Basic Relations between Stellar Counts on the CMD and SFH

1. Ultimately: Basic Relations between StellarCounts on the CMD and SFH 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) On the potentials and limitations of the Synthetic CMDs method Lectures on Stellar Populations

2. 4 Myr 40 Myr 0.2 Gyr 1 Gyr 15 Gyr Isochrones on the HRD Theoretical Isochrones With ages from 4 Myr to 15 Gyr Lectures on Stellar Populations

3. 10 Myr Ai describes the size of the Stellar Population on the isochrone (SSP) 100 Myr 500 Myr RGB mass loss Mass-Luminosity relation along isochrones 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). Lectures on Stellar Populations

4. maximum age contributing to j-th bin IMF M-L LF on the MS Consider a continuous Star Formation Rate ψ(t): the contribution to Δnj from the ages between τ and τ+dτ is proportional to ψ(τ)dτ, and Summing up all the relevant contributions we get: The mass and mass range contributing to the counts in the j-th bin depend on 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. Lectures on Stellar Populations

5. Color Function on the MS Gallart, Zoccali and Aparicio 2005 The CF on the MS is a better tracer of the SFH Young populations have more blue stars Typical color on the MS depends on age Lectures on Stellar Populations

6. approximations: valid for PMS phases m2 m1 mTO Post MS phases Consider an SSP: is the Stellar Evolutionary Flux: # of leaving the MS per unit time is the considered PMS evolutionary phase Lectures on Stellar Populations

7. Fuel Consumption Theorem(Renzini 1981) if F,L in solar units and b in #/yr Is the fuel burnt in the j-th PMS phase The Specific Evolutionary Flux depends weakly on the age of the SSP and on the IMF This can be used for: • Planning observations • Evaluate crowding effects • Tests of Evolution theory Lectures on Stellar Populations

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

9. Application to the SFH problem Start from: Characterize SSP by its Mass in m>0.6: Get: 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 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

10. Synthetic Tracksinterpolated within Padova 94-Z=0.004 generated a fine grid of synthetic tracks with masses of specific in order to finely investigate on the behaviour of at fixed Z=0.004 Lectures on Stellar Populations

11. The Specific Production of Post-MS Stars of SSPs Number of Stars produced by a 1000 Mo SSP of age τ Lectures on Stellar Populations

12. TauMag of SSPs Magnitude Location of Red stars in different phases as the SSP ages : Core HeliumBurners First RG ascent Second RG ascent (up to Ist pulse) RGB phase transition Lectures on Stellar Populations

13. Composite Stellar Populations: YOUNG 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

14. Young CSP: an example Lectures on Stellar Populations

15. 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

16. Composite Stellar Populations : OLD A given Mag bin now spans a wide age range: We get integrated information Consider: what we count The Specific Production of j-type stars from the CSP tool what we get Look at the Specific Production of CSPs under different SFH In specific magnitude bins Lectures on Stellar Populations

17. Specific Production of CSP: bright AGB stars number of bright AGB stars from a 1000 Mo CSP Lectures on Stellar Populations

18. Specific Production of CSP: Carbon stars Marigo, Girardi, Chiosi 2003 Marigo and Girardi 2001: Opacity independent of C abundance in the envelope C stars 2MASS data of LMC Marigo 2002: Opacity increases with increasing C abundance in the envelope Lectures on Stellar Populations

19. Specific Production of CSP: AGB stars Simulation: foreground contamination before Ist pulse and massive He burners TPAGB: Oxygen rich Carbon rich selected from 2MASS data of LMC Marigo, Girardi, Chiosi 2003 Lectures on Stellar Populations

20. Specific Production of CSP on bright RGB number of stars in the 2 upper I-mags of the RGB from a 1000 Mo CSP Lectures on Stellar Populations

21. Specific Production of CSP of He burning Stars at Clump Mags number of Stars at Clump Magnitudes from a 1000 Mo CSP Lectures on Stellar Populations

22. What have we learnt When running the simulations we should remember the following rules and check if the output numbers verify the fundamental relations between 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 Populations