12 C+ 12 C REACTION AND ASTROPHYSICAL IMPLICATIONS

1. 12C+12C REACTION AND ASTROPHYSICAL IMPLICATIONS Marco Limongi INAF – Osservatorio Astronomico di Roma, ITALY Institutefor the Physics and the Mathematicsof the Universe, JAPAN marco.limongi@oa-roma.inaf.it

2. INTRODUCTION Carbon Burning MainProducts: 20Ne, 23Na, 24Mg, 27Al Enuc= 4.00 1017 erg/g The cross section of this reaction should be known with high accuracy down to the ECM∼1.5 MeV Present day experimental measurements of the 12C+12C cross section for ECM>2.10 MeV Because of the resonance structure, extrapolation to the Gamow Energies is quite uncertain Since there is a resonance at nearly every 300 keV energy step, it is quite likely that a resonance exists near the center of the Gamow peak, say at Ecm∼1.5 MeV Which is the impact of such a hypothetical resonance on the behavior of stellar models?

3. STELLAR STRUCTURE: BASICS Hydrostatic equilibrium Non degenerate EOS A contracting star of mass M with constantcompositionsupported by an ideal gas pressure willincreaseitscentral temperature following the above relation. This relation willholduntilone of the aboveassumptionswill be violated.....

4. STELLAR STRUCTURE: BASICS NuclearIgnition: Whenthe temperature is high enough the thermonuclear fusion reactionsbecomeefficient Severallighter nuclei fuse to form a heavierone. The mass of the productnucleusislowerthan the total mass of the reactant nuclei The mass defectisconvertedintoenergy Thisenergy balances the energyradiatedaway The contractionhalts and the temperature remainsalmostconstant When the nuclearfuelisexhaustedcontractionstartsagainuntil the nextnuclearfuelisignited. N.B. The nuclear burning slows down the evolution along the path

5. STELLAR STRUCTURE: BASICS Onset of degeneracy: For sufficiently high densitiesthe electronsmaybecomedegenerate. Electron pressure tends to dominate over the total pressure If the electron gas becomeshighly degenerate The electron pressure gradient balances the gravity The contractionstops and the structureradiates and cools down does not hold anymore and the path in the plane changes The relation

6. STELLAR STRUCTURE: BASICS In differentregionsof the T-rplane, differentphysicalphenomenadominate the totalP Non Degenerate Non Relativistic Non Relativistic Degenerate Relativistic Degenerate The mass of the star plays a pivotalrole:

7. CRITICAL MASSES The comparisonbetween the path in the T-rplane and the ignition temperature of the variousfuelsdeterminesnaturally the existence of the variouscriticalmasses O burning Ne burning C burning He burning Increasing Mass H burning Non Degenerate Non Relativistic Non Relativistic Degenerate Relativistic Degenerate N.B. The nuclear burning slows down the evolution along the path When degeneracy takes place the relation does not hold anymore and the path in the T-r plane changes

8. He WD MASS LOSS RGB H degenerate He He ignition H ignition

9. CO WD He WD MASS LOSS MASS LOSS RGB TP-AGB H He H degenerate CO degenerate He He ignition H ignition C ignition

10. ONeMg WD CO WD ECSN He WD MASS LOSS MASS LOSS MASS LOSS SUPER-AGB H RGB TP-AGB He CO H He degenerate ONeMg H degenerate CO degenerate He O ignition He ignition H ignition C ignition

11. ONeMg WD CO WD ECSN He WD MASS LOSS CCSN MASS LOSS MASS LOSS SUPER-AGB H RGB TP-AGB He CO H H He degenerate ONeMg H He degenerate CO CO degenerate He NeO O SiS Fe O ignition He ignition H ignition C ignition

