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12C+12C REACTION AND ASTROPHYSICAL IMPLICATIONS
Marco LimongiINAF – Osservatorio Astronomico di Roma, ITALY
Institute for the Physics and the Mathematics of the Universe, JAPANmarco.limongi@oa-roma.inaf.it
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 pMg),(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 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 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 burning
Ne burningO burning
Non Relativistic Degenerate
Increasing Mass
Relativistic Degenerat
e
CRITICAL MASSES
The 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
H
degenerateHe
MASS LOSS
RGB
H ig
nit
ion
He ignit
ion
HHe
degenerateCO
He WD
H
degenerateHe
CO WD
MASS LOSS MASS LOSS
RGB TP-AGB
H ig
nit
ion
He ignit
ion
C ignit
ion
HHe
degenerateCO
He WD
HHe
CO
degenerateONeMg
H
degenerateHe
CO WD
MASS LOSS MASS LOSS
ONeMgWD
RGB TP-AGB
SUPER-AGB
MASS LOSS
ECSN
H ig
nit
ion
He ignit
ion
C ignit
ion
O ignit
ion
HHe
degenerateCO
He WD
HHe
CO
degenerateONeMg
HHe
CONeO
SiSO
FeH
degenerateHe
CO WD
MASS LOSS MASS LOSS
ONeMgWD
RGB TP-AGB
SUPER-AGB
MASS LOSS
ECSN
CCSN
H ig
nit
ion
He ignit
ion
C ignit
ion
O ignit
ion
HHe
degenerateCO
He WD
HHe
CO
degenerateONeMg
HHe
CONeO
SiSO
FeH
degenerateHe
CO WD
MASS LOSS MASS LOSS
ONeMgWD
RGB TP-AGB
SUPER-AGB
MASS LOSS
ECSN
LOW MASS STARS
INTERMEDIATE MASS STARS
MASSIVE STARSINTERMEDIATE HIGH MASS
STARS
H ig
nit
ion
He ignit
ion
C ignit
ion
O ignit
ion
CCSN
HHe
degenerateCO
He WD
HHe
CO
degenerateONeMg
HHe
CONeO
SiSO
FeH
degenerateHe
CO WD
MASS LOSS MASS LOSS
ONeMgWD
RGB TP-AGB
SUPER-AGB
MASS LOSS
ECSNSNIa SNII / SNIb/c
H ig
nit
ion
He ignit
ion
C ignit
ion
O ignit
ion
CCSN
LOW MASS STARS
INTERMEDIATE MASS STARS
MASSIVE STARSINTERMEDIATE HIGH MASS
STARS
HHe
degenerateCO
He WD
HHe
CO
degenerateONeMg
HHe
CONeO
SiSO
FeH
degenerateHe
CO WD
MASS LOSS MASS LOSS
ONeMgWD
RGB TP-AGB
SUPER-AGB
MASS LOSS
ECSNSNIa SNII / SNIb/c
H ig
nit
ion
He ignit
ion
C ignit
ion
O ignit
ion
CCSN
LOW MASS STARS
INTERMEDIATE MASS STARS
MASSIVE STARSINTERMEDIATE HIGH MASS
STARS
CRITICAL MASSES
Non DegenerateNon Relativistic
He burning
C burning
Ne burningO burning
Non Relativistic Degenerate
Relativistic Degenerat
e
H burning
He burning
C burning
Ne burningO burning
Non Relativistic Degenerate
Relativistic Degenerat
e
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
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 : aover= 0.2 hP
12C+12C cross section : Caughlan and Fowler (1988) (CF88)
NO ROTATION
Mixing-Length : a = 2.1
Semiconvection : asemi= 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 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 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 MODELS
M=8 M Z=Z Y=0.26 a=2.1 aover=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
CO
degenerateONeMg
HHe
CONeO
SiSO
FeH
degenerateHe
CO WD
MASS LOSS MASS LOSS
ONeMgWD
RGB TP-AGB
SUPER-AGB
MASS LOSS
ECSN
CCSN
SNIa SNII / SNIb/c
H ig
nit
ion
He ignit
ion
C ignit
ion
O ignit
ion
?
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“S
tandard
” C
ignit
ion
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
TEST CASES WITH MODIFIED 12C+12C REACTION
M=5 M Z=Z Y=0.26
Off center C ignitionConvective 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
C Conv. Core
Off center C ignition
TEST CASES WITH MODIFIED 12C+12C REACTION
M=5 M Z=Z Y=0.26
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
C Conv. Core
C Convective Shells
C Conv. Core
Off center C ignition
LOW MASS STARS
INTERMEDIATE MASS STARS
MASSIVE STARSINTERMEDIATE HIGH MASS
STARS
HHe
degenerateCO
He WD
HHe
CO
degenerateONeMg
HHe
CONeO
SiSO
FeH
degenerateHe
CO WD
MASS LOSS MASS LOSS
ONeMgWD
RGB TP-AGB
SUPER-AGB
MASS LOSS
ECSN
CCSN
SNIa SNII / SNIb/c
H ig
nit
ion
He ignit
ion
C ignit
ion
O ignit
ion
?
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 OO
SiSiOC
C
Ne OO
SiSiO
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
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 STAR
STANDARD 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
BA
CK
FALL
BA
CK
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 SNe
Increasing 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
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