THE STELLAR CONTENT OF GALAXIES: RESOLVED STELLAR POPULATIONS I. Theoretical foundations Laura Greggio - OAPd

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THE STELLAR CONTENT OF GALAXIES RESOLVED
STELLAR POPULATIONSI. Theoretical
foundationsLaura Greggio - OAPd

• Ciclo di Lezioni focalizzato sul problema della
  ricostruzione della Storia di Formazione Stellare
  dallanalisi dellla distribuzione delle stelle
  sul diagramma Colore-Magnitudine

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Carina Dwarf Spheroidal
Monelli et al. 2004
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Large Magellanic Cloud
Smecker-Hane et al. 2002
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NGC 1705 A Dwarf Blue Galaxy
observations
interpretation
Annibali et al. 2003
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Simulations
Color Coding Reflects AGE(Myr) lt10Myr 10?60 60?
1000 gt 1000
SFR constant from 10 Myr to 2 Gyr ago
SFR constant from now to 1 Gyr ago
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Outline of the Course

• Summary of Stellar Evolution
• Review of general properties of stellar tracks,
  which determine the
• appearance of the HRD and its systematics.
• Bolometric Corrections and Colors
• How we transform from the theoretical (Log L, Log
  Teff) plane to the
• observational (Mag,Color)
• Basic Relations between Stellar Counts in
  Selected Regions of the CMD and the SF History
• Illustrate potentials and limitations of the
  synthetic CMD method
• The Simulator and Some Examples
• Various technicalities, including the treatment
  of photometric errors

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Evolutionary Tracks

• Padova 94 set
• ZZo Y0.28

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RGB evolution
Back to HRD
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RGB bump and LF
Back to HRD
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Flash and After
Back to HRD
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Clump and Loops
Back to HRD
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AGB Bump
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PMS LFRGBHBAGB
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First Pulse and TAGB
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Massive Stars
Evolution affected by MASS LOSS
OVERSHOOTING
Chiosi and Maeder 1986
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Where the Stars are
Back to HRD
Dots are equally spaced in
There are 1000 dots along each track
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Dependence on Metallicity
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Evolutionary Lifetimes
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RGB Luminosities
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Helium Burning and beyond
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Isochrones Girardi et al. 2002

• As Z increases
• isochrones get
• fainter and redder
• loops get shorter
• WR stars are more
• easily produced

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Uncertainties and wish list
Core Convection affects
stars luminosity
H and He lifetimes
shape of tracks around Mhook
first H shell burning and runway for
intermediate mass stars
MS width
location of RGB bump
values of Mtr and Mup
ratios N(HB)/N(AGB)
loops extension

Mass Loss on the RGB affects
Temperature extension of HB on the AGB
affects value of Mup and TAGB for massive stars
affects surface abundances, upper limit of Red
SGs, productions of WR ..
Opacity affects MS width
occurrence and extension of loops
Blue to Red ratio
Mixing Length, rotation, diffusion, meridional
circulation, nuclear reactions Separate
dependence on Y and Z is important
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What have we learnt

• To place on the HRD whatever mass at whatever age
  we want to pay attention to
• Mtr Mup Mhook lifetimes and tracks
  discontinuities
• Place correctly RGB Tip (as distance indicator)
• Describe accurately the evolution in core He
  burning close to RGB transition (Lum extension
  during evolution)
• Allow spread of envelope masses for HB stars
• Describe extension of the loops, location of BSG,
  Back-to-the-Blue evolution of high mass stars
• .
• AND if we include a metallicity
  spread
• Correctly describe all these systematics as a
  function of Metallicity

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Bolometric Correctionsand Colors