12. INTERMEDIATE MASS STARS LOW MASS STARS INTERMEDIATE HIGH MASS STARS MASSIVE STARS ONeMg WD CO WD ECSN He WD MASS LOSS CCSN MASS LOSS MASS LOSS SUPER-AGB H RGB TP-AGB He CO H H He degenerate ONeMg H He degenerate CO CO degenerate He NeO O SiS Fe O ignition He ignition H ignition C ignition

13. INTERMEDIATE MASS STARS LOW MASS STARS INTERMEDIATE HIGH MASS STARS MASSIVE STARS ONeMg WD SNIa SNII / SNIb/c CO WD ECSN He WD MASS LOSS CCSN MASS LOSS MASS LOSS SUPER-AGB H RGB TP-AGB He CO H H He degenerate ONeMg H He degenerate CO CO degenerate He NeO O SiS Fe O ignition He ignition H ignition C ignition

14. INTERMEDIATE MASS STARS LOW MASS STARS INTERMEDIATE HIGH MASS STARS MASSIVE STARS ONeMg WD SNIa SNII / SNIb/c CO WD ECSN He WD MASS LOSS CCSN MASS LOSS MASS LOSS SUPER-AGB H RGB TP-AGB He CO H H He degenerate ONeMg H He degenerate CO CO degenerate He NeO O SiS Fe O ignition He ignition H ignition C ignition

15. CRITICAL MASSES O burning Ne burning C burning He burning H burning Non Relativistic Degenerate Relativistic Degenerate Non Degenerate Non Relativistic

16. CRITICAL MASSES Increasing the efficiency of the 12C+12C reaction due to the presence of a resonance at low temperatures (energies) would decrease the value of MUP O burning Ne burning C burning He burning H burning Non Relativistic Degenerate Relativistic Degenerate Non Degenerate Non Relativistic To be more quantitative detailed stellar models must be computed

17. SURVEY OF INTERMEDIATE MASS-MASSIVE STARS EVOLUTION STANDARD MODELS INITIAL SOLAR COMPOSITION (Asplund et al. 2009) – Y=0.26 FULL COUPLING of: Physical Structure - Nuclear Burning - Chemical Mixing (convection, semiconvection, rotation) Stability criterion for convection : Ledoux Overshooting : aover= 0.2 hP Semiconvection : asemi= 0.02 Mixing-Length : a = 2.1 NO ROTATION TWO NUCLEAR NETWORKS: - 163 isotopes (448 reactions) H/He Burning - 282 isotopes (2928 reactions) Advanced Burning 12C+12C cross section : Caughlanand Fowler (1988) (CF88) MASS LOSS : - Reimers + Vassiliadis and Wood (1993) - OB: Vink et al. 2000,2001 - RSG: de Jager 1988+Van Loon 2005 (Dust driven wind) - WR: Nugis & Lamers 2000/Langer 1989

18. STANDARD MODELS M=7 M Z=Z Y=0.26 Sequence of events after core He depletion The He burningshifts in a shellwhichprogressielyadvances in mass The CO core grows, contracts and heats up Degeneracybegins to take place An increasingfraction of the CO becomesprogressively degenerate and henceitscontraction and heatingprogressivelyslows down. Neutrino emissionbecomesprogressively more efficeint in the innermostzoneswhichprogressively cool down An off center maximum temperature developes due to the interplaybewteen the contraction and heating of the outerzonesinduced by the advancing of the He burningshell and cooling of the innermostregions due to neutrino emission The seconddredge up takesplacewhichstops the advancing of the He burningshell From this time onward the maximum temperature begins to decrease Since the maximum temperature doesnotreach the C ignitionvalue, no C burningoccurs TP-AGB

