1. The Giant Branches – Leiden 14/05/09 The Initial-Final Mass Relation Aldo Serenelli – MPA Salaris, Serenelli, Weiss & Miller Bertolami (2009)

2. The Giant Branches – Leiden 14/05/09 IFMR: M(MS)  M(WD)  Chemical evolution of stellar populations  Mass-to-light ratio  WD luminosity function  Upper mass limit for WD formation  Constraints on total mass loss & C/O core evolution

3. The Giant Branches – Leiden 14/05/09 Semi-empirical IFMR Basic data: WD spectrum & total age of WD (  tot =  cool +  prog ) ObservationsTheory (models) WD spectrumWD atmosphere models (Teff, log g) WD cooling models (  cool,M WD )

4. The Giant Branches – Leiden 14/05/09 Semi-empirical IFMR Basic data: WD spectrum & total age of WD (  tot =  cool +  prog ) Observational requirements difficult to meet simultaneously ObservationsTheory (models) WD spectrumWD atmosphere models (Teff, log g) WD cooling models (  cool,M WD ) WDs in clusters (and binaries): CMD, [Fe/H], E(B-V) Isochrones (  tot   prog ) Stellar models  Initial mass

5. The Giant Branches – Leiden 14/05/09 Weidemann (2000) ~ 15 objects Combination of semi-empirical and theoretical relations

6. The Giant Branches – Leiden 14/05/09 Ferrario et al. (2005) Observational efforts by Dobbie, Williams, Kalirai & others ~ 40 objects 7 clusters + Sirius Heterogeneous sources for cluster ages and stellar models Errors from observations (incl. cluster ages) Constraints on stellar models? Uncertainties from stellar and WD models

7. The Giant Branches – Leiden 14/05/09 New (homogeneous) determination of cluster distances and ages (ask Maurizio for details) All clusters around [Fe/H]  Cluster sample Pleiades85 Myr Hyades640 Myr Praesepe650 Myr NGC 2516130 Myr NGC 3532400 Myr M37320 Myr M35120 Myr NGC 7789 1500 Myr NGC 68192000 Myr NGC 1039150 Myr

8. The Giant Branches – Leiden 14/05/09 New (homogeneous) determination of cluster distances and ages (ask Maurizio for details) All clusters around [Fe/H]  Cluster sample Pleiades85 Myr Hyades640 Myr Praesepe650 Myr NGC 2516130 Myr NGC 3532400 Myr M37320 Myr M35120 Myr NGC 7789 1500 Myr NGC 68192000 Myr NGC 1039150 Myr Exception is M37 Despite variety of methods data and isochrones, ages compare well

9. The Giant Branches – Leiden 14/05/09 Cluster ages: consistency Two homogeneous sets of models Basti & Pauda isochrones give very similar results. Lower limit to systematic uncertainties in age determinations?

10. The Giant Branches – Leiden 14/05/09 Sources of uncertainties  White dwarfs: o Observational uncertainties (log g & Teff) (0.05 dex, 400 K – 0.25 dex, 1200 K) o Different cooling tracks (S00 – LPCODE) o Input physics (neutrino cooling, opacity) o WD core composition (C/O ratio) o H-envelope thickness

11. The Giant Branches – Leiden 14/05/09 Sources of uncertainties  White dwarfs: o Observational uncertainties (log g & Teff) (0.05 dex, 400 K – 0.25 dex, 1200 K) o Different cooling tracks (S00 – LPCODE) o Input physics (neutrino cooling, opacity) o WD core composition (C/O ratio) o H-envelope thickness  Progenitor stars: o Cluster age o [Fe/H] o Different isochrones & models (BASTI – PADUA)

12. The Giant Branches – Leiden 14/05/09 Sources of uncertainties  White dwarfs: o Observational uncertainties (log g & Teff) (0.05 dex, 400 K – 0.25 dex, 1200 K) o Different cooling tracks (S00 – LPCODE) o Input physics (neutrino cooling, opacity) o WD core composition (C/O ratio) o H-envelope thickness  Progenitor stars: o Cluster age o [Fe/H] o Different isochrones & models (BASTI – PADUA) Input physics & systematics:  i = (X + -X - )/2 Derive IFMR from Monte Carlo simulations

13. The Giant Branches – Leiden 14/05/09 Reference IFMR – 53 WDs – BASTI & S00 Larger uncertainties up to x2 Statistical agreement

14. The Giant Branches – Leiden 14/05/09 Reference IFMR – 53 WDs – BASTI & S00 Larger uncertainties up to x2 Statistical agreement Problematic objects in M37 (and NGC 3532?)

