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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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’
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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)
Lectures on Stellar Populations
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 )()(
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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)
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
TP AGB Phase: empiricalj
bol
j FBL
L)(1075.9 10
Maraston 1998 Marigo e Girardi 2001
Lectures on Stellar Populations
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
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
Lectures on Stellar Populations
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
Lectures on Stellar Populations
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.