19. STANDARD MODELS M=8 M Z=Z Y=0.26 The first part of the evolutionissimilar to that of the 7Mbut in this case the maximum off center temperature reaches the criticalvalue for C-ignition C burningignites off center Because of degeneracy the pressure doesnotincrease and thereis no consumption of energythroughexpansion the Temperature riseseven more and a flash occurs A convectiveshellforms and the matterheats up atconstantdensityuntildegeneracyisremovedthenitexpands. Beacuse of the the energy release the maximum temperature shiftsinward in mass and a second C flash occurs The followingevolutionproceedsthrough a number of C flashesprogressively more internal in mass until the nuclearburningreaches the center of the star  quiescent C burningbegins After core C depletion an ONeMg core isformedthatmay, or maynot, become degenerate  detailedcalculation of the followingevolutionisrequired

20. STANDARD MODELS M=8 M Z=Z Y=0.26 a=2.1 aover=0.2hP Off center C-ignition 1st dredge-up Convective Envelope He burning shell 2nd dredge-up H burning shell He Core C Convective Shells H Convective Core CO Core He Convective Core

21. INTERMEDIATE MASS STARS LOW MASS STARS INTERMEDIATE HIGH MASS STARS MASSIVE STARS ? ONeMg WD SNIa SNII / SNIb/c CO WD ECSN He WD MASS LOSS CCSN MASS LOSS MASS LOSS SUPER-AGB H RGB TP-AGB He CO H H He degenerate ONeMg H He degenerate CO CO degenerate He NeO O SiS Fe O ignition He ignition H ignition C ignition

22. TEST CASE WITH MODIFIED 12C+12C REACTION Modification of the 12C+12C cross section following the procedure described by Bravo et al. 2011 (in press): Include a resonance at ECM=1.7 MeV with a strength limited by the measured cross sections at low energy (2.10 MeV) accounts for the resonance found by Spillane et al. 2007 at ECM= 2.14 MeV, and the assumed low-energy ghost resonance. = energy at which there is assumed a resonance = ghost resonance strength

23. TEST CASE WITH MODIFIED 12C+12C REACTION We require that the ghost resonance at ER contributes to the cross section at ECM=2.10 MeV less than 10% of the value measured by Spillane et al. 2007 at the same energy In this case, the resonance strength is limited to 4.1 MeV for ER = 1.7 MeV, assuming the resonance width of GR= 10 keV “Standard” C ignition C burning test case C burning “standard” case Since in the standard case C burning occurs at T9∼0.9, i.e. Log(NA<sv>) ∼-12  in the test model it should begin atT9∼0.6

24. TEST CASES WITH MODIFIED 12C+12C REACTION M=4 M Z=Z Y=0.26 Degenerate CO core TP-ABG

25. TEST CASES WITH MODIFIED 12C+12C REACTION M=5 M Z=Z Y=0.26 Off center C ignition Convective Envelope 1st dredge-up He burning shell 2nd dredge-up C Convective Shells H burning shell He Core H Convective Core C Conv. Core He Convective Core CO Core

26. TEST CASES WITH MODIFIED 12C+12C REACTION M=5 M Z=Z Y=0.26 C Convective Shells Off center C ignition Convective Envelope 1st dredge-up C Conv. Core He burning shell 2nd dredge-up C Convective Shells H burning shell He Core H Convective Core C Conv. Core He Convective Core CO Core Off center C ignition

27. INTERMEDIATE MASS STARS LOW MASS STARS INTERMEDIATE HIGH MASS STARS MASSIVE STARS ? ONeMg WD SNIa SNII / SNIb/c CO WD ECSN He WD MASS LOSS CCSN MASS LOSS MASS LOSS SUPER-AGB H RGB TP-AGB He CO H H He degenerate ONeMg H He degenerate CO CO degenerate He NeO O SiS Fe O ignition He ignition H ignition C ignition

28. ASTROPHYSICAL CONSEQUENCES The presence of a resonance at ECM=1.7 MeV with a maximum strength limited by the measured cross sections at low energy (2.10 MeV) implies a reduction of MUP from 7 M to 4 M Lowering of the maximum mass for SNIa Increasing the CCSN/SNIa ratio Changing the hystory of the chemical enrichment (Fe production) of the Galaxy Increasing the ONeMg WD/CO WD ratio Evolutionary properties of the stars in the range MUP’-MUP’’

