12 C+ 12 C REACTION AND ASTROPHYSICAL IMPLICATIONS Marco Limongi INAF – Osservatorio Astronomico di Roma, ITALY Institute for the Physics and the Mathematics of the Universe, JAPAN

Carbon Burning Main Products: 20 Ne, 23 Na, 24 Mg, 27 Al E nuc = erg/g INTRODUCTION Present day experimental measurements of the 12 C+ 12 C cross section for E CM >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 E cm ∼ 1.5 MeV Which is the impact of such a hypothetical resonance on the behavior of stellar models? The cross section of this reaction should be known with high accuracy down to the E CM ∼ 1.5 MeV

STELLAR STRUCTURE: BASICS Hydrostatic equilibrium Non degenerate EOS A contracting star of mass M with constant composition supported by an ideal gas pressure will increase its central temperature following the above relation. This relation will hold until one of the above assumptions will be violated.....

This energy balances the energy radiated away Several lighter nuclei fuse to form a heavier one. The mass of the product nucleus is lower than the total mass of the reactant nuclei The mass defect is converted into energy The contraction halts and the temperature remains almost constant When the nuclear fuel is exhausted contraction starts again until the next nuclear fuel is ignited. STELLAR STRUCTURE: BASICS Nuclear Ignition: When the temperature is high enough the thermonuclear fusion reactions become efficient N.B. The nuclear burning slows down the evolution along the path

STELLAR STRUCTURE: BASICS For sufficiently high densities the electrons may become degenerate. Electron pressure tends to dominate over the total pressure If the electron gas becomes highly degenerate The electron pressure gradient balances the gravity The contraction stops and the structure radiates and cools down Onset of degeneracy: The relation does not hold anymore and the path in the plane changes

STELLAR STRUCTURE: BASICS The mass of the star plays a pivotal role: Non Degenerate Non Relativistic Non Relativistic Degenerate Relativistic Degenerate In different regions of the T-  plane, different physical phenomena dominate the total P

Non Degenerate Non Relativistic He burning C burning Ne burning O burning Non Relativistic Degenerate Increasing Mass Relativistic Degenerate CRITICAL MASSES The comparison between the path in the T-  plane and the ignition temperature of the various fuels determines naturally the existence of the various critical masses 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-  plane changes H burning

He WD H degenerate He MASS LOSS RGB H ignitionHe ignition

H He degenerate CO He WD H degenerate He CO WD MASS LOSS RGBTP-AGB H ignitionHe ignition C ignition

H He degenerate CO He WD H He CO degenerate ONeMg H degenerate He CO WD MASS LOSS ONeMg WD RGBTP-AGB SUPER-AGB MASS LOSS ECSN H ignitionHe ignition C ignition O ignition

H He degenerate CO He WD H He CO degenerate ONeMg H He CO NeO SiS O Fe H degenerate He CO WD MASS LOSS ONeMg WD RGBTP-AGB SUPER-AGB MASS LOSS ECSN CCSN H ignitionHe ignition C ignition O ignition

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

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

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

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

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

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

STANDARD MODELS M=7 M  Z=Z  Y=0.26 Sequence of events after core He depletion The He burning shifts in a shell which progressiely advances in mass The CO core grows, contracts and heats up Degeneracy begins to take place An increasing fraction of the CO becomes progressively degenerate and hence its contraction and heating progressively slows down. Neutrino emission becomes progressively more efficeint in the innermost zones which progressively cool down An off center maximum temperature developes due to the interplay bewteen the contraction and heating of the outer zones induced by the advancing of the He burning shell and cooling of the innermost regions due to neutrino emission The second dredge up takes place which stops the advancing of the He burning shell From this time onward the maximum temperature begins to decrease Since the maximum temperature does not reach the C ignition value, no C burning occurs  TP- AGB

STANDARD MODELS The first part of the evolution is similar to that of the 7M  but in this case the maximum off center temperature reaches the critical value for C-ignition C burning ignites off center Because of degeneracy the pressure does not increase and there is no consumption of energy through expansion  the Temperature rises even more and a flash occurs A convective shell forms and the matter heats up at constant density until degeneracy is removed then it expands. Beacuse of the the energy release the maximum temperature shifts inward in mass and a second C flash occurs The following evolution proceeds through a number of C flashes progressively more internal in mass until the nuclear burning reaches the center of the star  quiescent C burning begins After core C depletion an ONeMg core is formed that may, or may not, become degenerate  detailed calculation of the following evolution is required M=8 M  Z=Z  Y=0.26

STANDARD MODELS M=8 M  Z=Z  Y=0.26  =2.1  over =0.2h P Off center C-ignition Convective Envelope H Convective Core He Convective Core He Core 1 st dredge-up 2 nd dredge-up CO Core C Convective Shells He burning shell H burning shell

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

TEST CASE WITH MODIFIED 12 C+ 12 C REACTION Modification of the 12 C+ 12 C cross section following the procedure described by Bravo et al (in press): Include a resonance at E CM =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 at E CM = 2.14 MeV, and the assumed low-energy ghost resonance. = energy at which there is assumed a resonance = ghost resonance strength

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

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

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

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

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

ASTROPHYSICAL CONSEQUENCES 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 M UP ’-M UP ’’ The presence of a resonance at E CM =1.7 MeV with a maximum strength limited by the measured cross sections at low energy (2.10 MeV) implies a reduction of M UP from 7 M  to 4 M 

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. HHHe C C Ne O O Si O C C Ne O O Si O Central burning  formation of a convective core Central exhaustion  shell burning  convective shell Local exhaustion  shell burning shifts outward in mass  convective shell

ADVANCED BURNING STAGES: INTERNAL EVOLUTION C C C C He Ne O O O Si He H H C Ne O O Si 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. Si The basic rule is that the higher is the mass of the CO core, the lower is the 12 C left over by core He burning, the less efficient is the C shell burning and hence lower is the number of C convective shells.

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

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

THE FINAL FATE OF A MASSIVE STAR STANDARD MODELS The limiting mass between NS and BH froming SNe : M NS/BH ~ 22 M  Maximum mass contributing to the enrichment of the ISM: M pollute ~ 30 M 

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

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

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

CONSEQUENCES ON THE EXPLOSION FALLBACK

The presence of a resonance at E CM =1.7 MeV with a maximum strength limited by the measured cross sections at low energy (2.10 MeV) implies ASTROPHYSICAL CONSEQUENCES The increase of the limiting mass between NS and BH froming SNe : M NS/BH > 25 M  The increase of the maximum mass contributing to the enrichment of the ISM: M pollute > 30 M  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 The results shown for the 25 M  model can vary depending on the initial mass

SUMMARY 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 M UP ’-M UP ’’ Increasing of the limiting mass between NS and BH froming SNe Increasing of the maximum mass contributing to the enrichment of the ISM ATROPHYSICAL RELEVANCE OF THE 12 C+ 12 C REACTION Consequences of the presence of a hypothetical resonance close to the Gamow peak may: Decreasing M UP Measurements for energies down to the Gamow peak strongly needed in order to evaluate quantitatively these effects