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Probing the evolution of stellar systems

This article explores the stages and complexities of stellar evolution, using photometry and isochrones as tools to analyze star formation scenarios. It discusses the standard method and introduces a new statistical approach for better estimation of uncertainties and treatment of missing data.

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Probing the evolution of stellar systems

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

  4. Basic tool : Photometry

  5. Basic tool : Photometry

  6. Horizontal Branch Red Giant Branch Main Sequence

  7. CMDs : Simple cases

  8. The tools : Stellar Tracks (<m>| age, Mass, Z, stellar evolution)

  9. The tools : Isochrones The tools : Isochrones

  10. The tools : Isochrones

  11. The tools : Isochrones

  12. 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

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

  14. The “standard method”

  15. The “standard method”

  16. The “standard method”

  17. The “standard method”

  18. Complications • Incompleteness • Multiple populations • Uncertainties on isochrones

  19. CMDs: complications

  20. CMDs: complications

  21. CMDs: complications

  22. CMDs: more complications Detection probability

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

  24. The link with cal. uncertainties

  25. A new method • 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

  26. The test case : The SMC

  27. 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

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