Accretional Heating of Asymmetric Supernova Cores

The role of accretion in heating a stalled bounce shock in a core-collapse supernova is investigated. We show that effective accretional heating causes an asymmetric expansion of the shock, sufficient to impart a net impulse of ~300-400 km s^-1 to the neutron core. To simplify the analysis, we consider a failed accretion shock. Below such a shock, inward advection is faster than neutrino heating and the usual gain criterion does not suffice to determine a successful explosion. A mechanism that enhances buoyancy and inhibits mixing between hot and cold postshock fluid elements is required to revive the shock. We focus on the response of a magnetic field to the accretion flow. Ram heating and shearing of a low-density, magnetized fluid phase (``M-fluid'') is shown to be faster than neutrino cooling. The long duration of the accretion flow compared with the dynamical time allows for a large amplification of the magnetic energy. We calculate the stability of a spherical shock in the presence of a low-density hydrostatic atmosphere below it and show that below a critical atmospheric density the shock is unstable to a global Rayleigh-Taylor mode. We then calculate the equilibrium structure of this Rayleigh-Taylor plume as it accumulates energy and the critical size beyond which quasi-static expansion is no longer possible and its outer boundary converts to a running shock. Accretion continues while the shock expands, and an energy of ~10⁵¹ ergs is a direct consequence of the efficiency of ram heating close to the neutron core. The linear momentum imparted to the core is directly related to the mass profile of the precollapse core and explains the proper motions of (most) radio pulsars. We also estimate the net circulation imparted to the last 0.1-0.2 M_solar of collapsing material, which appears sufficient to torque the core down to a spin period of 1-100 ms. The effect of photodissociation on the shock jump conditions is calculated, and the implications for nucleosynthesis of iron peak elements are considered. Finally, the residual magnetic field advected out into the eventual supernova remnant is compared with the field generated by a rapidly spinning neutron star.