Transcript Late Burning Stages - University of Arizona

Late Burning Stages
Late Burning Stages
fuel
1H
4He
12C
20Ne
16O
28Si
56Ni
q(erg g-1)
5-8e18
7e17
5e17
1.1e17
5e17
0-3e17
-8e18
T/109
0.01
0.2
0.8
1.5
2
3.5
6-10
Late Burning Stages
fuel
1H
4He
12C
20Ne
16O
28Si
56Ni
q(erg g-1)
5-8e18
7e17
5e17
1.1e17
5e17
0-3e17
-8e18
T/109
0.01
0.2
0.8
1.5
2
3.5
6-10
Late Burning Stages
fuel
q(erg
g-1)
1H
5-8e18
4He
7e17
12C
5e17
20Ne 1.1e17
16O
5e17
28Si
0-3e17
56Ni
-8e18
T/109 length of core
burning
0.01 106-107 yr
0.2
105 yr
0.8
100 yr
1.5
1 yr
2
0.5 yr
3.5
few days
6-10 oh %#*@
Late Burning Stages
•QHe~QC+C~QO+O but He>> C+C >> O+O
O burning;  > 1020 erg g-1 s-1
C burning;  > 1017 erg g-1 s-1
He burning;  ~ 1012 erg g-1 s-1
If  = 99.9% of C+C rate of
burning must be 1000x
rate for 3 to produce
same  to support star fuel used up in 1/1000 of
the time
Carbon burning
 ~ 1010 s
Tignition ~6x108K (core), 1x109K (shell)
 ~ 105 g cm-3
SR ~ 0.4 (core), 1.5 (shell)
 (neutron excess) ~ 2x10-3
before C burning cores evolve at ~ constant SR T3
•  cooling reduces entropy, esp. at low mass where
degeneracy pressure prevents compressional
heating
• low masses have small C flash
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Carbon burning
• Several reaction channels
• 12C(12C,)20Ne
• 12C(12C,p)23Na
• 12C(12C,n)23Mg at high T
• 12C(12C,)24Mg small branching fraction
• Other relevant reactions
• 22Ne(,n)25Mg
• n excess in 22Ne & 18O ends up in 23Na, 25Mg, 26Mg,
27Al, & trans-Fe weak s-process below peak at N=50
(Cu, Ni, Zn, Ga, Ge, As, Se)
• 16O & 20Ne are most abundant species at C
exhaustion ~ 90%
Neon burning
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 ~ 3x107 s
T9 ~ 1.5
 > 105 g cm-3
SR ~ 0.1-0.2 (core), 1.5 (shell)
 (neutron excess) ~ 2x10-3
Ne ~ 1/3C+C, XNe ~ 30% - this is not a major burning
stage
Neon burning
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20Ne(,)16O
primary channel - photodisintegration,
not fusion, is the primary process for this stage
20Ne(,)24Mg also occurs
At end mostly 16O with 5-10% 24Mg & 28Si
small change in 
neutron excess mainly in 27Al, 29Si, 31P
Oxygen burning
 ~ 2x107 s
T9 ~ 2
 ~ 106 g cm-3
SR ~ 0.1-0.2 (core), 1.5 (shell)
 (neutron excess) ~ 6x10-3 in core, much higher than
solar - this material can’t get out of star
•  ~ 3x10-3 in shell since S higher  lower  ecapture less common
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Oxygen burning
• O burning more about competing processes
• 16O(16O,)32S dominates at low T
• 16O(16O,p)31P
• 16O(16O,n)31S
• 16O(16O,)28Si dominates at T9 > 2.8
• 16O(16O,2)24Mg
• 24Mg(,)28Si
•  moves into 34S
• 28Si & 32S dominate at end, but significant
abundances of other species
Silicon Burning?
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Not as such, in the sense of 28Si + 28Si  56Ni
More a matter of knocking ’s off of some things
and capturing them onto others
Different from other burning stages
1.
2.
3.
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Many competing processes
Rates are very fast
Reverse rates are important, I.e. rate[40Ca(,)44Ti] 
rate[44Ti(,)40Ca] - more common at high A where Q
values are small, prevents complete burning
Abundances reflect the available phase space
equilibrium between these various reactions
depends on T,,Ye
QSE & NSE

