Accretional Heating of Asymmetric Supernova Cores

Abstract

The role of accretion in heating a stalled bounce shock in a core-collapse supernova is investigated. We show that eUective accretional heating causes an asymmetric expansion of the shock, sufficient to impart a net impulse of D300¨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 —uid elements is required to revive the shock. We focus on the response of a magnetic —eld to the accretion —ow. Ram heating and shearing of a low-density, magnetized —uid phase (ii M-—uid ˇˇ) is shown to be faster than neutrino cooling. The long duration of the accretion —ow compared with the dynamical time allows for a large ampli—cation of the magnetic energy. We calculate the stability of a spherical shock in the presence of a low-density hydro- static 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 D1051 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 pro—le 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 of collapsing material, which appears sufficient to torque the core down M _ to a spin period of 1¨100 ms. The eUect of photodissociation on the shock jump conditions is calculated, and the implications for nucleosynthesis of iron peak elements are considered. Finally, the residual mag- netic —eld advected out into the eventual supernova remnant is compared with the —eld generated by a rapidly spinning neutron star. Subject headings: accretion, accretion disksshock wavesstars: magnetic —elds ¨ stars: neutronsupernovae: general