W. Bauer, Breckenridge 031 Supernova Collapse Dynamics Wolfgang Bauer Michigan State University Pre-collapse dynamics Pre-collapse dynamics Kinetic theory for collapse Kinetic theory for collapse Similarities to nuclear dynamics simulation Similarities to nuclear dynamics simulation

W. Bauer, Breckenridge 032 Nassau Declared victory in search for fragmentation critical point properties Declared victory in search for fragmentation critical point properties

W. Bauer, Breckenridge 033 Supernova Explosion Galaxy NGC3310 Supernova 1991N Galaxy NGC3310 Supernova 1991N N.A.Sharp, G.J.Jacoby/NOAO/AURA/NSF After Before Typical light curve

W. Bauer, Breckenridge 034 Supernova Remnants Cassiopeia supernova remnant observed in X- rays (Chandra), 10,000 light years from Earth Cassiopeia supernova remnant observed in X- rays (Chandra), 10,000 light years from Earth Color composite of supernova remnant E : X-ray (blue), optical (green), and radio (red) Color composite of supernova remnant E : X-ray (blue), optical (green), and radio (red)

W. Bauer, Breckenridge 035 Crab Nebula – 6500 light years from here – Supernova in 1054 – Visible in broad daylight for several weeks – Left behind neutron star the size of Manhattan Hubble Hubble Chandra / Hubble

W. Bauer, Breckenridge 036 Supernovae Type 1 Type 1 – White dwarf exceeds its Chandrasekhar Mass (~1.4 M  ) due to accretion and collapses Type 2 Type 2 – Powered by gravitational energy released during star’s late stage iron core collapse – Mass range 11 M  to 40 M  at ZAMS (zero age main sequence; mass of star at start of its evolution) Type 2 has hydrogen lines, type 1 does not Type 2 has hydrogen lines, type 1 does not Here: focus on type 2 and use M=15 M  Here: focus on type 2 and use M=15 M 

W. Bauer, Breckenridge 037 Stellar Evolution Conventional stellar energy production via hydrogen fusion (t~10 7 y for 20 M  ) Conventional stellar energy production via hydrogen fusion (t~10 7 y for 20 M  ) Late stages of evolution Late stages of evolution – Triple alpha process (t~ 10 6 y) – Burning of C (t~300y), Ne, O (t~6months), Si (2days) occurs successively in the center of the star (higher and higher T) – Final products: 56 Ni, 56 Fe or 54 Fe (iron core mass typically 10%)

W. Bauer, Breckenridge 038 Initial Conditions for Core Collapse Woosley, Weaver 86 Iron Core

W. Bauer, Breckenridge 039 Instabilities and Onset of Collapse Electron Capture (dominant for ZAMS < 20 M  ) Electron Capture (dominant for ZAMS < 20 M  ) – Reaction – Reduced electron fraction and therefore decrease stabilizing electron pressure – Neutrinos carry entropy and energy out of star Photodisintegration (dominant for ZAMS > 20 M  ) Photodisintegration (dominant for ZAMS > 20 M  ) – Reactions – Also reduce temperature and therefore pressure

W. Bauer, Breckenridge 0310

W. Bauer, Breckenridge 0311 Supernova Nucleosythesis Mezzacappa

W. Bauer, Breckenridge D Hydro Simulations Strong convection effects Strong convection effects Turbulence Turbulence Mezzacappa et al. (98)

W. Bauer, Breckenridge d Fryer, Warren, ApJ 02 Very preliminaryVery preliminary Similar convection as seen in their 2d workSimilar convection as seen in their 2d work Explosion energy 3foe Explosion energy 3foe t expl = s t expl = s

W. Bauer, Breckenridge 0314 Hydro Simulations Tough problem for hydro Tough problem for hydro – Length scales vary drastically in time – Multiple fluids – Strongly time dependent viscosity – Very large number of time steps Special relativity, causality, … Special relativity, causality, … Huge magnetic fields Huge magnetic fields 3D simulations needed 3D simulations needed – Giant grids

W. Bauer, Breckenridge 0315 Simulations of Nuclear Collisions Hydro, mean field, cascades Hydro, mean field, cascades Numerical solution of transport theories Numerical solution of transport theories – Need to work in 6d phase space => prohibitively large grids (20 3 x40 2 x80~10 9 lattice sites) – Idea: Only follow initially occupied phase space cells in time and represent them by test particles – One-body mean-field potentials ( , p,  ) via local averaging procedures – Test particles scatter with realistic cross sections => (exact) solution of Boltzmann equation (+Pauli, Bose) – Very small cross sections via perturbative approach – Coupled equations for many species no problem – Typically test particles/nucleon

W. Bauer, Breckenridge 0316 Example Density in reaction plane Density in reaction plane Integration over momentum space Integration over momentum space Cut for z= fm Cut for z= fm

