1. THE EFFECT OF ROTATION ON THE HYDROSTATIC AND EXPLOSIVE YIELDS OF MASSIVE STARS and Alessandro Chieffi INAF – Istituto di Astrofisica e Planetologia Spaziali, Italy Centre for Stellar and Planetary Astrophysics, Monash Univesity, Australia alessandro.chieffi@iasf-roma.inaf.it Marco Limongi INAF – Osservatorio Astronomico di Roma, ITALY Institute for the Physics and Mathematics of the Universe, JAPAN marco.limongi@oa-roma.inaf.it

2. HYDROSTATIC AND EXPLOSIVE YIELDS OF MASSIVE STARS mass cut Remnant Ejecta

3. HYDROSTATIC AND EXPLOSIVE YIELDS OF MASSIVE STARS ElementProduction Site N ( 14 N)Hydrostatic H burning F ( 19 F)Hydrostatic He convective shell C ( 12 C) O ( 16 O) Hydrostatic core He burning ( 16 O partially modified by Cshell and Ne x ) Ne ( 20 Ne) Na ( 23 Na) Mg ( 24 Mg) Al ( 27 Al) Hydrostatic C convective shell Partially destroyed by C x ( 23 Na) and Ne x ( 20 Ne) Partially produced by Ne x ( 24 Mg, 27 Al) P ( 31 P)Ne x Cl ( 35 Cl, 37 Cl)Ne x +O x K ( 39 K)OxOx Sc ( 45 Sc)Hydrostatic C convective shell Ne x +O x Si ( 28 Si) S ( 32 S) Ar ( 36 Ar) Ca ( 40 Ca) O x +Si i V ( 51 Cr) Cr ( 52 Cr, 52 Fe) Mn ( 55 Mn, 55 Co) Si i Ti ( 48 Cr)O x +Si i +Si c Fe ( 56 Ni) Co ( 59 Co, 59 Ni) Ni ( 58 Ni, 60 Ni) Si c mass cut Remnant Ejecta

4. HYDROSTATIC AND EXPLOSIVE YIELDS OF MASSIVE STARS Hydrostatic Yields mainly depend on the presupernova evolution (convective history, diffusive mixing, core masses, mass loss) Each zone keeps track of the various central or shell, convective and/or ratidative, burning C C C C He Ne O O O Si He H

5. Explosive Yields mainly depend on the presupernova chemical and density structure Complete Si burning Incomplete Si burning Explosive O burning Explosive Ne burning Explosive C burning No Modification NSE Sc Ti Fe Co Ni QSE 1 Clusters Cr V Mn QSE 2 Cluster Si S Ar K Ca Mg Al P Cl Ne Na 3700500064001175013400 RADIUS (Km) Mass-Radius relation, Y e profile, Chemical Stratification @ Presupernova Stage Complete Si burning Incomplete Si burning Explosive O burning Explosive Ne burning Explosive C burning No Modification NSE Sc Ti Fe Co Ni QSE 1 Clusters Cr V Mn QSE 2 Cluster Si S Ar K Ca Mg Al P Cl Ne Na INTERIOR MASS HYDROSTATIC AND EXPLOSIVE YIELDS OF MASSIVE STARS

6. PRESUPERNOVA EVOLUTION Grid of models: 13, 15, 20, 25, 30, 40, 60, 80 and 120 M  Initial Solar Composition (Asplund et al. 2009) All models computed with the FRANEC (Frascati RAphson Newton Evolutionary Code) 6.0 Major improvements compared to the release 4.0 (ML & Chieffi 2003) and 5.0 (ML & Chieffi 2006) -FULL COUPLING of: Physical Structure - Nuclear Burning - Chemical Mixing (convection, semiconvection, rotation) - INCLUSION OF ROTATION: - Conservative rotation law/Shellular Rotation (Meynet & Maeder 1997) - Transport of Angular Momentum (Advection/Diffusion, Maynet & Maeder 2000) - Coupling of Rotation and Mass Loss - TWO NUCLEAR NETWORKS: - 163 isotopes (448 reactions) H/He Burning - 282 isotopes (2928 reactions) Advanced Burning - MASS LOSS: - OB: Vink et al. 2000,2001 - RSG: de Jager 1988+Van Loon 2005 (Dust driven wind) - WR: Nugis & Lamers 2000/Langer 1989

7. FRANEC 6.0 (Chieffi & ML in prep.) (Coupled and solved simultaneously) (4 th order  4 ODE soved by means of a relaxation method) or

