Carina: Dwarf Spheroidal

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


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Carina: Dwarf Spheroidal

Monelli et al. 2004


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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


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NGC 1705 – A Dwarf Blue Galaxy

observations

interpretation

Annibali et al. 2003


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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


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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


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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


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RGB evolution

RGB Bump

0.8 Mo

2 Mo

100Ro

10 Ro

Back to HRD


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RGB : bump and LFBack to HRD

1.2 Mo

1 Mo


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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


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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


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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


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PMS LF

RGB

HB

AGB

Bump

Clump

Bump

Bump

Clump


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First Pulse and TAGB

TAGB

Ist Pulse

TRGB


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Massive Stars

Chiosi and Maeder 1986

Evolution affected by MASS LOSS OVERSHOOTING


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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


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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


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Evolutionary Lifetimes

tot

MS

overshooting

RGB phase transition

rgb

He burning


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RGB Luminosities

Base

TIP


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Helium Burning and beyond

Ist Pulse

He burn L-band

RGB trans


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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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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


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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


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



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.



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



Effect of gravity

Gravity effects are very

Important for very hot

And very cool stars

A0

B0

B5

K5

M2

M5



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



Bolometric Corrections: Empirical

Hottest and Coolest stars

are 3-4 mags fainter in V

than in Bolometric

Gravity dependence can

amount to 0.5mags



Model Atmospheres:Kurucz Grid revised by Castelli

Models Empirical



Model Atmospheres:dependence on gravity

Models Empirical



Model Atmospheres:dependence on

Metallicity

Blanketing

Molecules



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])



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



Colors from Model Atmospheres

Origlia and Leitherer 1998: Bessel, Castelli and Pletz models through Ground Based Filters



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:



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)



M&M: attach empirical calibrations

Montegriffo et al. (1998) traslated

Go back



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



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



Dwarfs

Giants

K

NM



GiantsDwarfs

Dwarfs



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



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



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



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



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



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



Converted Tracks: B and V



Converted Tracks: V and I



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.



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.



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



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.



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.



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.



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

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Dnj,3

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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


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


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


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


Eqs

Dnj,3

plots

CSPsFCT

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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


Eqs

Dnj,3

plots

CSPsFCT

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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:


Eqs

Dnj,3

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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 )(


Eqs

Dnj,3

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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


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CSPsFCT

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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


Eqs

Dnj,3

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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


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


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


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


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


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plots

CSPsFCT

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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


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


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


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


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


Eqs

Dnj,3

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CSPsFCT

Eqs

Isocs

Mixture of Pulsators:fundamental & first over-tone


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


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


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..


Interpolation between tracks: lifetimes


Interpolation between Tracks: L and Teff of low mass stars


Interpolation between Tracks:L and Teff of intermediate mass stars


Photometric Error: Completeness

NGC 1705(Tosi et al. 2001)

Completeness levels:0.95 % thick0.75 % thin0.50 % thick0.25% thin


Photometric errors: σDAO and Δm


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


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


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


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


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


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


•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


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.”


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


• 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


Simulation


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.

Documents

Carina: Dwarf Spheroidal