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The Initial-Final Mass Relation

The Initial-Final Mass Relation. Salaris, Serenelli, Weiss & Miller Bertolami (2009). Aldo Serenelli – MPA. IFMR: M(MS)  M(WD). Chemical evolution of stellar populations Mass-to-light ratio WD luminosity function Upper mass limit for WD formation

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The Initial-Final Mass Relation

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  1. The Initial-Final Mass Relation Salaris, Serenelli, Weiss & Miller Bertolami (2009) Aldo Serenelli – MPA

  2. 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. Observations Theory (models) WD spectrum WD atmosphere models (Teff, log g) WD cooling models (cool,MWD) Semi-empirical IFMR Basic data: WD spectrum & total age of WD (tot = cool + prog)

  4. Observations Theory (models) WD spectrum WD atmosphere models (Teff, log g) WD cooling models (cool,MWD) WDs in clusters (and binaries): CMD, [Fe/H], E(B-V) Isochrones (tot  prog) Stellar models  Initial mass Semi-empirical IFMR Basic data: WD spectrum & total age of WD (tot = cool + prog) Observational requirements difficult to meet simultaneously

  5. Weidemann (2000) ~ 15 objects Combination of semi-empirical and theoretical relations

  6. 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. Cluster sample Pleiades 85 Myr Hyades 640 Myr Praesepe 650 Myr NGC 2516 130 Myr NGC 3532 400 Myr M37 320 Myr M35 120 Myr NGC 7789 1500 Myr NGC 6819 2000 Myr NGC 1039 150 Myr New (homogeneous) determination of cluster distances and ages (ask Maurizio for details) All clusters around [Fe/H]8

  8. Cluster sample Despite variety of methods data and isochrones, ages compare well Pleiades 85 Myr Hyades 640 Myr Praesepe 650 Myr NGC 2516 130 Myr NGC 3532 400 Myr M37 320 Myr M35 120 Myr NGC 7789 1500 Myr NGC 6819 2000 Myr NGC 1039 150 Myr Exception is M37 New (homogeneous) determination of cluster distances and ages (ask Maurizio for details) All clusters around [Fe/H]8

  9. Cluster ages: consistency Two homogeneous sets of models Basti & Pauda isochrones give very similar results. Lower limit to systematic uncertainties in age determinations?

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

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

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

  13. Reference IFMR – 53 WDs – BASTI & S00 Larger uncertainties up to x2 Statistical agreement

  14. Reference IFMR – 53 WDs – BASTI & S00 Larger uncertainties up to x2 Statistical agreement Problematic objects in M37 (and NGC 3532?)

  15. Reference IFMR – 53 WDs – BASTI & S00 Larger uncertainties up to x2 Statistical agreement Problematic objects in M37 (and NGC 3532?) Intrinsic spread in Mf around Mi= 3 – 3.5M8

  16. Uncertainties I. Different isochrones and stellar models Changes << than overall uncertainty

  17. Uncertainties II. Different WD cooling tracks Relevant effect for Mi > 5M8

  18. Uncertainties III. WD physics Relevant effect for hot & massive WDs

  19. Uncertainties IV: WDs WD masses: dominated by observational uncertainties (M-R relation is robust)

  20. Uncertainties IV: WDs WD masses: dominated by observational uncertainties (M-R relation is robust) WD ages: observations & physics/models matter

  21. Uncertainties V: progenitors Progenitor ages & masses: cluster age dominant but WD age important as well

  22. Comparison with theoretical IFMR Semi-empirical above theoretical relation Favours core growth during TP-AGB (constraint on OV at the He-shell? but PG-1159 abundances) BASTI LPCODE

  23. Comparison with theoretical IFMR Semi-empirical above theoretical relation Favours core growth during TP-AGB (constraint on OV at the He-shell? but PG-1159 abundances) BASTI LPCODE Spread around 3-3.5M8 coincident with steep theoretical relation

  24. Comparison with theoretical IFMR Semi-empirical above theoretical relation Favours core growth during TP-AGB (constraint on OV at the He-shell? but PG-1159 abundances) BASTI LPCODE Spread around 3-3.5M8 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. BASTI One word on no-OV (MS) models Younger cluster ages  higher initial masses; many above the 8M8, or even negative prog Models with no-OV in MS strongly disfavoured

  26. 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. Summary I • Consistent determination of cluster ages; ~[Fe/H]8 (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 3-3.5M8 seems real: reflects steep theoretical IFMR, or star to star variation at fixed Mi? • Uncertainties dominated by observational errors (but hot-WD)

  28. 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. 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

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