# Weak Shock Propagation with Accretion. III. A Numerical Study On Shock Propagation & Stability

## TL;DR

This study uses numerical simulations to analyze how shocks of varying initial strengths propagate and stabilize in stellar envelopes, revealing that shocks tend to evolve toward known self-similar solutions over time.

## Contribution

It demonstrates that shocks in stellar envelopes evolve toward specific self-similar solutions, and highlights the slow evolution of shocks near the weak shock solution, providing new insights into shock behavior in supernovae.

## Key findings

- Shocks evolve toward either strong or weak self-similar solutions.
- Shocks with initial strengths near the weak solution evolve very slowly.
- Low-energy stellar explosions retain initial shock strength longer.

## Abstract

Core-collapse supernovae span a wide range of energies, from much less than to much greater than the binding energy of the progenitor star. As a result, the shock wave generated from a supernova explosion can have a wide range of Mach numbers. In this paper, we investigate the propagation of shocks with arbitrary initial strengths in polytropic stellar envelopes using a suite of spherically symmetric hydrodynamic simulations. We interpret these results using the three known self-similar solutions for this problem: the Sedov-Taylor blastwave describes an infinitely strong shock and the self-similar solutions from Coughlin et al. (2018b) (Paper I) and Coughlin et al. (2019) (Paper II) describe a weak and infinitely weak shock (the latter being a rarefaction wave). We find that shocks, no matter their initial strengths, evolve toward either the infinitely strong or infinitely weak self-similar solutions at sufficiently late times. For a given density profile, a single function characterizes the long-term evolution of a shock's radius and strength. However, shocks with strengths near the self-similar solution for a weak shock (from Paper I) evolve extremely slowly with time. Therefore, the self-similar solutions for infinitely strong and infinitely weak shocks are not likely to be realized in low-energy stellar explosions, which will instead retain memory of the shock strength initiated in the stellar interior.