hrd dots he b band he b band life time rgb lum june 2005lectures on stellar populations the stellar...
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June 2005 Lectures on Stellar Populations
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THE STELLAR CONTENT OF GALAXIES: THE STELLAR CONTENT OF GALAXIES: RESOLVED STELLAR POPULATIONSRESOLVED STELLAR POPULATIONS
II. Theoretical foundations. Theoretical foundations
Laura Greggio - OAPdLaura Greggio - OAPd
Ciclo di Lezioni focalizzato sul problema della ricostruzione della Storia di Formazione Stellare
dall’analisi dellla distribuzione delle stelle sul diagramma Colore-Magnitudine
June 2005 Lectures on Stellar Populations
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RGB
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Carina: Dwarf Spheroidal
Monelli et al. 2004
June 2005 Lectures on Stellar Populations
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time
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HRDLarge Magellanic Cloud
Smecker-Hane et al. 2002
DISK FIELD BAR FIELD
Recent enhancement (from 0.1 Gyr ago)
Old SF (from 10-3.0 Gyr ago)
Enhancement at 3.5 Gyr ago
June 2005 Lectures on Stellar Populations
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NGC 1705 – A Dwarf Blue Galaxy
observations
interpretation
Annibali et al. 2003
June 2005 Lectures on Stellar Populations
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Simulations:
ColorCodingReflects AGE(Myr):
<10Myr10↔6060↔1000 > 1000
SFR constant from 10 Myr to 2 Gyr ago
SFR constant from now to 1 Gyr ago
June 2005 Lectures on Stellar Populations
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Outline of the Course:
• Summary of Stellar EvolutionReview of general properties of stellar tracks, which determine theappearance of the HRD and its systematics.
• Bolometric Corrections and ColorsHow we transform from the theoretical (Log L, Log Teff) plane to theobservational (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 ExamplesVarious technicalities, including the treatment of photometric errors
June 2005 Lectures on Stellar Populations
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Evolutionary Tracks
Padova 94 set
Z=Zo Y=0.28
1MO
2.5 MO
2.5 MO
5 MO
20 MO
1 MO
100 MO
PAGB0.6 MO
2.5 MO
5 MO
To WD
ZAHB
ZAMS
RGB
PN
June 2005 Lectures on Stellar Populations
HRD
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RGB
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RGB evolution
RGB Bump
0.8 Mo
2 Mo
100Ro
10 Ro
Back to HRD
June 2005 Lectures on Stellar Populations
HRD
dots
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Life
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RGB : bump and LFBack to HRD
1.2 Mo
1 Mo
June 2005 Lectures on Stellar Populations
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Flash and After
M tr
RGB tip
RGB base
RGB tip
10 Ro1 Ro
P-EAGB
100 Ro
0.030.07
0.12
Back to HRD
June 2005 Lectures on Stellar Populations
HRD
dots
RGB
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Life
time
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Clump and LoopsBack to HRD
TRGB
ZAHB
2.2 Mo
9 Mo
4
7
6
5
3
15
10 Ro
Age indicator
Distan
ce
ind Lmax,He
Lmin,He
June 2005 Lectures on Stellar Populations
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AGB Bump
2.2 Mo
5 Mo
4 Mo
3 Mo
1 Mo with cost=-1
1.5 Mo with cost=-0.5
BUMP
BUMP
RGB
RGB
June 2005 Lectures on Stellar Populations
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PMS LF
RGB
HB
AGB
Bump
Clump
Bump
Bump
Clump
June 2005 Lectures on Stellar Populations
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First Pulse and TAGB
TAGB
Ist Pulse
TRGB
June 2005 Lectures on Stellar Populations
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Massive Stars
Chiosi and Maeder 1986
Evolution affected by MASS LOSS OVERSHOOTING
June 2005 Lectures on Stellar Populations
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Where the Stars are
WR
C stars
Miras
Clump
Ceph
HB
RRLyrWD
BSG
RSG
Back to HRD
Dots are equally spaced in
evol
There are 1000 dots alongeach track
June 2005 Lectures on Stellar Populations
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Dependence on Metallicity
30 Mo
15 Mo
5 Mo
3 Mo
0.9 Mo
Clumps
0.5 Mo
0.55 Mo
0.6 Mo
AGB Manque’
Post E-AGBClumps
June 2005 Lectures on Stellar Populations
HRD
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RGB
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Evolutionary Lifetimes
tot
MS
overshooting
RGB phase transition
rgb
He burning
June 2005 Lectures on Stellar Populations
HRD
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RGB
Lum
Life
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RGB Luminosities
Base
TIP
June 2005 Lectures on Stellar Populations
HRD
dots
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Life
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Helium Burning and beyond
Ist Pulse
He burn L-band
RGB trans
June 2005 Lectures on Stellar Populations
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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
June 2005 Lectures on Stellar Populations
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HRDUncertainties and wish list
Core Convection: affects star’s 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 ..
