Homologous Core Collapse in a Massive Star and Self-Similar Evolution of Rebound Shocks

TL;DR

This paper develops analytical and numerical self-similar solutions for the collapse and rebound shocks in massive star cores during supernovae, modeling the hot, relativistic gas with a polytropic index of 4/3 to better understand supernova shock evolution.

Contribution

It introduces a generalized self-similar model for core collapse and rebound shocks in massive stars, extending previous work with new solutions and comparisons.

Findings

Derived various asymptotic and exact solutions for shock dynamics.

Constructed models including central void solutions with shocks.

Provided insights into supernova shock evolution and benchmarking methods.

Abstract

During the gravitational core collapse of a massive progenitor star which may give rise to at least a class of gamma-ray bursts (GRBs) associated with supernovae, a stellar core rapidly passes through a short yet important phase of neutronization, producing a huge amount of energetic neutrinos and photons which contribute to the total pressure within the progenitor core. The collection of neutrinos, photons and gas materials together may be approximated as a fluid with a polytropic index $\gamma=4/3$ under the action of self-gravity. With a substantial generalization and using analytical and numerical methods (Lou & Cao 2008), we recently constructed and examined various self-similar solutions to describe collapses, rebound shocks and flows systematically in a $\gamma=4/3$ polytropic gas mixture with spherical symmetry, and compare our results with those of Goldreich & Weber (1980). It is also possible to construct central void solutions without or with shocks. Various features and characteristics of this nonlinear relativistically hot gas dynamics, including asymptotic and exact solutions, are presented. This more general polytropic model analysis provides the dynamic basis of understanding the evolution of rebound shocks in supernovae (SNs) and the results may be also utilized to benchmark hydrodynamic simulations.