Dynamical Model of an Expanding Shell

TL;DR

This paper develops a comprehensive dynamical model for expanding blast waves in astrophysics, accounting for both energy density and pressure, and unifies descriptions across relativistic and non-relativistic regimes.

Contribution

It introduces a new equation for blast wave evolution that includes pressure effects, extending previous models that only considered energy.

Findings

The model converges to known ultra-relativistic solutions.

The model converges to Newtonian solutions.

Provides a unified description across regimes.

Abstract

Expanding blast waves are ubiquitous in many astronomical sources, such as supernovae remnants (SNRs), X-ray emitting binaries (XRBs) and gamma-ray bursts (GRBs). I consider here the dynamics of such an expanding blast wave, both in the adiabatic and the radiative regimes. As the blast wave collects material from the surrounding, it decelerates. A full description of the temporal evolution of the blast wave requires consideration of both the energy density and the pressure of the shocked material. The obtained equation is different than earlier works in which only the energy was considered. The solution converges to the familiar results in both the ultra-relativistic and the sub-relativistic (Newtonian) regimes.