• We do not observe Bolometric, we observe through
  filters

depends on .... stellar radius
system throughput
depends on Teff, gravity and Z
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Average of Observed Stellar SpectraDwarfs
SpT T(K) F c.g.s.
O 50000 3.5e14 A 10000 5.7e11 G 6000 7.3e10 M 3500 8.5e09
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Dwarfs SED Filters
BC strongly depends on SpT
Cool stars detected in Red Hot stars detected in
Blue
COLORS
are Temperature Indicators
Cool stars are Red Hot stars are Blue
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Effect of gravity
Gravity effects are very Important for very hot
And very cool stars
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COLORS Empirical
B-V colors are good Teff indicators for late A,
F, G and early K stars For Hot stars SpT is
preferred
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Bolometric Corrections Empirical
Hottest and Coolest stars are 3-4 mags fainter in
V than in Bolometric Gravity dependence
can amount to 0.5mags
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Model AtmospheresKurucz Grid revised by
Castelli
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Model Atmospheresdependence on gravity
Models
Empirical
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Model Atmospheresdependence on Metallicity
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Model AtmospheresCalibration

• 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)
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Go Back
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Colors from Model Atmospheres
Origlia and Leitherer 1998 Bessel, Castelli and
Pletz models through Ground Based Filters
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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
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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)
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MM attach empirical calibrations
Go back
Montegriffo et al. (1998) traslated
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Bessel, Castelli Pletz (1998, AA 333, 231)

• Compare Kuruczs 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
• There is a general good agreement for most of the
  parameter space
• B-V predicted too blue for late type stars,
  likely due to missing atomic and molecular
  opacity
• NMARCS to be preferred to ATLAS9 below 4000 K

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The models are shown as curves The data are shown
as points The ptype encodes the literature source
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Dwarfs
Giants
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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

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Lejeune Models Z dependenceCheck 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
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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
INDO-US Valdes et al. 2004 885 spectra
between 3460 and 9464 A 400 with smaller
wavelength range sp. res. 1 A
STELIB Le Borgne et al. 2003 249 spectra
between 3200 and 9500 A, sp.res. 3 A
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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
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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/Fe0,0.4
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/Fe0,0.4
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Converted Tracks B and V
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Converted Tracks V and I
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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.

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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.

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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
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Deriving metallicity from RGB
The RGBs can be very different especially at high
Z The difference is already substantial at
MI1.5 where the BCs can still be trusted (Te
4500) The comparison to Savianes lines Seem to
favour Teramo at high Z, but the models do not
bend enough at the bright end.
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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. Obser
vations are not decisive, But undersampling at
TRGB should lead to systematically faint
observed TRGB.
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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.

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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.

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Basic Relations between StellarCounts on the CMD
and SFH

• On the potentials and limitations of the
  Synthetic CMDs method

• We will go through
• SSPs isochrones, MS and PMS phases,
  FCT,Number-Mass connection
• CSPs SSPs with an age distribution, to elucidate
  relations between ?N and M(CSP)

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Isochrones on the HRD
Theoretical Isochrones With ages from 4 Myr to
15 Gyr
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Mass-Luminosity relation along isochrones
In the j-th luminosity bin each i-th isochrone
contributes
Lower and upper integration limits depend on the
isochrone, i.e. on age (and Z).
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LF on the MS
Consider a continuous Star Formation Rate ?(t)
the contribution to ?nj from the ages between t
and tdt is proportional to ?(t)dt, and Summing
up all the relevant contributions we get
The mass and mass range contributing to the
counts in the j-th bin depend on the age. If we
neglect this dependence (on the MS we may)
The LF on the MS is proportional to the IMF
through the M-L relation AND to the SFR over the
relevant age range.
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Color Function on the MS
Gallart, Zoccali and Aparicio 2005
The CF on the MS is a better tracer of the SFH
Young populations have more blue
stars Typical color on the MS depends on age
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Post MS phases
Consider an SSP
is the Stellar Evolutionary Flux of
leaving the MS per unit time
is the considered PMS evolutionary phase
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Fuel Consumption Theorem( Renzini 1981)
if F,L in solar units and b in /yr
Is the fuel burnt in the j-th PMS phase

• The Specific Evolutionary Flux depends
• weakly on the age of the SSP and on the IMF
• This can be used for
• Planning observations
• Evaluate crowding effects
• Tests of Evolution theory

