1. Lectures on Stellar Populations LUCE INTEGRATA DA POPOLAZIONI STELLARI. Fondamenti Teorici Laura Greggio - OAPd LUCE INTEGRATA DA POPOLAZIONI STELLARI. Fondamenti Teorici Laura Greggio - OAPd Proprieta’ delle popolazioni stellari rilevanti per la determinazione di Eta’,Metallicita’ e Massa di insiemi di stelle dalla loro Luce Integrata

2. Lectures on Stellar Populations Why should it work Young populations are bright Young populations are hot Metal poor populations are hot Old populations are faint Old populations are cool Metal rich populations are cool

3. Lectures on Stellar Populations Integrated Colors hold the Key Young populations are BLUE Metal poor populations are BLUE Old populations are RED Metal rich populations are RED From Colors From Magnitudes + AGE, Z MASS

4. 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 populations RGBs are mostly dependent on Z Break degeneracy by considering more ‘COLORS’

5. 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 ignition Arimoto & 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

6. Lectures on Stellar Populations SSP Bolometric Light: Isochrone Synthesis One isochrone of given (AGE,Z) is {m, L, Te} IMF: Salpeter Kroupa A is the scale factor: The total light of an SSP is directly proportional to the mass ORIGINALLYtransformed into Stars

7. Lectures on Stellar Populations MASS RETURN M(env) SSP give back to the ISM a substantial fraction of their initial mass: after 15 Gyr the fraction is 30% (Salpeter) 45% (Kroupa)

8. Lectures on Stellar Populations Stellar Mass along the Isochrone In the Post-MS phases the stellar mass is a poor variable The evolutionary mass is almost the same along the whole Post-MS portion of the isochrone

9. Lectures on Stellar Populations FCT Approximation: substitute L(m,  ) with L(m TO,t) approximations: valid for PMS phases is the Stellar Evolutionary Flux: # of leaving the MS per unit time m TO m2m2 m1m1 is the considered PMS evolutionary phase

10. Lectures on Stellar Populations Fuel Consumption Theorem b(  ) is the stellar evolutionary flux at the TO (# per year) t j is the lifetime of the PMS phase j t j L j = energy radiated in the j-th phase ~ nuclear energy released in the j-th phase  F j = [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:all evaluated @ the turn off mass instead of @ the evolutionary mass  n x N A x M o /L o x (sec in 1 yr) -1 10 -5 erg/particle 6 10 23 particles 0.5 (gr sec)/erg (3.15 10 7 ) -1

11. Lectures on Stellar Populations PMS Luminosity PMS luminosity decreases as age increases because the evolutionary flux decreases: less and less stars enter the PMS phase, in spite of the IMF @ TO (Maraston 98)

12. 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 overshooting more H burned on the MS Transitions shifted at older ages

13. Lectures on Stellar Populations L bol : dependence on IMF 1Mo SSPs in stars between 0.1 and 120 Mo For stars with m>0.5 Mo Flatter IMF yields more rapid evolution Of both the MS and the PMS luminosity

14. Lectures on Stellar Populations Contributions of phases Only at young ages does the MS provide most of the bolometric light Past 1 Gyr most of the light comes from the MS (TO) plus RGB

15. 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 Specific Evolutionary Flux (stars per year per solar Luminosity) Almost independent of age: Older than 1 Gyr it’s about 2 10 -11 stars/yr/Lo

16. Lectures on Stellar Populations TP AGB Phase The 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 Pulses These models can be used with the tracks by Girardi, and isochrones can be computed The models need specification of several parameters, among which The core mass-luminosity relation Conditions for 3rd dredge up Envelope Burning the Mass Loss Rate IpIp

17. Lectures on Stellar Populations TP AGB Phase: empirical Maraston 1998 Marigo e Girardi 2001

18. Lectures on Stellar Populations Test of FCT on M3 (Renzini and Fusi Pecci, 1988, ARAA 26, 199)

19. Lectures on Stellar Populations Test on MC Cs Data from Ferraro et al. 1995: Intermediate age clusters in the LMC Empirical luminosities Fuel consumption Increase through the RGB phase transition

20. 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

21. 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 light This applies to both the MS and the PMS contributions.