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 ? lt 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 cant 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 (Ye0.5) 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 wont 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 cant 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 lets 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 lets 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 lets 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
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
• v1D speed of shock
• v2v1-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
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 gt P1, v1 gt 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 (P2gtgtP1) 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 P1.15e24 g s-2
  cm-3, T3.5e9 K, ?3.7e6 g cm-3. We send through
  a shock at 20,000 km s-1
• P21.3e25 g s-2 cm-3 ? T 6.4e9 K. ?22.6e7 g
  cm-3
• NSE conditions