Core Collapse Supernovae

1. Core Collapse Supernovae

2. Core Collapse 0.  cooling gives a small core & large mantle - calculations without it have overly large Fe cores. Get a Chandrasekhar mass Fe core • Bad: binding energy of Fe peak nuclei very small or negative - no energy generation • Worse: neutronization removes electrons • Worse yet: e-e+ pair production removes energy from photons, drives EOS  < 4/3 • Worst: photodisintegration of Fe peak into ’s removes 8 MeV/nucleon

3. Core Collapse  until core material more dense than nuclei - neutron degeneracy pressure takes over support - hot proto-neutron star Collapse is supersonic - infall of material from inside out Early infall bounces off proto-NS, propagating shock through star - super... No... wait... ’s leak out - pressure drops photodisintegration - pressure drops Shock can’t overcome ram pressure of infalling material Shock stalls - forms standing accretion shock Need extra energy source

4. Core Collapse

5. Core Collapse Explosion needs an extra energy source Minimum observed NS mass ~ 1.3 M Mchandra (Ye=0.5) = 1.44 M Newtonian binding energy Mass deficit is gravitational binding energy of NS - two orders of magnitude larger than energy needed to disrupt rest of star 1% of binding energy can power supernova, BUT energy comes out almost entirely as neutrinos How to couple?

6. Core Collapse •  transport: Full transport calculations show  heating alone won’t power the supernova •  gain region: ’s trapped in a region inside stalled shock - convection draws energy & entropy from ’s near NS, where trapping efficient, transport to vicinity of shock where coupling efficient, repeat - Heat engine cycle growsslowly until it can overcome ram pressure  usually at sharp density drop at a composition boundary. Can create successful explosions in 3D, weak explosions in 180o of 2D, or fail in 90o of 2D - caveat emptor • Rotating collapse generating an MHD jet - looks unlikely in most cases but can’t be ruled out yet

7. Core Collapse Convective region

8. Core Collapse • Bottom line: mechanism very uncertain • Calculation extremely difficult - has to be 3D, limited by courant condition with sound speed ~ 1/3c • Our simulations run at ~ 20/week, so introduce approximations: • Bad - remove NS and replace with hard boundary condition - changes energetics, remnant mass, & yields • Worse - Say to hell with it and go in 1D - much faster, but eliminates any realistic mixing and fallback. Also, explosion energies completely arbitrary unless modelling a particular SN with observational constraints on explosion energy • The phrase “mass cut” may be the worst thing to every happen to the supernova field • Never trust a 1D yield. Or 3D, but 1D is worse.

9. Supernovae • Nature can make a SN, so let’s continue blithely along • Shock gets restarted somehow and propagates through star • Shock is aspherical from several sources • rotation-low order global modes

10. Supernovae • Nature can make a SN, so let’s continue blithely along • Shock gets restarted somehow and propagates through star • Shock is aspherical from several sources • rotation -low order global asymmetries • waves - low order global modes + high order stochastic modes

11. Supernovae • Nature can make a SN, so let’s continue blithely along • Shock gets restarted somehow and propagates through star • Shock is aspherical from several sources • rotation -low order global asymmetries • waves - low order global modes + high order stochastic modes • Rayleigh-Taylor & Richtmeyer-Meshkov instabilities as high entropy shock moves through low entropy star

12. Supernovae • Observations • Obvious morphology in remnants

13. Supernovae • Observations • Obvious morphology in remnants • Many unresolved remnants have polarization which indicates bipolarity

14. Supernovae • Observations • Obvious morphology in remnants • Many unresolved remnants have polarization which indicates bipolarity • H at low velocities & Ni at high velocities in SN87A. Material which starts at smallest radii should have smallest velocities

15. Supernova Nucleosynthesis • Many processes represented • C & Ne burning - quasistatic -occurs during stellar evolution. C & Ne burning shells get ejected in the explosion. This includes weak s-process (~Cu-Ge) • O burning - explosive - occurs when shock passes through O burning shell. Products of stellar oxygen burning are significantly reprocessed by explosion

16. v2 v2’ v1 D 2, 2, P2 2, 2, P2 1, 1, P1 1, 1, P1 Interlude, with shocks downstream (unshocked gas) upstream (shocked gas) direction of shock In shock reference frame In gas frame. D = shock speed

17. Shocks • Assume shock infinitesimally thin, so /t =0, v = 0 v1=D speed of shock v2’=v1-v2 = D-v2 velocity of shocked material wrt unshocked gas: speed of material after shock passes Mach # of shock = D/c1 1v1 = 2v2 = j (mass flux/area) P1+ 1v12 = P2 + 2v22 pressure + ram pressure 1 + 1/2v12 + P1/1 = 2 + 1/2v22 + P2/2 total energy or 1D = 2(D-v2’) = j (mass flux/area) P1+ 1D2 = P2 + 2 (D-v2’)2 pressure + ram pressure 1 + 1/2D2 + P1/1 = 2 + 1/2(D-v2’)2 + P2/2 total energy

18. P2,v2 slope = j2 P1,v1 Shocks • Say we know all quantities 1. We can get 2 from P2, 2 with an equation of state. So we have 3 eqns with 3 unknowns. Shocks have 1 parameter, given an EOS and P1, 1 • Note, P2 always > P1, v1 > v2 • Entropy always increases for shocks. Greater P  greater S. Shocks are an irreversible thermodynamic process. Kinetic energy goes into internal energy of gas • Hugoniot curve connects P1,v1 to all other points in shocked material. Tangent to Hugoniot is an adiabat

19. Shocks • Useful expressions of the shock relations: • note, specific volume V = 1/

20. Shocks • Useful expressions of the shock relations: • note h = enthalpy =  + PV •  with EOS give Hugoniot. • In the strong shock limit (P2>>P1) change in internal energy = change in kinetic energy • energy conservation:  = PV

21. Shocks • For an ideal gas (P, cs2=P/)

22. Shocks • For an ideal gas (P, cs2=P/)

23. Shocks • Consider a region of a star with P=1.15e24 g s-2 cm-3, T=3.5e9 K, =3.7e6 g cm-3. We send through a shock at 20,000 km s-1 • P2~1.3e25 g s-2 cm-3  T = 6.4e9 K. 2~2.6e7 g cm-3 • NSE conditions