1. Late Burning Stages

2. fuelq(erg g -1 )T/10 9 1H1H5-8e180.01 4 He7e170.2 12 C5e170.8 20 Ne1.1e171.5 16 O5e172 28 Si0-3e173.5 56 Ni-8e186-10

3. Late Burning Stages fuelq(erg g -1 )T/10 9 1H1H5-8e180.01 4 He7e170.2 12 C5e170.8 20 Ne1.1e171.5 16 O5e172 28 Si0-3e173.5 56 Ni-8e186-10

4. Late Burning Stages fuelq(erg g -1 ) T/10 9 length of core burning 1H1H5-8e180.0110 6 -10 7 yr 4 He7e170.210 5 yr 12 C5e170.8100 yr 20 Ne1.1e171.51 yr 16 O5e1720.5 yr 28 Si0-3e173.5few days 56 Ni-8e186-10oh %#*@

5. Late Burning Stages Q He ~Q C+C ~Q O+O but  He >>  C+C >>  O+O O burning;  > 10 20 erg g -1 s -1 C burning;  > 10 17 erg g -1 s -1 He burning;  ~ 10 12 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

6. Carbon burning  ~ 10 10 s T ignition ~6x10 8 K (core), 1x10 9 K (shell)  ~ 10 5 g cm -3 S R ~ 0.4 (core), 1.5 (shell)  (neutron excess) ~ 2x10 -3 before C burning cores evolve at ~ constant S R -  T 3 cooling reduces entropy, esp. at low mass where degeneracy pressure prevents compressional heating low masses have small C flash

7. Carbon burning Several reaction channels 12 C( 12 C,  ) 20 Ne 12 C( 12 C,p) 23 Na 12 C( 12 C,n) 23 Mg at high T 12 C( 12 C,  ) 24 Mg small branching fraction Other relevant reactions 22 Ne( ,n) 25 Mg n excess in 22 Ne & 18 O ends up in 23 Na, 25 Mg, 26 Mg, 27 Al, & trans-Fe weak s-process below peak at N=50 (Cu, Ni, Zn, Ga, Ge, As, Se) 16 O & 20 Ne are most abundant species at C exhaustion ~ 90%

8. Neon burning  ~ 3x10 7 s T 9 ~ 1.5  > 10 5 g cm -3 S R ~ 0.1-0.2 (core), 1.5 (shell)  (neutron excess) ~ 2x10 -3  Ne ~ 1/3  C+C, X Ne ~ 30% - this is not a major burning stage

9. Neon burning 20 Ne( ,  ) 16 O primary channel - photodisintegration, not fusion, is the primary process for this stage 20 Ne( ,  ) 24 Mg also occurs At end mostly 16 O with 5-10% 24 Mg & 28 Si small change in  neutron excess mainly in 27 Al, 29 Si, 31 P

10. Oxygen burning  ~ 2x10 7 s T 9 ~ 2  ~ 10 6 g cm -3 S R ~ 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

11. Oxygen burning O burning more about competing processes 16 O( 16 O,  ) 32 S dominates at low T 16 O( 16 O,p) 31 P 16 O( 16 O,n) 31 S 16 O( 16 O,  ) 28 Si dominates at T 9 > 2.8 16 O( 16 O,2  ) 24 Mg 24 Mg( ,  ) 28 Si  moves into 34 S 28 Si & 32 S dominate at end, but significant abundances of other species

12. Silicon Burning? Not as such, in the sense of 28 Si + 28 Si  56 Ni More a matter of knocking  ’s off of some things and capturing them onto others Different from other burning stages 1.Many competing processes 2.Rates are very fast 3.Reverse rates are important, I.e. rate[ 40 Ca( ,  ) 44 Ti]  rate[ 44 Ti( ,  ) 40 Ca] - 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, ,Y e

13. QSE & NSE calculate abundances from chemical potentials in the usual thermodynamic way Minimize free energy of the ensemble derivative of free energy = chemical potential Y i (T, ,Y l ) for thermal equilibrium, where Y l is the ratio of leptons to nucleons if ’s can escape (usually the case) use Y e instead, where Y e is the usual e - fraction Y(e - ) - Y(e + ) This is Nuclear Statistical Equilibrium (NSE) Usually holds at T 9 > 5

14. 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) = Z  p + (A-Z)  n,   = 2(  p +  n ) Iterate to get abundances for all elements in network

15. 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 T 9 = 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 (Z 1,A 1 ) is arbitrary  (Z,A) =  (Z 1,A 1 ) + (Z-Z 1 )  p + (A-A 1 -Z+Z 1 )  n

16. QSE & NSE in stars As T,  increase, equilibrium shifts from 28 Si in a QSE process dominated by  captures up through intermediate mass nuclei (Ca,Ti,Cr,Mn) to Fe peak If 28 Si  Fe peak faster than timescale for weak reactions (  decay, ec) (explosive)  56 Ni (Z=N) which decays to 56 Fe if T is low  54 Fe+2p if T high so  drive off 2p If 28 Si  Fe peak slow (~10 5 s, T 9 ~ 3.5 - Si burning)  goes up & equilibrium settles on nuclei w/  =7x10 -2  54 Fe,  =0.1  56 Fe

17. 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 56 Ni  54 Fe  56 Fe  58 Fe  54 Cr +  At T 9 > 5 or Y e < 0.497 28 Si  54 Fe instead of 56 Ni –for typical conditions in stellar cores 54 Fe/ 56 Fe ~ 15, while solar value is 0.061 –Neutron rich material in core doesn’t get out - 56 Fe comes from decay of Z=N 56 Ni

18. QSE & NSE in stars At T 9 > 5 or Y e < 0.497 28 Si  54 Fe instead of 56 Ni – 28 Si  56 Ni is exothermic, 28 Si  54 Fe 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

19. 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

20. Dynamics of Shell Burning A still life is a poor representation of a star

21. Dynamics of Shell Burning Caveats about 2D vs. 3D simulations: –Vortex pinning in 2D gives cyclonic behavior –amplitudes are ~ 10x too large

22. 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…

23. 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

24. Dynamics of Shell Burning wave velocities comparable to convective velocities - F waves > F rad, correlated on large spatial scales for S R = 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

25. 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