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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 marco.limongi@ oa-roma.inaf.it. INTRODUCTION. Carbon Burning. Main Products :.

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12 C+ 12 C REACTION AND ASTROPHYSICAL IMPLICATIONS

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12 c 12 c reaction and astrophysical implications

12C+12C REACTION AND ASTROPHYSICAL IMPLICATIONS

Marco Limongi

INAF – Osservatorio Astronomico di Roma, ITALY

Institutefor the Physics and the Mathematicsof the Universe, JAPAN

[email protected]


12 c 12 c reaction and astrophysical implications

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?


12 c 12 c reaction and astrophysical implications

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.....


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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:


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

He WD

MASS LOSS

RGB

H

degenerate

He

He ignition

H ignition


12 c 12 c reaction and astrophysical implications

CO WD

He WD

MASS LOSS

MASS LOSS

RGB

TP-AGB

H

He

H

degenerate

CO

degenerate

He

He ignition

H ignition

C ignition


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

CRITICAL MASSES

O burning

Ne burning

C burning

He burning

H burning

Non Relativistic Degenerate

Relativistic Degenerate

Non Degenerate

Non Relativistic


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

TEST CASES WITH MODIFIED 12C+12C REACTION

M=4 M Z=Z Y=0.26

Degenerate CO core

TP-ABG


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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’’


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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.


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

PRESUPERNOVA EVOLUTION OF MASSIVE STARS: TEST CASE

A strong resonance at Gamow energies makes the C burning more efficient

Test Model


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

CONSEQUENCES ON THE EXPLOSION

FALLBACK

FALLBACK


12 c 12 c reaction and astrophysical implications

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


12 c 12 c reaction and astrophysical implications

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


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