1. Probing the evolution of stellar systems Andreas Zezas Harvard-Smithsonian Center for Astrophysics

2. The lives of stars : fighting against gravity Defining parameter : Mass To avoid implosion stars must generate energy from fusion reactions The stages of stars are determined by the type of fuel left: hydrogen, helium, carbon etc

3. The complicated lives of stars … but, after some time they run out of fuel White dwarf (≤8 M  ) Supernova (≥8 M  ) Neutron star (M~1.4-3.0 M  ) Black-hole (M >3.0 M  )

4. Basic tool : Photometry

7. Main Sequence Red Giant Branch Horizontal Branch

8. CMDs : Simple cases

9. The tools : Stellar Tracks ( | age, Mass, Z, stellar evolution)

10. The tools : Isochrones

13. The recipe Assume a star-formation scenario (model) Take some isochrones (calibration) Weight them by the IMF : N  M -  Mix them Simulate (include observational biases) Compare with observed CMD

14. Analogy with X-rays Isochrones  RMF Detection probability  ARF

15. The “standard method”

19. Complications Incompleteness Multiple populations Uncertainties on isochrones

20. CMDs: complications

23. CMDs: more complications Detection probability

24. Gaussian statistics (as usually…)  2 fits All stars have equal weight Complex mixture problem with several free correlated parameters Several different sets of isochrones Problems with standard method

25. The link with cal. uncertainties

26. Estimate the likelihood that each data point comes from a given isochrone Find the likelihood for all points Advantages Easily generalized to n-dimensions Easily estimate effect of different isochrones Proper statistical treatment of uncertainties Can include correlated uncertainties and data augmentation for missing data Can treat as mixture problem A new method

27. The test case : The SMC

28. The test case Nearby galaxy (60 kpc) Recent star-formation (a bit complex) … but can observe very deep and set good constraints on star-formation also can obtain additional constrains from spectroscopy ….useful for testing the results and setting priors