lectures on stellar populations luce integrata da popolazioni stellari. fondamenti teorici laura...

Lectures on Stellar Populations

LUCE INTEGRATA DA LUCE INTEGRATA DA POPOLAZIONI STELLARI.POPOLAZIONI STELLARI.

Fondamenti Teorici Fondamenti Teorici

Laura Greggio - OAPdLaura Greggio - OAPd

Proprieta’ delle popolazioni stellari rilevanti per la determinazione di Eta’ ,Metallicita’ e Massa di insiemi

di stelle dalla loro Luce Integrata


Why should it work

Young populations are bright Young populations are hotMetal poor populations are hot

Old populations are faintOld populations are coolMetal rich populations are cool


Integrated Colors hold the Key

Young populations are BLUEMetal poor populations are BLUE

Old populations are REDMetal rich populations are RED

From ColorsFrom Magnitudes +

AGE, ZAGE, ZMASSMASS


Age – Z degeneracy: a taste of it

Turn-Off region can be reproduced with either Young and Metal Rich or Old and Metal Poor populationsRGBs are mostly dependent on ZBreak degeneracy by considering more ‘COLORS’


Population Synthesis Technique

Compute integrated spectrophotometry of Stellar Systems by adding up the light of each star

Used to recover information like AGE and Z of Stellar Populations

Pioneered by Beatrice Tinsley (1980)Bruzual 1983 – tracks only up to Helium ignitionArimoto & Yoshii 1986; Guiderdoni & Rocca-Volmerange 1987 – collection of tracks from different authors

(models of Galaxy formation and evolution)Renzini & Buzzoni (1986); Buzzoni (1989) – use FCT for Post MS stages

Charlot & Bruzual (1991) - almost homogeneous set of tracks (Maeder & Meynet 1987) + updates

Worthey 1994 – schematic evolution for PMS; only populations older than 1 Gyr

Bressan, Chiosi and Fagotto 1994 – use Padova tracks + updates

Maraston 1998 – use FCT + updates

IMPORTANT IS:• Include ALL RELEVANT evolutionary phases• Parametrize the “unknown” + Nail the parameter with appropriate

observables


SSP Bolometric Light: Isochrone Synthesis

dmmmLLd

i

m

m

SSP )()(

35.2)( mAm

One isochrone of given (AGE,Z) is {m, L, Te}

IMF:Am)(

3.2

3.1

5.0

m

m

5.0

5.0

m

m

s

i

m

m

SSPMdmmm 0)(

s

i

m

m

SSP

dmAmm

MA

]/)([

0

Salpeter

Kroupa

A is the scale factor:

The total light of an SSP is directly proportional tothe mass ORIGINALLY transformed into Stars


MASS RETURN

)()( tRtdt

dM s

TO

m

m mm dmwmtmtR ))(()()(

t

t

dtt

dttM

0

0

)(

)(1

M(env)

SSP give back to the ISM a substantial fractionof their initial mass: after 15 Gyr the fraction is 30% (Salpeter) 45% (Kroupa)


Stellar Mass along the Isochrone

In the Post-MS phasesthe stellar mass is a poor variable

The evolutionary mass is almost thesame along the whole Post-MS portion of the isochrone

dmmmLLd

i

m

m

SSP )()(


FCT Approximation: substitute L(m,) with L(mTO,t)

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


Fuel Consumption Theorem

TO

i

m

m PMSjj

SSPPMS

SSPMS

SSP LndmmmLLLL )()(

jj tbn )(

TO

i

m

m PMSTOj

SSPPMS

SSPMS

SSP mFbdmmmLLLL )()(1075.9)()( 10

b() is the stellar evolutionary flux at the TO (# per year)tj is the lifetime of the PMS phase j

tj Lj = energy radiated in the j-th phase ~ nuclear energy released in the j-th phase

Fj = [m(H) + 0.1 m(He)]j

with b() in 1/yr F in solar masses L in solar luminosities

The contribution to the total luminosity of any PMS stage is proportional to the Amount of equivalent fuel burned during that stage.