• calculate abundances from chemical potentials in the
usual thermodynamic way
• Minimize free energy of the ensemble
H
• Yi  i
derivative of free energy = chemical potential
• Yi(T,,Yl) for thermal equilibrium, where Yl is the ratio of
leptons to nucleons
• if ’s can escape (usually the case) use Ye instead,
where Ye is the usual e- fraction Y(e-) - Y(e+)
• This is Nuclear Statistical Equilibrium (NSE)
• Usually holds at T9 > 5
QSE & NSE
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calculating NSE
nucleus (Z,A) connected to (Z-1,A-1) by (,p), (p,)
so (Z,A) = (Z-1,A-1)+p
similarly, (Z,A) = (Z,A-1)+n
use recursion relations to get
(Z,A) = Zp + (A-Z)n,  = 2(p + n)
3/2

2  

N(i) 2
2
i  kT ln

  mic

 gi mi kT  

• Iterate to get abundances for all elements in network

QSE & NSE
• Now assume conditions are such that no equilibrium link exists
between two groups of nuclei because T or  are too low
– Si burning at T9 = 3-4
– -rich freezeout in SNe (more later)
– BB nucleosynthesis
• Each equilibrium group can be treated like NSE with a pivot nucleus
instead of p,n. The nucleus (Z1,A1) is arbitrary
• (Z,A) = (Z1,A1) + (Z-Z1)p + (A-A1-Z+Z1)n
QSE & NSE in stars
• As T, increase, equilibrium shifts from 28Si in a QSE
process dominated by  captures up through
intermediate mass nuclei (Ca,Ti,Cr,Mn) to Fe peak
• If 28Si  Fe peak faster than timescale for weak
reactions ( decay, ec) (explosive)
 56Ni (Z=N) which decays to 56Fe if T is low
 54Fe+2p if T high so  drive off 2p
• If 28Si  Fe peak slow (~105 s, T9 ~ 3.5 - Si burning) 
Z Z
goes up & equilibrium settles on nuclei w/ N  N
• =7x10-2  54Fe, =0.1  56Fe

QSE & NSE in stars
• At very high T photodisintegration important &
equilibrium shifts back to lower A
• Also occurs for very high 
• Dominant nuclei change from 56Ni  54Fe  56Fe 
58Fe  54Cr + 
• At T9 > 5 or Ye < 0.497 28Si  54Fe instead of 56Ni
– for typical conditions in stellar cores 54Fe/56Fe ~ 15, while solar
value is 0.061
– Neutron rich material in core doesn’t get out - 56Fe comes from
decay of Z=N 56Ni
QSE & NSE in stars
• At T9 > 5 or Ye < 0.497 28Si  54Fe instead of 56Ni
–
28Si
 56Ni is exothermic, 28Si  54Fe strongly endothermic
• Nuclear stability peaks at A = 56
– means Fe peak at peak of binding energy curve - requires
energy to go to either heavier or lighter nuclei
– no energy production - no hydrostatic support
Dynamics of Shell Burning
• The standard way of
describing shell burning is
the onion-skin model
• Happy, well-adjusted,
concentric layers of burning
products
• Each region has a spherical
layer where the appropriate
species is consumed, driving
a narrow convective shell
which lasts until all of the fuel
goes away, then a new shell
starts outside
Dynamics of Shell Burning
• A still life is a poor representation of a star
Dynamics of Shell Burning
• Caveats about 2D vs. 3D simulations:
– Vortex pinning in 2D gives cyclonic behavior
– amplitudes are ~ 10x too large
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Dynamics of Shell Burning
• For early burning stages the conventional pictures gives more
or less the right structure even though it’s missing physics
• for late stages though…
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Dynamics of Shell Burning
• for late stages though the behavior is fundamentally
different
• convective shell separated by radiative layers with
step-like composition changes is wrong picture
• Entire shell burning region of star is dynamically
connected & probably materially as well
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Dynamics of Shell Burning
• wave velocities comparable to convective velocities - Fwaves >
Frad, correlated on large spatial scales
• for SR = 1.5,  ~ 1.34 - star is only marginally stable - large
displacements
• entire region subject to non-linear instabilities & mixing
• radial displacements of >10% - large asymmetries w/ low order
modes
• center of mass may not coincide w/ geometric center
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Dynamics of Shell Burning
• material may be drawn all the way from C layer to Si layer
• C-rich material will burn at the appropriate T at a given radius energy generation will make the parcel buoyant, turn it around
• Shell burning region consists of streamers of material
potentailly traversing entire region which flash-burn at
conditions depending on composition
• energy generation not spherical - positive feedback when large
plume ingests fuel
• effect on nucleosynthesis, Urca,  cooling
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.