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Late Burning Stages

Late Burning Stages. Late Burning Stages. Late Burning Stages. Late Burning Stages. 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.

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Late Burning Stages

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  1. Late Burning Stages

  2. Late Burning Stages

  3. Late Burning Stages

  4. Late Burning Stages

  5. 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

  6. 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

  7. 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%

  8. 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 ~ 1/3C+C, XNe ~ 30% - this is not a major burning stage

  9. 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

  10. 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

  11. 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

  12. 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

  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 • Yi(T,,Yl) for thermal equilibrium, where Yl is the ratio of leptons to nucleons • if ’s can escape (usually the case) use Yeinstead, where Ye is the usual e- fraction Y(e-) - Y(e+) • This is Nuclear Statistical Equilibrium (NSE) • Usually holds at T9 > 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 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

  16. 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

  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 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

  18. 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

  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 - 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

  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

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