Mixing Length, rotation, diffusion, meridional circulation, nuclear reactions…
Separate dependence on Y and Z is important
Opacity: affects MS width occurrence and extension of loops Blue to Red ratio
June 2005 Lectures on Stellar Populations
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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
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Bolometric Correctionsand Colors
We do not observe Bolometric, we observe through filters:
oioi
ii M
L
LLogM ,
,
5.2
0
dSLL ii
system throughput
kL
LLogMMBC
iiboli
5.2 k
F
FLog
i
5.2
depends on Teff, gravity and Z
depends on .... stellar radius
ijjiBCBCCol
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Average of Observed Stellar Spectra:Dwarfs
O 50000 3.5e+14
A 10000 5.7e+11
G 6000 7.3e+10
M 3500 8.5e+09
SpT T(K) F c.g.s.
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Dwarfs SED & Filters
IVB
U
Cool stars detected in Red
Hot stars detected in Blue
BC strongly depends on SpT
COLORS:
kL
LLogMM
2
121 5.2
are Temperature Indicators
Cool stars are Red
Hot stars are Blue
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Effect of gravity
Gravity effects are very
Important for very hot
And very cool stars
A0
B0
B5
K5
M2
M5
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
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
Def BCPTracksCalibCol emp
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
Def BCPTracksCalibCol emp
Model Atmospheres:Kurucz Grid revised by Castelli
Models Empirical
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Model Atmospheres:dependence on gravity
Models Empirical
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Model Atmospheres:dependence on
Metallicity
Blanketing
Molecules
June 2005 Lectures on Stellar Populations
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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
Def BCPTracksCalibCol emp
07.0
5.2
,,
oVobolVo
Vo
oVo
MMBC
kF
FLogBC
0
5.2,2
,1
Vega
Vega
VegaVega
Col
kF
FLogCol
Balmer Jump
Go Back
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Colors from Model Atmospheres
Origlia and Leitherer 1998: Bessel, Castelli and Pletz models through Ground Based Filters
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
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
Def BCPTracksCalibCol emp
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
Def BCPTracksCalibCol emp
M&M: attach empirical calibrations
Montegriffo et al. (1998) traslated
Go back
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
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
Def BCPTracksCalibCol emp
Hot Dwarfs
A-K Dwarfs
GKM Giants
The models are shown as curves
The data are shown as points
The ptype encodes the literature source
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Dwarfs
Giants
K
NM
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
GiantsDwarfs
Dwarfs
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
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
Def BCPTracksCalibCol emp
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 calibrationIn terms of Z which is consistent with both color –temperatureRelations AND GCs ridge lines (with existing isochrones)”
Westera et al. 2002
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
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 Librariestake a sample of well observed stars with known parameters Log Te, Log g, [Fe/H]
and derive their spectra
STELIB – Le Borgne et al. 2003249 spectra between 3200 and 9500 A, sp.res. ~ 3 A
INDO-US – Valdes et al. 2004 885 spectra between 3460 and 9464 A+ 400 with smaller wavelength rangesp. res. ~ 1 A
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Libraries with high Spectral resolution
THEORETICAL MODELSUsually 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 ASpecial care to describe non-LTE and sphericity effects
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Martins et al. 2005
30262 4.18 0.02
13622 3.80 0.05
7031 4.04 0.01
4540 0.88 0.02
3700 1.3 0.01
3540 0 0.02
Check versus STELIB stars
Check versus INDO-US stars
3910 1.6 0.01
300004.50.02
140004.50.02
35001.00.01
45000.00.01
70004.00.02
40001.00.02
35000.00.02
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Other Models:
Bertone et al. : 2500 spectra with resolution of ~ 0.3 A UV grid Optical gridbetween 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
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
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
Def BCPTracksCalibCol emp
Converted Tracks: B and V
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Converted Tracks: V and I
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
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
Def BCPTracksCalibCol emp
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
Def BCPTracksCalibCol emp
Age-dating from Turn-off Magnitude
In general the turn-off magnitudeat given age agrees
Teramo models fit the turn offMagnitude with older ages(at intermediate ages)
Notice some difference in isochrone shapes , and SGBfor old isochrones
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Deriving metallicity from RGB
The RGBs can be very differentespecially at high Z
The difference is already substantialat MI=1.5 where the BCs can stillbe trusted (Te ~ 4500)
The comparison to Saviane’s linesSeem to favour Teramo at high Z,but the models do not bendenough at the bright end.
