The Expulsion of Stellar Envelopes in Core-Collapse Supernovae
We examine the relation between presupernova stellar structure and the distribution of ejecta in core-collapse supernovae, assuming adiabatic, spherically symmetric flow. We develop a simple yet accurate formula for the blastwave shock velocity, and demonstrate that the entire final density distribution can be approximated with simple models for the final pressure distribution, along with the approximate shock-deposited entropy, in a way that matches the results of simulations. We find that the distribution of density in a star's ejecta depends on whether its outer envelope is radiative or convective, and if convective, on the composition structure of the star; simple approximate forms are presented for red and blue supergiant ejecta. Our models are most accurate for the high-velocity ejecta from the periphery of a star, where the shock dynamics are predictable. We present formulae for the final density distribution of this material, for both radiative and efficiently convective envelopes. These formulae limit to the well-known planar, self-similar solutions for mass shells approaching the stellar surface. But, the assumption of adiabatic flow fails at low optical depth, so this planar limit need not be attained. Formulae are given for the observable properties of the X-ray burst accompanying shock emergence, and their dependence on the parameters of the explosion. Motivated by the relativistic expansion recently inferred by Kulkarni et al. (1998) for the synchrotron shell around SN1998bw, we estimate the criterion for relativistic mass ejection and the rest mass of relativistic ejecta.