12C+12C
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
12
C( 12 C, α )20 Ne
23
12
C( 12 C, p)23 Na
22
Ne(α  )24 Mg
20
Na( p, α )20 Ne
23
26
O( α,  )20 Ne
Mg( p, γ ) Al( β ) Mg
24
Mg (n,  ) 25 Mg
24
Mg( ,  ) 28 Si
23
Na(α, p) Mg
23
Na(n,  ) 24 Na(  ) 24 Mg
26
 26
27
Carbon Burning
 25
24
Na( p, γ) 24 Mg
Ne(α, n) Mg( p, γ) Al( β ) Mg( p, γ) Al
25
16
25
Main Products:
Al(n,  ) 28 Al(   ) 28 Si
27
Al( p,  ) 28 Si
27
27
20Ne, 23Na, 24Mg, 27Al
Enuc = 4.00 1017 erg/g
Al( p,  ) 24 Mg
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 E >2.10 MeV
CM
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?
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.....
STELLAR STRUCTURE: BASICS
Nuclear Ignition:
When the temperature is high enough the thermonuclear fusion reactions
become efficient
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
This energy balances the energy radiated away
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.
N.B. The nuclear burning slows down the evolution along the path
STELLAR STRUCTURE: BASICS
Onset of degeneracy:
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
The relation
does not hold anymore and the path in the plane changes
STELLAR STRUCTURE: BASICS
In different regions of the T-r plane, different physical phenomena dominate the total P
Non Degenerate
Non Relativistic
Non Relativistic
Degenerate
The mass of the star plays a pivotal role:
Relativistic
Degenerate
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
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
He WD
MASS LOSS
H
degenerate
He
He ignition
H ignition
RGB
CO WD
MASS LOSS
MASS LOSS
RGB
TP-AGB
degenerate
He
H
He
degenerate
CO
C ignition
H
He ignition
H ignition
He WD
CO WD
MASS LOSS
MASS LOSS
RGB
TP-AGB
degenerate
He
MASS LOSS
SUPER-AGB
H
He
CO
H
He
degenerate
CO
degenerate
C ignition
H
ECSN
ONeMg
O ignition
He WD
He ignition
H ignition
ONeMg
WD
CO WD
MASS LOSS
MASS LOSS
RGB
TP-AGB
degenerate
He
MASS LOSS
H
He
CO
H
He
degenerate
CO
CCSN
SUPER-AGB
degenerate
C ignition
H
ECSN
ONeMg
O ignition
He WD
He ignition
H ignition
ONeMg
WD
H
He
CO
NeO
O
SiS
Fe
INTERMEDIATE
MASS STARS
INTERMEDIATE
HIGH MASS STARS
He WD
CO WD
MASS LOSS
MASS LOSS
RGB
TP-AGB
degenerate
He
CO
CCSN
SUPER-AGB
H
He
CO
H
He
degenerate
ECSN
MASS LOSS
degenerate
C ignition
H
He ignition
H ignition
ONeMg
WD
MASSIVE STARS
ONeMg
O ignition
LOW MASS
STARS
H
He
CO
NeO
O
SiS
Fe
INTERMEDIATE
MASS STARS
INTERMEDIATE
HIGH MASS STARS
He WD
CO WD
MASS LOSS
MASS LOSS
RGB
TP-AGB
degenerate
He
ONeMg
WD
CO
CCSN
SUPER-AGB
H
He
CO
H
He
degenerate
ECSN
SNII / SNIb/c
MASS LOSS
degenerate
C ignition
H
He ignition
H ignition
SNIa
MASSIVE STARS
ONeMg
O ignition
LOW MASS
STARS
H
He
CO
NeO
O
SiS
Fe
INTERMEDIATE
MASS STARS
INTERMEDIATE
HIGH MASS STARS
He WD
CO WD
MASS LOSS
MASS LOSS
RGB
TP-AGB
degenerate
He
ONeMg
WD
CO
CCSN
SUPER-AGB
H
He
CO
H
He
degenerate
ECSN
SNII / SNIb/c
MASS LOSS
degenerate
C ignition
H
He ignition
H ignition
SNIa
MASSIVE STARS
ONeMg
O ignition
LOW MASS
STARS
H
He
CO
NeO
O
SiS
Fe
CRITICAL MASSES
O burning
Ne burning
C burning
He burning
H burning
Non Degenerate
Non Relativistic
Non Relativistic
Degenerate
Relativistic
Degenerate
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 Degenerate
Non Relativistic
Non Relativistic
Degenerate
Relativistic
Degenerate
To be more quantitative detailed stellar models must be computed
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 : over= 0.2 hP
