12 c+ 12 c reaction and astrophysical implications

12C+12C REACTION AND ASTROPHYSICAL IMPLICATIONS

Marco LimongiINAF – Osservatorio Astronomico di Roma, ITALY

Institute for the Physics and the Mathematics of the Universe, [email protected]

Ne)C,C( 201212 α

Na)C,C( 231212 p

Ne),Na( 2023 αp

Mgγ),Na( 2423 p

Mg)Ne( 2420 α Ne)O( 2016 ,α

Mg)Na( 2623 pα,

Mg),(Mg 2524 n

Mg)Al()Mg( 252524 βγp,

Mg)Na(),(Na 242423 n

Si),(Mg 2824

Alγ),Mg()Al(γ),Mg()Ne( 2726262522 pβpnα,

Si),(Al 2827 p

Mg),(Al 2427 p

Si)Al(),(Al 282827 n

Carbon Burning

Main Products: 20Ne, 23Na, 24Mg, 27Al

Enuc = 4.00 1017 erg/g

INTRODUCTION

Present day experimental measurements of the 12C+12C cross

section for ECM>2.10 MeVBecause 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 MeVWhich 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

ECM∼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 nucleiThe mass defect is converted into energy

The contraction halts and the temperature remains almost constantWhen the nuclear fuel is exhausted contraction starts again until the next nuclear fuel is ignited.


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


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


The mass of the star plays a pivotal role:

Non DegenerateNon Relativistic Non

Relativistic Degenerate

Relativistic Degenerat

e

In different regions of the T-r plane, different physical phenomena dominate the total P

Non DegenerateNon Relativistic

He burning

C burningNe burningO burning

Non Relativistic Degenerate

Increasing Mass


e

CRITICAL MASSESThe comparison between the path in the T-r 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-r plane changes

H burning

He WD

Hdegenerate

He

MASS LOSSRGB

H ig

nitio

n

He ig

nitio

n

HHe

degenerateCO

He WD

Hdegenerate

He

CO WD

MASS LOSS MASS LOSSRGB TP-AGB

H ig

nitio

n

He ig

nitio

n

C ig

nitio

n

HHe

degenerateCO

He WD

HHe

COdegenerate

ONeMgHdegenerate

He

CO WD

MASS LOSS MASS LOSS

ONeMgWD

RGB TP-AGBSUPER-AGB

MASS LOSSECSN

H ig

nitio

n

He ig

nitio

n

C ig

nitio

n

O ig

nitio

n

HHe

degenerateCO

He WD

HHe

COdegenerate

ONeMg

HHe

CONeOSiSOFeH

degenerateHe

CO WD

MASS LOSS MASS LOSS

ONeMgWD

RGB TP-AGBSUPER-AGB

MASS LOSSECSN

CCSN

H ig

nitio

n

He ig

nitio

n

C ig

nitio

n

O ig

nitio

n

HHe

degenerateCO

He WD

HHe

COdegenerate

ONeMg

HHe

CONeOSiSOFeH

degenerateHe

CO WD

MASS LOSS MASS LOSS

ONeMgWD

RGB TP-AGBSUPER-AGB

MASS LOSSECSN

LOW MASS STARS

INTERMEDIATE MASS STARS MASSIVE STARSINTERMEDIATE

HIGH MASS STARS

H ig

nitio

n

He ig

nitio

n

C ig

nitio

n

O ig

nitio

n

CCSN

HHe

degenerateCO

He WD

HHe

COdegenerate

ONeMg

HHe

CONeOSiSOFeH

degenerateHe

CO WD

MASS LOSS MASS LOSS

ONeMgWD

RGB TP-AGBSUPER-AGB

MASS LOSSECSN

SNIa SNII / SNIb/c

H ig

nitio

n

He ig

nitio

n

C ig

nitio

n

O ig

nitio

n

CCSN

LOW MASS STARS


HIGH MASS STARS

CRITICAL MASSES

Non DegenerateNon Relativistic

He burning




e

H burning

He burning




e

CRITICAL MASSESIncreasing the efficiency of the 12C+12C reaction due to the presence of a resonance at low temperatures (energies) would decrease the value

of MUP

To be more quantitative detailed stellar models must be computed

H burningNon DegenerateNon Relativistic

STANDARD MODELS

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

Overshooting : over= 0.2 hP

12C+12C cross section : Caughlan and Fowler (1988) (CF88)

NO ROTATIONMixing-Length : = 2.1Semiconvection : semi= 0.02

Stability criterion for convection : Ledoux

SURVEY OF INTERMEDIATE MASS-MASSIVE STARS EVOLUTION

INITIAL SOLAR COMPOSITION (Asplund et al. 2009) – Y=0.26FULL COUPLING of: Physical Structure - Nuclear Burning - Chemical Mixing (convection, semiconvection, rotation)

