Discrete Self-Similarity in Ultra-Relativistic Type-II Strong Explosions

TL;DR

This paper presents a novel solution to ultra-relativistic strong explosion problems with complex density gradients, revealing discretely self-similar behaviors and validating them through numerical simulations.

Contribution

It introduces discretely self-similar solutions for perturbations in ultra-relativistic explosions with non-power law density profiles, expanding understanding of such phenomena.

Findings

Discovered discretely self-similar solutions for specific density perturbations.

Validated theoretical solutions with numerical simulations.

Generalized solutions to arbitrary small spherically symmetric perturbations.

Abstract

A solution to the ultra-relativistic strong explosion problem with a non-power law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power-law with small, spherically symmetric, and log-periodic density perturbations. We find discretely self-similar solutions to the perturbation equations and compare them to numerical simulations. These results are then generalized to encompass small spherically symmetric perturbations with arbitrary profiles.