Semiconvection : semi= 0.02
Mixing-Length :  = 2.1
NO ROTATION
TWO NUCLEAR NETWORKS:
- 163 isotopes (448 reactions) H/He Burning
- 282 isotopes (2928 reactions) Advanced Burning
12C+12C
cross section : Caughlan and 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
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  TPAGB
STANDARD MODELS
M=8 M Z=Z Y=0.26
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
STANDARD MODELS
M=8 M Z=Z Y=0.26 =2.1 over=0.2hP
Off center C-ignition
1st dredge-up
Convective Envelope
He burning shell
2nd dredge-up
H burning shell
He Core
H Convective
Core
He Convective
Core
CO Core
C Convective Shells
INTERMEDIATE
MASS STARS
INTERMEDIATE
HIGH MASS STARS
?
CO WD
MASS LOSS
MASS LOSS
RGB
TP-AGB
degenerate
He
ONeMg
WD
CO
CCSN
SUPER-AGB
H
He
CO
H
He
degenerate
ECSN
SNII / SNIb/c
MASS LOSS
degenerate
C ignition
H
He ignition
H ignition
SNIa
He WD
MASSIVE STARS
ONeMg
O ignition
LOW MASS
STARS
H
He
CO
NeO
O
SiS
Fe
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
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
“Standard” C ignition
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
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 at T9∼0.6
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 ignition
Convective Envelope
1st dredge-up
He burning shell
2nd dredge-up
C Convective Shells
H burning shell
He Core
H Convective
He Convective
Core
Core
CO Core C Conv.
Core
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
He Convective
Core
Core
CO Core C Conv.
Off center C ignition
Core
INTERMEDIATE
MASS STARS
INTERMEDIATE
HIGH MASS STARS
?
CO WD
MASS LOSS
MASS LOSS
RGB
TP-AGB
degenerate
He
ONeMg
WD
CO
CCSN
SUPER-AGB
H
He
CO
H
He
degenerate
ECSN
SNII / SNIb/c
MASS LOSS
degenerate
C ignition
H
He ignition
H ignition
SNIa
He WD
MASSIVE STARS
ONeMg
O ignition
LOW MASS
STARS
H
He
CO
NeO
O
SiS
Fe
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’’
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
He
C
C
O
Ne O
Si
O Si
H
He
C
C
O
Ne O
Central burning  formation of a convective core
Central exhaustion  shell burning  convective shell
Local exhaustion  shell burning shifts outward in mass
 convective shell
Si
O Si
ADVANCED BURNING STAGES: INTERNAL EVOLUTION
He
He
C
O
C
O
C
H
He
C
Ne O
Si
C
Si
H
He
Ne O
O
Si
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.
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
A less efficient nuclear burning means stronger contraction of the CO core.
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
EXPLOSION AND FALLBACK
Shock Wave
Compression and
Heating
Induced
Expansion
and
Explosion
Initial
Remnant
Matter
Falling Back
Matter Ejected into the
ISM
Ekin1051 erg
Mass Cut
Initial
Remnant
Final Remnant
Fe core
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
PRESUPERNOVA EVOLUTION OF MASSIVE STARS: TEST CASE
A strong resonance at Gamow energies makes the C burning more efficient
Test Model
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
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
FALLBACK
FALLBACK
CONSEQUENCES ON THE EXPLOSION
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 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
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
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 limiting mass between NS and BH froming SNe
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