W. Bauer, Breckenridge 0317 Momentum Space Output quantities (not input!) Output quantities (not input!) Momentum space information on Momentum space information on – Thermalization & equilibration – Flow – Particle production Shown here: local temperature Shown here: local temperature

W. Bauer, Breckenridge 0318 Try this for Supernovae! 2 M  in iron core = 2x10 57 baryons 2 M  in iron core = 2x10 57 baryons 10 7 test particles => 2x10 50 baryons/test particle 10 7 test particles => 2x10 50 baryons/test particle Need time-varying grid for (non-gravity) potentials, because whole system collapses Need time-varying grid for (non-gravity) potentials, because whole system collapses Need to think about internal excitation of test particles Need to think about internal excitation of test particles Can create -test particles and give them finite mean free path => Boltzmann solution for - transport problem Can create -test particles and give them finite mean free path => Boltzmann solution for - transport problem Can address angular momentum question Can address angular momentum question

W. Bauer, Breckenridge 0319 Numerics Test particle equations of motion Test particle equations of motion Nuclear EoS evaluated on spherical grid Nuclear EoS evaluated on spherical grid Newtonian monopole approximation for gravity Newtonian monopole approximation for gravity

W. Bauer, Breckenridge 0320 Equation of State Low density: Low density: – Degenerate e-gas High density High density – Dominated by nuclear EoS – Isospin term in nuclear EoS becomes dominant, Y e ~0.4 High density neutron rich EoS can be explored by GSI upgrade and/or RIA High density neutron rich EoS can be explored by GSI upgrade and/or RIA

W. Bauer, Breckenridge 0321 Electron Fraction, Y e Strongly density dependent Strongly density dependent Neutrino cooling Neutrino cooling

W. Bauer, Breckenridge 0322 Internal Heating of Test Particles Test particles represent mass of order M earth. Test particles represent mass of order M earth. Internal excitation of test particles becomes important for energy balance Internal excitation of test particles becomes important for energy balance

W. Bauer, Breckenridge 0323 Neutrinos Neutrinos similar to pions at RHIC Neutrinos similar to pions at RHIC – Not present in entrance channel – Produced in very large numbers (RHIC: 10 3, here ) – Essential for reaction dynamics Different: No formation time or off -shell effects Different: No formation time or off -shell effects Represent 10 N neutrinos by one test particle Represent 10 N neutrinos by one test particle – Populate initial neutrino phase space uniformly – Sample test particle momenta from a thermal dist. Neutrino test particles represent “2 nd fluid”, do NOT escape freely (neutrino trapping), and need to be followed in time. Neutrino test particles represent “2 nd fluid”, do NOT escape freely (neutrino trapping), and need to be followed in time.

W. Bauer, Breckenridge 0324 Neutrino Test particles Move on straight lines (no mean field) Move on straight lines (no mean field) Scattering with hadrons Scattering with hadrons – NOT negligible! – Convolution over all  A  A 2 (weak neutral current) – Resulting test particle cross section angular distrib.:  cm  f  f -  i  – Center of mass picture: PiPi p N,i PfPf p N,f => Internal excitation

W. Bauer, Breckenridge 0325 Effects of Angular Momentum

W. Bauer, Breckenridge 0326 Results “mean field” level “mean field” level 1 fluid: hadrons 1 fluid: hadrons

W. Bauer, Breckenridge 0327 00 (a)Initial conditions (b)After 2 ms (c)After 3 ms (d)Core bounce (e)1 ms after core bounce 120 km

W. Bauer, Breckenridge 0328 Vortex Formation

W. Bauer, Breckenridge 0329 Some Supernovae are Not Spherical! 1987A remnant shows “smoke rings” 1987A remnant shows “smoke rings” Cylinder symmetry, but not spherical Cylinder symmetry, but not spherical Consequence of high angular momentum collapse Consequence of high angular momentum collapse HST Wide Field Planetary Camera 2

W. Bauer, Breckenridge 0330 More Qualitative Neutrino focusing along poles gives preferred direction for neutrino flux Neutrino focusing along poles gives preferred direction for neutrino flux Neutrinos have finite mass, helicity Neutrinos have finite mass, helicity Parity violation on the largest scale Parity violation on the largest scale Net excess of neutrinos emitted along “North Pole” Net excess of neutrinos emitted along “North Pole” => Strong recoil kick for neutron star supernova remnant => Strong recoil kick for neutron star supernova remnant => Non-thermal contribution to neutron star velocity distribution => Non-thermal contribution to neutron star velocity distribution

W. Bauer, Breckenridge 0331 The Man who did the Work Tobias Bollenbach (M.S. Thesis, MSU, 2002) Funding from NSF, Studienstiftung des Deutschen Volkes, and Alexander von Humboldt Foundation