8. INFLUENCE OF ROTATION ON CORE H BURNING

10. Almost same H exhausted core @ core H depletion (exception for M=120 M  ) Shallower chemical profiles in rotating models due to rotationally induced mixing Different path in the HR diagram  different mass loss history  Mass Loss does not scale monotonically with rotation INFLUENCE OF ROTATION ON CORE H BURNING H-rich envelope enriched by core H burning products

11. M≤60 M  : Rotational mixing dominates Rotational induced mixing beyond the He convective core Reduced  -gradient barrier  larger convective cores INFLUENCE OF ROTATION ON CORE AND SHELL He BURNING v=0 km/s v=300 km/s

12. M≤60 M  : Rotational mixing dominates Rotational induced mixing beyond the He convective core Reduced  -gradient barrier  larger convective cores Larger CO cores Continuous inward mixing of fresh 4 He fuel  Lower 12 C left over at core He depletion INFLUENCE OF ROTATION ON CORE AND SHELL He BURNING v=0 km/s v=300 km/s

13. M≤60 M  : Rotational mixing dominates Rotational induced mixing beyond the He convective core Reduced  -gradient barrier  larger convective cores Larger CO cores Continuous inward mixing of fresh 4 He fuel  Lower 12 C left over at core He depletion Formation of He convective shell in the region of variable He  He convective shell hotter  more 12 C and 16 O produced locally Rotating and Non Rotating models show completely different structures INFLUENCE OF ROTATION ON CORE AND SHELL He BURNING v=0 km/s v=300 km/s

14. M>60 M  : Mass Loss dominates Mass Loss uncovers the He core at the beginning of Core He burning INFLUENCE OF ROTATION ON CORE AND SHELL He BURNING v=0 km/s v=300 km/s

15. M>60 M  : Mass Loss dominates Mass Loss uncovers the He core at the beginning of Core He burning He convective core progressively recedes in mass and leaves a region of variable He INFLUENCE OF ROTATION ON CORE AND SHELL He BURNING v=0 km/s v=300 km/s

16. M>60 M  : Mass Loss dominates Mass Loss uncovers the He core at the beginning of Core He burning He convective core progressively recedes in mass and leaves a region of variable He In these stars this region is not due to the rotationally induced mixing but to the efficient mass loss that progressively erodes the He core INFLUENCE OF ROTATION ON CORE AND SHELL He BURNING v=0 km/s v=300 km/s

17. M>60 M  : Mass Loss dominates Mass Loss uncovers the He core at the beginning of Core He burning He convective core progressively recedes in mass and leaves a region of variable He In these stars this region is not due to the rotationally induced mixing but to the efficient mass loss that progressively erodes the He core Formation of He convective shell in the region of variable He in both rotating and non rotating models Rotating and Non Rotating models show similar structures INFLUENCE OF ROTATION ON CORE AND SHELL He BURNING v=0 km/s v=300 km/s

18. ADVANCED BURNING STAGES: INTERNAL EVOLUTION OF ROTATING AND NON ROTATING STARS Properties of the CO core at Core C-ignition Differences progressively reduce with the initial mass Rotating models show larger CO cores and smaller 12 C mass fractions at core He depletion compared to the non rotating ones

19. ADVANCED BURNING STAGES: INTERNAL EVOLUTION Four major burning, i.e., carbon, neon, oxygen and silicon. Central burning  formation of a convective core Central exhaustion  shell burning  convective shell Local exhaustion  shell burning shifts outward in mass  convective shell C C C C He Ne O O O Si He H

20. ADVANCED BURNING STAGES: INTERNAL EVOLUTION The details of this behavior (number, timing, mass extension and overlap of convective shells) is mainly driven by the CO core mass and by its chemical composition ( 12 C, 16 O) CO core mass Thermodynamic history 12 C, 16 O Basic fuel for all the nuclear burning stages after core He burning At core He exhaustion both the mass and the composition of the CO core scale with the initial mass… v=0 km/s

21. ADVANCED BURNING STAGES: INTERNAL EVOLUTION C C C C He Ne O O O Si He H H C Ne O O Si...hence, the evolutionary behavior scales as well In general, one to four carbon convective shells and one to three convective shell episodes for each of the neon, oxygen and silicon burning occur. Basic rule: the larger is the CO core, the lower is the 12 C at core He exhaustion. the less efficient is the C burning shell, the lower is the number of convective episodes Si

