Late Burning Stages

Late Burning Stages

fuel q(erg g-1) T/109

1H 5-8e18 0.014He 7e17 0.212C 5e17 0.820Ne 1.1e17 1.516O 5e17 228Si 0-3e17 3.556Ni -8e18 6-10

Late Burning Stages

fuel q(erg g-1) T/109

1H 5-8e18 0.014He 7e17 0.212C 5e17 0.820Ne 1.1e17 1.516O 5e17 228Si 0-3e17 3.556Ni -8e18 6-10

Late Burning Stages

fuel q(erg g-1)

T/109 length of core burning

1H 5-8e18 0.01 106-107 yr4He 7e17 0.2 105 yr12C 5e17 0.8 100 yr20Ne 1.1e17 1.5 1 yr16O 5e17 2 0.5 yr28Si 0-3e17 3.5 few days56Ni -8e18 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

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

~ 3x107 s

• T9 ~ 1.5

> 105 g cm-3

• SR ~ 0.1-0.2 (core), 1.5 (shell)

(neutron excess) ~ 2x10-3

Ne ~ 1/3C+C, XNe ~ 30% - this is not a major burning stage

Neon burning

• 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 e- capture less common

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?

• 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

– 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• 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

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∂H

∂Yi

= μ i

QSE & NSE

• 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) = Zp + (A-Z)n, = 2(p + n)

• Iterate to get abundances for all elements in network

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i = kT lnN(i)

gi

2πh2

mikT

⎛

⎝ ⎜

⎞

⎠ ⎟

3 / 2 ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥+ mic

2

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) goes up & equilibrium settles on nuclei w/

• =7x10-2 54Fe, =0.1 56Fe

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Z

N≈

Z

N

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

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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…

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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

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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

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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

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