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Deriving distance from RGB Tip
The RGB Tip is an effective distance indicator in the I band and at low ZsThe theoretical location depends on the bolometric magnitude and onThe BC in the I band.
There is a trend of Padova models to yield relatively faint TRGB atall metallicities.
Observations are not decisive,But undersampling at TRGB shouldlead to systematically faint observed TRGB.
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Magnitude location of the HB
The HB luminosity can be used as distance indicator as well as to deriveAges 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 thanTeramo.
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 sameTeff point in both observations and models.
June 2005 Lectures on Stellar Populations
Def BCPTracksCalibCol emp
Summary
• The TO magnitude at given age of the stellar population seems independent of the set of tracks , except for obvious systematics withinput 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.
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
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 ΔN and M(CSP)
Ultimately: )( jj ageMN
)( jSF aget )(
)(j
SFj aget
MageSFR
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Isochrones on the HRD
4 Myr
40 Myr
0.2 Gyr
1 Gyr
15 Gyr
Theoretical Isochrones
With ages from
4 Myr to 15 Gyr
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Mass-Luminosity relation along isochrones
RGB mass loss
10 Myr
100 Myr
500 Myr
ij
ij
ij
ij
m
m
m
m
iij dmmAdmmn,1
,
1,
,
)(,
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).
120
6.0
6.0,)1( SSP
mii MdmmA
Ai describes the size of the StellarPopulation on the isochrone (SSP)
SSPmii MfA 6.0,
3.12519.02
368461.06.2
250347.035.2
% 1.06.01.0extrff
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
LF on the MS
ijijSSPiij mmMfn ,,,
Consider a continuous Star Formation Rate ψ(t): the contribution toΔnj from the ages between τ and τ+dτ is proportional to ψ(τ)dτ, andSumming up all the relevant contributions we get:
The mass and mass range contributing to the counts in the j-th bin dependon 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.
})({)(
0
jj
j
j mmdfn
maximum age contributing to j-th bin
)()(0 jLogL
mmf
LogL
nj
jj
j
IMF M-L
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Color Function on the MS
The CF on the MS is a bettertracer of the SFH
Young populations have more blue stars
Typical color on the MS depends on age
Gallart, Zoccali and Aparicio 2005
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Post MS phases
2
1
2,15.12,1 )()(m
m
mmdmmn
)( 5.12,1
1
2,1
5.1
mtdm
dtm
m
ev
jjTOTOPMSj tbtmmn )()(
)()(
)()(
5.1
5.1
5.1
TOevev
TO
ev
m
ev
TO
mtmt
dm
dt
dm
dt
mm
approximations:valid for PMS phases
)(b is the Stellar Evolutionary Flux:# of leaving the MS per unit time
mTO
m2
m1
j is the considered PMS evolutionaryphase
Consider an SSP:
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Fuel Consumption Theorem( Renzini 1981)
MS PMSj
PMSjj
SSPPMS
SSPMS
SSPT nLdmmLmLLL ** )()(
PMSj
jjPMSj PMSj
jPMSjj FbktLbnL )()( **
Hej
Hjj mmF 1.0
)()(1075.9)( 10* PMS
MS
SSPT FbdmmLmAL
Is the fuel burnt in the j-th PMS phase
if F,L in solar unitsand b in #/yr
Am
TL
bB
)()(
The Specific Evolutionary Flux dependsweakly on the age of the SSP and on the IMF
This can be used for:•Planning observations•Evaluate crowding effects•Tests of Evolution theory
jTPMSj tBLn )(
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Test of FCT on M3(Renzini and Fusi Pecci, 1988, ARAA 26, 199)
jTj FBLL )(1075.9 10
jTSSPj tLBn )(
oT LL 30000 111015.2)( B
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Application to the SFH problem
jj tbn )( TOTO mmAb )()(
120
6.0
1)( dmmAM SSP
Start from:
fMA SSP )(
SSPj
SSPj
SSPj nMtMn
Characterize SSP by its
Mass in m>0.6:
Get:
TOTO mmf 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
SSPjn is the Specific Production of j type Stars