Approximations: jjev Ftmm , , ),( all evaluated @ the turn off mass instead of @ the evolutionary mass

n x NA x Mo/Lo x (sec in 1 yr)-1

10-5 erg/particle 6 1023 particles 0.5 (gr sec)/erg (3.15 107)-1


PMS Luminosity

PMS luminosity decreases as age increasesbecause the evolutionary flux decreases: less and less stars enter the PMS phase, in spite of the IMF

)()(1075.9 10TO

PMSjMS mFbLL

@ TO(Maraston 98)


L(MS) and L(PMS) – dependence on overshooting

Maraston 04

•b(τ) almost insensitive on oversh.dominated by the derivative of the TO mass

•MS Luminosity is higher, PMS Luminosity is lower for tracks with overshootingmore H burned on the MS

•Transitions shifted at older ages


Lbol : dependence on IMF

)()(1075.9)()( 10TO

PMSjTOTO

m

m

mFmmdmmmLLTO

i

1Mo SSPs in stars between 0.1 and 120 Mo

For stars with m>0.5 Mo

Flatter IMF yields more rapid evolutionOf both the MS and the PMS luminosity


Contributions of phases

•Only at young ages does the MSprovide most of the bolometric light

•Past 1 Gyr most of the light comes fromthe MS (TO) plus RGB


Advantages of FCT•Fuel is a better variable in PMS phases•Fuel formulation allows us to include uncertain evolutionary stages and parametrize the effect•SSP models are easily checked

bol

jbol

j

jj

LbB

FBL

L

FbL

/)()(

)(1075.9

)(1075.9

10

10

Specific Evolutionary Flux(stars per year per solar Luminosity)

Almost independent of age:Older than 1 Gyr it’s about2 10-11 stars/yr/Lo


TP AGB PhaseThe evolution of stars through the TP AGB phase is difficult to compute;AGB Termination depends on Mass Loss

Envelope models by Marigo describe the evolution through Thermal PulsesThese models can be used with the tracks by Girardi, and isochrones can be computed

The models need specification ofseveral parameters, among which•The core mass-luminosity relation•Conditions for 3rd dredge up•Envelope Burning•the Mass Loss Rate

Ip


TP AGB Phase: empiricalj

bol

j FBL

L)(1075.9 10

Maraston 1998 Marigo e Girardi 2001


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


Test on MC CsData from Ferraro et al. 1995: Intermediate age clusters in the LMCEmpirical luminosities

Fuel consumptionIncrease through the RGB phase transition

jbol

j FBL

L)(1075.9 10


What have we learnt

• SSPs fade as they age

Mass to Light ratio is low in young, high in old systems

• The bolometric Light of an SSP is always proportional to the mass that went into stars in the Burst of SF

The mass in stars of a stellar population secularly decreases because of

the mass return

• FCT: the contribution to the bolometric luminosity of any PMS phase is proportional to the amount of fuel burned in that phase

A reasonable and useful approximation

• At ages older than about 1 Gyr most of the SSP bolometric light originates from the MS(TO) plus the RGB (by similar amounts)

HB, AGB, SGB make a smaller contribution


What have we learnt

• At ages older than about 1 Gyr the specific evolutionary flux is about 2 10-11 stars/yr/Lo, almost insensitive to Age and IMF

Useful in a number of applications , e.g. estimate of number of stars in a PMS phase from the sampled luminosity; crowding conditions of a frame from

surface brightness.• When tracks with overshooting are used: b() is unchanged, the MS

luminosity is larger, the PMS lower; various transitions are shifted at older ages

• Flatter IMFs lead to faster fading of SSP lightThis applies to both the MS and the PMS contributions.

lectures on stellar populations luce integrata da popolazioni stellari. fondamenti teorici laura...

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