22. PRESUPERNOVA STAR The higher is the mass of the CO core (the lower is the 12 C at the core He exhaustion ), the more compact is the structure at the presupernova stage v=0 km/s Less efficient C shell burning means stronger contraction of the CO core

23. ADVANCED BURNING STAGES: INTERNAL EVOLUTION OF ROTATING AND NON ROTATING STARS Properties of the CO core at Core C-ignition Differences progressively reduce with the initial mass Rotating models show larger CO cores and smaller 12 C mass fraction at core He depletion compared to the non rotating ones

24. PRESUPERNOVA MODELS: ROTATING vs NON ROTATING STARS....hence the behavior of any given rotating star during the more advanced burning stages will resemble that of a non rotating star having a higher mass (80-120 exceptions) Presupernova rotating models appear much more compact compared to the non rotating ones and with larger Fe cores Rotating models have a larger binding energy compared to the non rotating ones

25. PRESUPERNOVA MODELS: ROTATING vs NON ROTATING STARS

26. THE FINAL FATE Hydrodynamical simulations based on induced explosions for E expl =10 51 erg (ML & Chieffi 2003, Chieffi & ML 2012 in prep) Larger binding energies  Larger fallback masses after the explosion  Rotating models less efficient in polluting the ISM with heavy elements Difficult to compare the ejected masses in this case In both cases no, or very few, heavy elements ejected for models with M>20 M 

27. EJECTED MASSES: COMPARISON Comparison made for a fixed amount of 56 Ni ejected Differences confined with a factor of 2 for the majority of the elements

28. EJECTED MASSES: COMPARISON Comparison made for a fixed amount of 56 Ni ejected Differences confined with a factor of 2 for the majority of the elements Overproduction of C and O in low-mass rotating models

29. EJECTED MASSES: COMPARISON Comparison made for a fixed amount of 56 Ni ejected Differences confined with a factor of 2 for the majority of the elements Overproduction of C and O in low-mass rotating models Overproduction of F in rotating models with mass 20-40 M 

30. EJECTED MASSES: COMPARISON Comparison made for a fixed amount of 56 Ni ejected Differences confined with a factor of 2 for the majority of the elements Overproduction of C and O in low-mass rotating models Overproduction of F in rotating models with mass 20-40 M  Overproduction of Si-Sc elements in rotating models with mass ~ 20-25 M 

31. EJECTED MASSES: COMPARISON Comparison made for a fixed amount of 56 Ni ejected Differences confined with a factor of 2 for the majority of the elements Overproduction of C and O in low-mass rotating models Overproduction of F in rotating models with mass 20-40 M  Overproduction of Si-Sc elements in rotating models with mass ~ 13-25 M  Overproduction of s-process elements in rotating models with mass 20-40 M 

32. ElementProduction SiteEjected Mass Ratio (Rot/No Rot) Reason CHydrostatic Core and Shell He burning ~3-2 for M<30 M  Larger CO cores/Hotter He convective shells (In spite of the lower 12 C left by core He burning) OHydrostatic Core He burning ~5-2 for M<25 M  Larger CO cores/Larger 16 O left by Core He burning FHydrostatic He convective shell ~20 around M=30 M  Hotter He convective shell Si-ScExplosive burning~2 for M<30 M  More compact PreSN structure  more mass synthesized by all the explosive burning s-processHydrostatic Core He burning and Hydrostatic Convective C burning ~7 around M=30 M  Longer He burning lifetimes Larger He convective cores Hotter C convective shell EJECTED MASSES: COMPARISON

33. Rotating models produce more metals compared to the non rotating ones because of the larger CO cores and more compact structures ENRICHMENT OF THE INTERSTELLAR MEDIUM Differences reduce with the mass 56 Ni=0.1 M 

34. PRODUCTION FACTORS

35. SUMMARY AND CONCLUSIONS Influence of rotation on the presupernova evolution (from the point of view of the hydrostatic and explosive yields) Negligible effect on the H exhausted core @ core H depletion Larger CO cores and smaller 12 C mass fractions @ core He depletion Differences progressively reduced with the initial mass Presupernova models more compact and with larger Fe cores Larger binding energies Larger fallback masses  less efficient enrichment of heavy elements for low explosion energies Differences in the final yields confined within a factor of ~2 for the majority of the elements Overproduction of C and O more pronounced in the low-mass models Overproduction of Si-Sc elements in models with mass ~ 20-25 M  Overproduction of F and s-process elements in models with mass ~ 20-40 M  F and s-process elments distribution closer to the solar one in stars with mass ~ 25-40 M 