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Test of FCT on M3(Renzini and Fusi Pecci, 1988,
ARAA 26, 199)
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Application to the SFH problem
Start from
Characterize SSP by its Mass in mgt0.6
Get
Where
is the Specific Evolutionary Flux of stars
leaving the MS per unit time,per unit MASS of the
SSP function of IMF, Age, Metallicity
is the Specific Production of j type Stars of j
stars from SSP with unitary Mass function of IMF,
Age, Metallicity
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Synthetic Tracksinterpolated within Padova
94-Z0.004
generated a fine grid of synthetic tracks with
masses of specific
in order to finely investigate on the behaviour
of
at fixed Z0.004
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The Specific Production of Post-MS Stars of SSPs
Number of Stars produced by a 1000 Mo SSP of age
t
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TauMag of SSPs
Magnitude Location of Red stars in different
phases as the SSP ages Core Helium
Burners First RG ascent Second RG ascent (up to
Ist pulse)
RGB phase transition
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Composite Stellar Populations YOUNG
In general for a CSP, the number of stars in
the j-th magnitude bin is
where the integration spans the ages
contributing to the j-th bin
If the bin intercepts stars from a small age
range
where

• This is the case for Young CSPs ( 100 Myrs) for
  which
• The number of stars in the j-th mag bin speaks
  for the power of the SF episode at a specific age
• The LF reflects the SFR as a function of age

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Young CSP an example
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Blue Helium Burners
SFH at Young ages is best Sampled by the Blue
Helium Burners. Get detailed SFH up to 0.3 Gyr
ago
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Composite Stellar Populations OLD
A given Mag bin now spans a wide age range We
get integrated information
Consider
what we count
The Specific Production of j-type stars from the
CSP
tool
what we get
Look at the Specific Production of CSPs under
different SFH In specific magnitude bins
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Specific Production of CSP bright AGB stars
number of bright AGB stars from a 1000 Mo CSP
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Specific Production of CSP Carbon stars
Marigo, Girardi, Chiosi 2003
Marigo and Girardi 2001 Opacity independent of
C abundance in the envelope
C stars
2MASS data of LMC
Marigo 2002 Opacity increases with increasing
C abundance in the envelope
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Specific Production of CSP AGB stars
Simulation foreground contamination before Ist
pulse and massive He burners TPAGB Oxygen rich
Carbon rich
selected from 2MASS data of LMC
Marigo, Girardi, Chiosi 2003
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Mixture of Pulsatorsfundamental first
over-tone
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Specific Production of CSP on bright RGB
number of stars in the 2 upper I-mags of the RGB
from a 1000 Mo CSP
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Specific Production of CSP of He burning Stars at
Clump Mags
number of Stars at Clump Magnitudes from a 1000
Mo CSP
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What have we learnt

• When running the simulations we should remember
  the following
• rules and check if the output numbers verify the
  fundamental relations
• between stellar counts and extracted Total Mass
  of the CSP
• The MS LF is sensitive to both the SFR and IMF
• For the PMS phases there exists a simple and
  direct relation between the stellar counts in
  specific regions of the CMD and the Mass of the
  Stellar Population that produced them
• The bright portion of the LF of PMS stars allows
  to recover the SFH with a fair degree of detail,
  up to 300 Myr (both blue and red)
• For older ages, it is possible to derive with
  some confidence the total mass of the underlying
  CSP
• On the average there is about 1 bright E-AGB star
  every 20000 Mo of CSP
• 
  1 upper RGB star every 2000 Mo of CSP
• 
  1 He burning star every 200 Mo of CSP
• The determination of the SFR is prone to the
  non-easy gauge of the age range of the counted
  stars

