1. M up Oscar Straniero & Luciano Piersanti --------- INAF - Osservatorio di Teramo

2. Becker and Iben 1979 where: Z o =0.02 Y o =0.28

3. Status of the art

4. CLASSICAL MODELS (bare Schwarzschild criterion) In order of appearance: Siess 2007 versus Becker Iben formula 1979 (same Z,Y than Siess)

5. Beyond the core He burning: the early-AGB CO H-rich He -cooling H burning He burning Conv. Env.

6. The golden rule It exists a critical-core mass for the C ignition. It exists a critical-core mass for the C ignition. It is M H ~1.08 M ʘ (with the “current” physics). It is M H ~1.08 M ʘ (with the “current” physics). To evaluate M up, we have to take under control: The physics of the C ignition: neutrinos, 12C+12C, amount of C left (12C+  ), thermodynamics of a dense plasma (EOS)…. The physics of the C ignition: neutrinos, 12C+12C, amount of C left (12C+  ), thermodynamics of a dense plasma (EOS)…. The initial-to-final mass relation for an intermediate mass stars (5 - 9 M ʘ ), which depends on: The initial-to-final mass relation for an intermediate mass stars (5 - 9 M ʘ ), which depends on: 1. The extension of the H-exhausted core at the end of the MS phase. 2. The duration of the core-He burning phase (when H is burned in shell). 3. The efficiency of the 2nd dredge up.

7. Varying the convective scheme Classical OvershootSemi Convection

8. Classical versus Semiconvection (core-He burning) ≈ 0.9 M ʘ ≈ In order of appearance: Siess 2007 versus Straniero et al. 2003, see also Dominguez et al. 1999

9. Classical versus Overshoot In order of appearance: Siess 2007 (squares) versus Girardi 2000 (triangles) Both: OV (red) noOV (black) Siess07 OV ≈ 1.6 M ʘ ≈ 1.7 M ʘ ?

10. Semiconvection versus overshoot In order of appearance: Straniero et al. 2003 (semiconv.) versus Siess 2007 (overshoot) ≈ 0.7 M ʘ

11. Varying the composition (Y) Larger He  larger   larger T C  larger CC  larger final M H and, then: Larger He  larger   larger T C  larger CC  larger final M H and, then: SMALLER M UP Y M UP 0.299.5 0.348.7 0.377.7 Z=0.04, Bono et al. 2000

12. Varying the composition (Z) Larger Z  larger (external)  and more expanded and cooler structures Larger Z  larger (external)  and more expanded and cooler structuresBUT Larger Z  more CNO and more efficient H-burning Larger Z  more CNO and more efficient H-burning Z> 10 -3 Z M UP Z> 10 -3 Z M UP 10 -5 <Z< 10 -3 Z M UP Z< 10 -5 Z M UP Z< 10 -5 Z M UP

13. Varying the composition (Z)

14. Approaching the C ignition  nuclear =|  

15. Varying the neutrino rate Varying the neutrino rate (  ) In order of appearance: Esposito et al. 2003 (same for Haft et al 1995 or Itoh et al. 1996) versus Munakata et al. 1986

16. Varying Varying  or X( 12 C)  x5  /5 Equivalent to a reduction/multiplication of X( 12 C) by sqrt(5) (0.1 to 0.6), the range of uncertainty implied by the 12 C+   16 O see Straniero et al. 2003)

17. Varying the 12 C+ 12 C Laboratory measurements available down to about 3 MeV (the Gamow peak for M up is 1.5 MeV). Laboratory measurements available down to about 3 MeV (the Gamow peak for M up is 1.5 MeV). Several evidences of “molecular” structure producing narrow resonances at low energy (see Wiescher 2007, Spillane et al. 2007, Cooper et al. 2009). Several evidences of “molecular” structure producing narrow resonances at low energy (see Wiescher 2007, Spillane et al. 2007, Cooper et al. 2009). A (possible) resonance near the Gamow peak would significantly increase the rate, thus reducing both the critical M H and, in turn, M up A (possible) resonance near the Gamow peak would significantly increase the rate, thus reducing both the critical M H and, in turn, M up

19. Core burning SNe Ia What a resonance at 1.5 MeV would imply M=7M  Z=Z  (dashed line)

20. M upZCF88NEW0.00016.64.5 0.00106.74.7 0.00607.25.3 0.01497.85.8 0.02988.36.1 M up reduces of ~2 M 

21. Astrophysical Consequences of a variation of M up (numbers will be given for a  M up ~2 M Astrophysical Consequences of a variation of M up (numbers will be given for a  M up ~2 M ʘ )

22. Astrophysical consequences I The number of super-AGB (ONeMg WD or electron-capture SNe) is larger. The number of super-AGB (ONeMg WD or electron-capture SNe) is larger. By adopting a (Salpeter like) power-low IMF (  =2.35), SAGB would be 2/3 of the stars with M>M_up’ (the progenitors of “normal” core collapse SNe). By adopting a (Salpeter like) power-low IMF (  =2.35), SAGB would be 2/3 of the stars with M>M_up’ (the progenitors of “normal” core collapse SNe). 1.5 MeV resonance, semiconv., classical mod.

23. Astrophysical Consequences II Massive CO WDs cut off: M WD max reduced down to 0.95 M ʘ ). Massive CO WDs cut off: M WD max reduced down to 0.95 M ʘ ). BUT ROTATION MAY HELP see Dominguez et al 1996

24. Massive CO WD: the lifting effect of rotation delays the II dredge up, allowing more massive M H (Dominguez et al. 1996) Convective envelope He-rich zone CO core 6.5 M ʘ Z= Z ʘ

25. Astrophysical Consequences III Less Massive AGB  less space left for Hot Bottom Burning Less Massive AGB  less space left for Hot Bottom Burning

26. Astrophysical Consequences IV SN Ia rates, both scenarios, Single Degenerate and Double Degenerate, 4 times less frequent!! SN Ia rates, both scenarios, Single Degenerate and Double Degenerate, 4 times less frequent!! Prompt SNIa suppressed Prompt SNIa suppressed First SNe Ia delayed First SNe Ia delayed (see Piersanti et al. 2010)

27. Astrophysical consequences V It is more easy to produce low mass core collapse SNe, down to ~6 M ʘ (electron capture), down to ~8 M ʘ (normal core collapse) It is more easy to produce low mass core collapse SNe, down to ~6 M ʘ (electron capture), down to ~8 M ʘ (normal core collapse) Somewhat in agreement with recent progenitor mass estimations: e.g. Smartt et al. 2008 found a minimum mass at 8.5 ± 1.5 M ʘ Somewhat in agreement with recent progenitor mass estimations: e.g. Smartt et al. 2008 found a minimum mass at 8.5 ± 1.5 M ʘ

28. Astrophysical Consequences VI Carbon Burning in massive stars and SAGB. More extended convective zones should be favoured by a larger 12C+12C rate. Carbon Burning in massive stars and SAGB. More extended convective zones should be favoured by a larger 12C+12C rate. Consequences for the final mass-radius relation, explosion energy release and related nucleosynthesis Consequences for the final mass-radius relation, explosion energy release and related nucleosynthesis

29. M=11.0 M  Z=0.0149 Y=0.2645

30. The value of M up M=8.5 M  Z=0.0149 Y=0.2645 CF88 NEW RATE ‘

31. Summary Combining present uncertainties, M up is known no better than  M=2 M ʘ (conservative error estimate). Combining present uncertainties, M up is known no better than  M=2 M ʘ (conservative error estimate). The (many) astrophysical/observational consequences have been illustrated. The (many) astrophysical/observational consequences have been illustrated.