# of j stars from SSP with unitary Mass
function of IMF, Age, Metallicity
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Synthetic Tracksinterpolated within Padova 94-Z=0.004
)(, gridbaseRGB m
generated a fine grid
of synthetic tracks with
masses of specific
in order to finely investigate on the behaviour of
)( jn
at fixed Z=0.004
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
The Specific Production of Post-MS Stars of SSPs
SSP
jj
SSPj M
ntn
Number of Stars
produced by a
1000 Mo SSP of
age τ
TOTO mmf
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
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
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Composite Stellar Populations: YOUNG
Max
dnMN SSPjj
min
)()(
jj nMN
M
Md
dj
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
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Young CSP: an example
MM
)]M([)()M( d
dnMN
jj nMN
07.2M237.07
73
10
02.110
n
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Blue Helium Burners
SFH at Young ages is best
Sampled by the Blue Helium
Burners.
Get detailed SFH up
to 0.3 Gyr ago
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Composite Stellar Populations : OLD
Max
dnMN SSPjj
min
)()(
A given Mag bin now spans a wide age range:
We get integrated information
Consider:
M
SSPj
SSPj
CSPj n
dM
dnM
M
NMax
Max
min
min
)(
)()(
The Specific Production
of j-type stars from the CSP
what we count
toolwhat we get
Look at the Specific Production of CSPs under different SFH
In specific magnitude bins
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Specific Production of CSP: bright AGB stars
CSPjn 3, number of bright AGB stars
from a 1000 Mo CSP
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Specific Production of CSP: Carbon starsMarigo, Girardi, Chiosi 2003
2MASS data of LMC C stars
Marigo and Girardi 2001: Opacity independent
of C abundance in the envelope
Marigo 2002: Opacity increases with
increasing C abundance in the envelope
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Specific Production of CSP: AGB stars
Marigo, Girardi, Chiosi 2003
selected from 2MASS data of LMC
Simulation: foreground contamination
before Ist pulse and massive He burners
TPAGB: Oxygen rich Carbon rich
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Mixture of Pulsators:fundamental & first over-tone
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Specific Production of CSP on bright RGB
CSPjn 3,
)101(
)10(
CSP
CSP
M
Mf
number of stars in the 2 upper I-mags
of the RGB from a 1000 Mo CSP
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
Specific Production of CSP of He burning Stars at Clump Mags
CSPjn 3,
)101(
)10(
CSP
CSP
M
Mf
number of Stars at Clump Magnitudes
from a 1000 Mo CSP
Lectures on Stellar Populations Dnj,3
Eqs
Dnj,3
plots
CSPsFCT
Eqs
Isocs
What have we learnt
When running the simulations we should remember the followingrules and check if the output numbers verify the fundamental relationsbetween 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
Lectures on Stellar PopulationsJune 2005
The Simulator
Random Extraction of Mass-Age pair
(AT FIXED METALLICITY)
Place Synthetic Star on HRD
Convert (L,Teff) into (Mag,Col)
Apply Photometric Error
Test to STOP
y
y
r
r nn
dyyndrrn )()(
r random in 0↔1
x
n
n
y
y
y
y
dyyn
dyyn
r
)(
)(
EXITYESNO Notify: Astrated Mass,
# of WDs,BHs,TPAGB..
Lectures on Stellar PopulationsJune 2005
Interpolation between tracks: lifetimes
Lectures on Stellar PopulationsJune 2005
Interpolation between Tracks: L and Teff of low mass stars
Lectures on Stellar PopulationsJune 2005
Interpolation between Tracks:L and Teff of intermediate mass stars
Lectures on Stellar PopulationsJune 2005
Photometric Error: Completeness
NGC 1705(Tosi et al. 2001)
Completeness levels:0.95 % thick0.75 % thin0.50 % thick0.25% thin
Lectures on Stellar PopulationsJune 2005
Photometric errors: σDAO and Δm
Lectures on Stellar PopulationsJune 2005
Crowding
..erjj Sn
2jn
2''..