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The Simulator
(AT FIXED METALLICITY)
Random Extraction of Mass-Age pair
Place Synthetic Star on HRD
Convert (L,Teff) into (Mag,Col)
Apply Photometric Error
YES
NO
Notify Astrated Mass, of WDs,BHs,TPAGB..
EXIT
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Interpolation between tracks lifetimes
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Interpolation between Tracks L and Teff of low
mass stars
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Interpolation between TracksL and Teff of
intermediate mass stars
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Photometric Error Completeness
NGC 1705 (Tosi et al. 2001) Completeness
levels 0.95 thick 0.75 thin 0.50
thick 0.25 thin
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Photometric errors sDAO and ?m
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Crowding
of stars j in one resolution element (r.e.)
where Sj is the srf density of j stars and
sr.e. is the area intercepted
Probability of jj blend is
Degree of Crowding in the frame With Nr.e
resolution elements is
depends on SFH
In VII Zw 403 (BCD) we detect with HST 55 RSG,
140 bright AGB and 530 RGT(1) stars/Kpc2 Observed
with OmegaCAM we get crow0.1 at 17,10 and 5.6
Mpc for the 3 kinds resp.
In Phoenix (DSp) we detect gt4200 RC stars/Kpc2
with OmegaCAM crow is 0.1 already at 2 Mpc
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Another way to put it(Renzini 1998)
of blends in my frame is
of j stars in my frame (if SSP) is
where L is the lum sampled by the r.e.
of blends in my frame becomes
of blends increases with the square of the
Luminosity and decreases with the number of
resolution elements
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Pixels and Frames Example
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How Robust is the Result?
The statistical estimator does not account for
systematic errors
Theoretical
Transformed
Errors Applied
EACH STEP BRINGS ALONG ITS OWN UNCERTAINTIES THE
SYSTEMATIC ERROR IS DIFFUCULT TO GAUGE
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Why and How Well does the Method Work?

• Think of the composite CMD as a superposition of
  SSPs,
• each described by an isochrone

The number of stars in is proportional to
the Mass that went into stars at t 0.1 Gy This
is valid for all the PMS boxes, with different
proportionality factors
Perform the exercise for all isochrones
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Methods for Solution Blind Fitused by
Hernandez, Gilmore and Valls GabaudHarris and
Zaritsky (STARFISH)Cole Holtzman Dolphin

• Dolphin 2002, MNRAS 332,91 Review of methods
  and description of Blind fit
• Generate a grid of partial model CMD with stars
  in small ranges of ages and metallicities
• Construct Hess diagram for each partial model CMD
• Generate a grid of models by combining partial
  CMDs according to SFR(t) and Z(t)

DATA
PARTIAL CMD
PURE MODEL
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• Use a statistical estimator to judge the fit
• mi is the number of synthetic objects in bin
  i
• ni is the number of data points in bin i

• Minimize fit --? get best fit
• a quantitative measure
  of the quality of the fit

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My prejudice

• The model CMDs may NOT contain the solution

• The method requires a lot of computing
• Does this really improve the solution?
• (apart from giving a quantitative estimate
• of the quality of the fit)

Dolphin The solution with RGBHB was
extremely successful, measuring the SFH with
nearly the same accuracy as the fit to the
entire CMD.
If wrong Z is used, the blind method will give a
solution, but not THE SOLUTION
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Methods for Solution Tailored Fit

Count the stars in the diagnostic boxes Their
number scales with the mass in Stars in the
corresponding age range
Construct partial CMD constrained to
reproduce the stars counts within the boxes. The
partial CMDs are coherently populated also with
stars outside the boxes
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• Compare the total simulation to the data

Use your knowledge of Stellar evolution to
improve the fit AND decide where you cannot
improve, and where you need a perfect match
The two methods should be viewed as complementary
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Simulation
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What have we learnt

• When computing the simulations we should pay
  attention to
• The description of the details in the shape of
  the tracks, and
• the evolutionary lifetimes (use normalized
  independent variable)
• The description of photometric errors, blending
  and completeness
• (evaluate crowding conditions if there is
  more than 1 star per resolution
• element the photometry is bad crowding
  condition depends on sampled
• luminosity, size of the resolution element
  and stars magnitude)
• Different methods exist to solve for the SFH
• the BLIND FIT is statistically good, but
  does not account for systematic errors it seems
  too complicated on one hand,
• could miss the real target of measuring the
  mass in stars on the other
• the TAILORED FIT goes straight to the point
  of measuring the mass
• in stars of the various components of the
  stellar population its
• unfit for automatic use the solution
  reflects the prejudice of the modeler
• the quality of the fit is judged only in a
  rough way.