29. PRESUPERNOVA EVOLUTION OF MASSIVE STARS Massive stars ignite C (and all the subsequent fuels) up to a stage of NSE in the core, by definition Four major burning, i.e., carbon, neon, oxygen and silicon. C C H He H He O O C C Si Si O O Ne Ne Si Si O O Central burning  formation of a convective core Central exhaustion  shell burning  convective shell Local exhaustion shellburningshiftsoutward in mass  convectiveshell

30. ADVANCED BURNING STAGES: INTERNAL EVOLUTION He He C O C C Si O C H He He H O Si Ne Si O C O Ne Si In general, one to four carbon convectiveshells and one to threeconvectiveshellepisodes for each of the neon, oxygen and siliconburningoccur. The basic rule is that the higher is the mass of the CO core, the lower is the 12C left over by core He burning, the less efficient is the C shell burning and hence lower is the number of C convective shells.

31. PRESUPERNOVA STAR A less efficient nuclear burning means stronger contraction of the CO core. The densitystructure of the star at the presupernova stage reflectsthis trend Higher initial mass  higher CO core  less 12C left by core He burning  less efficient nuclear burning  more contraction  more compact presupernova star

32. Shock Wave Compression and Heating Matter Falling Back Matter Ejected into the ISM Ekin1051 erg Induced Expansion and Explosion Mass Cut Initial Remnant Final Remnant Initial Remnant Fe core EXPLOSION AND FALLBACK The fallbackdependson the bindingenergy Higher initial mass  higher CO core  less 12C left by core He burning  less efficient nuclear burning  more contraction  more compact presupernova star  more fallback  less enrichment of ISM with heavy elements

33. THE FINAL FATE OF A MASSIVE STAR STANDARD MODELS • The limiting mass between NS and BH fromingSNe : MNS/BH ~ 22 M • Maximum mass contributing to the enrichment of the ISM: Mpollute ~ 30 M

34. PRESUPERNOVA EVOLUTION OF MASSIVE STARS: TEST CASE A strong resonance at Gamow energies makes the C burning more efficient Test Model

35. PRESUPERNOVA EVOLUTION OF MASSIVE STARS: TEST CASE A strong resonance at Gamow energies makes the C burning more efficient Test Model C Conv. Shell C Convective Shell C Conv. Core

36. PRESUPERNOVA STAR A strong resonance at Gamow energies makes the C burning more efficient  makes the test model less compact than the corresponding standard one The presupernova density structure of a test 25 M resembles that of standard one with mass between 15-20 M

37. CONSEQUENCES ON THE EXPLOSION FALLBACK FALLBACK

38. ASTROPHYSICAL CONSEQUENCES The presence of a resonance at ECM=1.7 MeV with a maximum strength limited by the measured cross sections at low energy (2.10 MeV) implies • The increase of the limitingmass between NS and BH fromingSNe : MNS/BH > 25 M • The increase of the maximum mass contributing to the enrichment of the ISM: Mpollute > 30 M The results shown for the 25 M model can vary depending on the initial mass A quantitative determination of these two quantities requires the calculation of the presupernova evolution as well as the explosion of the full set of massive star models

39. SUMMARY ATROPHYSICAL RELEVANCE OF THE 12C+12C REACTION Consequences of the presence of a hypothetical resonance close to the Gamow peak may: Decreasing MUP • Lowering of the maximum mass for SNIa • Increasing the CCSN/SNIa ratio • Changing the hystory of the chemical enrichment (Fe production) of the Galaxy • Increasing the ONeMg WD/CO WD ratio • Evolutionary properties of the stars in the range MUP’-MUP’’ • Increasing of the limitingmass between NS and BH fromingSNe • Increasing of the maximum mass contributing to the enrichment of the ISM Measurements for energies down to the Gamow peak strongly needed in order to evaluate quantitatively these effects