TWO NUCLEAR NETWORKS: - 163 isotopes (448 reactions) H/He Burning - 282 isotopes (2928 reactions) Advanced Burning

STANDARD MODELSM=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 upDegeneracy 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 emissionThe second dredge up takes place which stops the advancing of the He burning shellFrom 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 centerBecause of degeneracy the pressure does not increase and there is no consumption of energy through expansion the Temperature rises even more and a flash occursA 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 MODELSM=8 M Z=Z Y=0.26 =2.1 over=0.2hP

Off center C-ignition

Convective Envelope

H Convective Core He Convective

Core

He Core

1st dredge-up

2nd dredge-up

CO Core

C Convective Shells

He burning shell

H burning shell

INTERMEDIATE HIGH MASS

STARS

INTERMEDIATE MASS STARS

HHe

degenerateCO

He WD

HHe

COdegenerate

ONeMg

HHe

CONeOSiSOFeH

degenerateHe

CO WD

MASS LOSS MASS LOSS

ONeMgWD

RGB TP-AGBSUPER-AGB

MASS LOSSECSN

CCSN

SNIa SNII / SNIb/c

H ig

nitio

n

He ig

nitio

n

C ig

nitio

n

O ig

nitio

n

?LOW MASS

STARS MASSIVE STARS

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

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 energyIn this case, the resonance strength is limited to 4.1 MeV for ER = 1.7 MeV, assuming the resonance width of GR = 10 keV

“Sta

ndar

d” C

igni

tion

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 at T9∼0.6

C burning “standard”

case

C burning test case

TEST CASE WITH MODIFIED 12C+12C REACTION

TEST CASES WITH MODIFIED 12C+12C REACTION

M=4 M Z=Z Y=0.26

Degenerate CO core TP-ABG


M=5 M Z=Z Y=0.26

Off center C ignition Convective Envelope


Core

He Core

1st dredge-up

2nd dredge-up

CO Core

C Convective Shells

He burning shell

H burning shell

C Conv. Core

Off center C ignition


M=5 M Z=Z Y=0.26

Convective Envelope


Core

He Core

1st dredge-up

2nd 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


HIGH MASS STARS

HHe

degenerateCO

He WD

HHe

COdegenerate

ONeMg

HHe

CONeOSiSOFeH

degenerateHe

CO WD

MASS LOSS MASS LOSS

ONeMgWD

RGB TP-AGBSUPER-AGB

MASS LOSSECSN

CCSN

SNIa SNII / SNIb/c

H ig

nitio

n

He ig

nitio

n

C ig

nitio

n

O ig

nitio

n

?

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 MUP’-MUP’’

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

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.

H HHe He CC

Ne O O Si SiOCC

Ne O O Si SiO

Central burning formation of a convective coreCentral exhaustion shell burning convective shell

Local exhaustion shell burning shifts outward in mass convective shell

ADVANCED BURNING STAGES: INTERNAL EVOLUTION

C

C

CC

He

NeO

OO

Si

Si

HeH H He

C

He

Ne OO

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 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.

PRESUPERNOVA STAR

The density structure of the star at the presupernova stage reflects this trend

Higher initial mass higher CO core less 12C 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 WaveCompression and Heating

Induced Expansion

and Explosion

Initial Remnan

t

Matter Falling Back

Mass Cut

Initial Remnan

t

Final Remnant

Matter Ejected into the ISMEkin1051 erg

The fallback depends on the binding energy

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

THE FINAL FATE OF A MASSIVE STARSTANDARD MODELS

The limiting mass between NS and BH froming SNe :

MNS/BH ~ 22 M

Maximum mass contributing to the enrichment of the ISM:

Mpollute ~ 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 Shell

C 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 15-20 M

CONSEQUENCES ON THE EXPLOSION

FALL

BACK

FALL

BACK

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

ASTROPHYSICAL CONSEQUENCES

The increase of the limiting mass between NS and BH froming SNe : MNS/BH > 25 M

The increase of the maximum mass contributing to the enrichment of the ISM:

Mpollute > 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 MUP’-

MUP’’Increasing of the limiting mass between NS and BH froming SNeIncreasing of the maximum mass contributing to the enrichment of the ISM

ATROPHYSICAL RELEVANCE OF THE 12C+12C REACTION

Consequences of the presence of a hypothetical resonance close to the Gamow peak may:

Decreasing MUP

Measurements for energies down to the Gamow peak strongly needed in order to evaluate quantitatively these effects

12 c+ 12 c reaction and astrophysical implications

Documents

resonance structure

path stellar structure

ignition temperature

total mass

plane changesstellar

mev stellar structure

star of mass

basicsnuclear ignition