15. The Giant Branches – Leiden 14/05/09 Reference IFMR – 53 WDs – BASTI & S00 Larger uncertainties up to x2 Statistical agreement Problematic objects in M37 (and NGC 3532?) Intrinsic spread in M f around M i = 3 – 3.5M 

16. The Giant Branches – Leiden 14/05/09 Uncertainties I. Different isochrones and stellar models Changes << than overall uncertainty

17. The Giant Branches – Leiden 14/05/09 Uncertainties II. Different WD cooling tracks Relevant effect for M i > 5M 

18. The Giant Branches – Leiden 14/05/09 Uncertainties III. WD physics Relevant effect for hot & massive WDs

19. The Giant Branches – Leiden 14/05/09 Uncertainties IV: WDs WD masses: dominated by observational uncertainties (M-R relation is robust)

20. The Giant Branches – Leiden 14/05/09 Uncertainties IV: WDs WD masses: dominated by observational uncertainties (M-R relation is robust) WD ages: observations & physics/models matter

21. The Giant Branches – Leiden 14/05/09 Uncertainties V: progenitors Progenitor ages & masses: cluster age dominant but WD age important as well

22. The Giant Branches – Leiden 14/05/09 Comparison with theoretical IFMR BASTI LPCODE Semi-empirical above theoretical relation Favours core growth during TP-AGB (constraint on OV at the He-shell? but PG-1159 abundances)

23. The Giant Branches – Leiden 14/05/09 Comparison with theoretical IFMR BASTI LPCODE Semi-empirical above theoretical relation Favours core growth during TP-AGB (constraint on OV at the He-shell? but PG-1159 abundances) Spread around 3-3.5M  coincident with steep theoretical relation

24. The Giant Branches – Leiden 14/05/09 Comparison with theoretical IFMR BASTI LPCODE Semi-empirical above theoretical relation Favours core growth during TP-AGB (constraint on OV at the He-shell? but PG-1159 abundances) Spread around 3-3.5M  coincident with steep theoretical relation General agreement w/models  no gross disagreement with mass loss prescriptions (but interplay with core growth!) Problems with M37 point out the importance of accurate cluster parameters

25. The Giant Branches – Leiden 14/05/09 One word on no-OV (MS) models Younger cluster ages  higher initial masses; many above the 8M , or even negative  prog Models with no-OV in MS strongly disfavoured BASTI

26. The Giant Branches – Leiden 14/05/09 Parallel effort (Catalan et al. 2008 a,b) Include uncertainties in WD structure Include WDs in common proper motion pairs with FGK Potentially very interesting: large number of systems, range of metallicities, coverage of low-mass end Difficult to determine total age: based on isochrones/models & X-ray luminosity (Courtesy S. Catalan)

27. The Giant Branches – Leiden 14/05/09 Summary I  Consistent determination of cluster ages; ~[Fe/H]  (but WD obs. data from literature)  Systematic study of uncertainties  No WDs near Chandrasekhar limit (but see GD50 in talk by E. Garcia-Berro)  MS models without OV disfavoured  Theoretical IFMR OK if CO core grows along TP-AGB  Spread around 3-3.5M  seems real: reflects steep theoretical IFMR, or star to star variation at fixed M i ?  Uncertainties dominated by observational errors (but hot-WD)

28. The Giant Branches – Leiden 14/05/09 Summary II  No gross disagreement between mass loss prescriptions and total mass lost (but coupled to core growth)  Problems with M37 illustrates the necessity of reliable cluster parameters  Models with similar (up-to-date) physics lead to similar semi-empirical IFMR

29. The Giant Branches – Leiden 14/05/09 Summary II  No gross disagreement between mass loss prescriptions and total mass lost (but coupled to core growth)  Problems with M37 illustrates the necessity of reliable cluster parameters  Models with similar (up-to-date) physics lead to similar semi-empirical IFMR