of the HB
The HB luminosity can be used as distance indicator as well as to derive
Ages of GCs, from the difference between the HB and the TO luminosity
(dependence on Z is crucial for this).
The models show substantial discrepancies,
again with Padova models fainter than
Teramo.
Observations are very discrepant as well;
major difficulties stem from
• the correction for luminosity evolution on the
Horizontal Branch;
• the necessity to trace the ZAHB to the same
Teff point in both observations and models.
June 2005
Lectures on Stellar Populations
Summary
• The TO magnitude at given age of the stellar population seems
independent of the set of tracks , except for obvious systematics with
input physics (but Teramo models need further investigation)
this feature can be safely used for age-dating;
• The TO temperatures, and in general the shape of the isochrones, seems
more uncertain, as they differ in different sets;
• The colors of RGB stars and their dependence on metallicity are very
uncertain; the derivation of Z and Z distribution from RGB stars needs
a careful evaluation on systematic error;
• The magnitude level of the ZAHB and its trend with Z show a substantial
discrepancy in the various sets of models AND in the various observational
data sets. This is a major caveat for the distance and age determinations
based on the level of HB stars. A theoretical error of about 0.2 is also to
be associated to the distance determination from the TRGB.
June 2005
Lectures on Stellar Populations