5
..
..2
104.2 Mpcsq
erjjerj
erj dSnNn
Nncrow
# of stars j in one resolution element (r.e.)
jS
2.. )5.0( er
where Sj is the srf density of j stars and σr.e. is the area intercepted
Probability of j+j blend is
Degree of Crowding in the frameWith 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 crow=0.1 at 17,10 and 5.6 Mpc for the 3 kinds resp.
In Phoenix (DSp) we detect >4200 RC stars/Kpc2: with OmegaCAM crow is 0.1 already at 2 Mpc
Lectures on Stellar PopulationsJune 2005
Another way to put it:(Renzini 1998)
..2
erj Nn
jj tLBn )(
..
222
..2
.. ))((er
framejerjer N
LtBNtLB
# of blends in my frame is
# of j stars in my frame (if SSP) is where L is the lum sampledby the r.e.
# of blends in my frame becomes
# of blends increases with the square of the Luminosity and decreaseswith the number of resolution elements
Lectures on Stellar PopulationsJune 2005
Pixels and Frames: Example
)mod(4.010 BoBB MABL 11102.2)15( GyrBBbol LL 5.2
MyrtLPV 25.0 MyrtRGBT 5
(2)(3)
(1)
(4)
(1) A.O.: σ(r.e.) ≈ 0.14x0.14 ….. nRGT ≈ 8 in one r.e.(2) HST: σ(r.e.) ≈ 0.06x0.06…..nRGTxnRGT≈2e-04 … N(r.e.)≈1e+05(3) …………………………………………≈ 2e-05…..(4) GB : σ(r.e.)≈0.3 sq.arcsec….n RGTxnRGT≈0.044…N(r.e.)≈1.3e+04
Lectures on Stellar PopulationsJune 2005
How Robust is the Result?The statistical estimator does not account for systematic errors
Theoretical Transformed Errors Applied
EACH STEP BRINGS ALONG ITS OWN UNCERTAINTIESTHE SYSTEMATIC ERROR IS DIFFUCULT TO GAUGE
Lectures on Stellar PopulationsJune 2005
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 τ ≈0.1 GyThis is valid for all the PMS boxes, with different proportionality factors
)( 0 starsboxj MN
Perform the exercise for all isochrones
)(starsM
Lectures on Stellar PopulationsJune 2005
Methods for Solution: Blind Fit
used 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 PURE MODEL PARTIAL CMD
Ages: 1112 Gyr[M/H]:-1.75 -1.65
Lectures on Stellar PopulationsJune 2005
•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
i i
iiii
ii
n
i i
i
m
nnnmPLRfit
mnn
mPLR
i
)ln(2ln2
)exp(
•Minimize fit -- get best fit + a quantitative measure of the quality of the fit
Lectures on Stellar PopulationsJune 2005
My prejudice:
•The model CMDs may NOT contain the solution
If wrong Z is used, the blind method will give a solution,but not 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 RGB+HB was extremely successful, measuring…the SFH with nearly the sameaccuracy as the fit to the entireCMD.”
Lectures on Stellar PopulationsJune 2005
Methods for Solution: Tailored Fit
Count the stars in the diagnostic boxes:Their number scales with the mass inStars in the corresponding age range
Younger than 10 Myr
Between 10 and 50 Myr
Between 50 Myr and 1 Gyr
Construct partial CMD constrained to reproducethe star’s counts within the boxes.The partial CMDs are coherently populated alsowith stars outside the boxes
Lectures on Stellar PopulationsJune 2005
• Compare the total simulation to the data
Use your knowledge ofStellar evolution to improvethe fit AND decide where you cannot improve, andwhere you need a perfectmatch
The two methods shouldbe viewed as complementary
Lectures on Stellar PopulationsJune 2005
Simulation
Lectures on Stellar PopulationsJune 2005
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 star’s 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; it’s unfit for automatic use; the solution reflects the prejudice of the modeler; the quality of the fit is judged only in a rough way.