The "Fireshell" model in the Swift era

TL;DR

This paper critically re-evaluates the commonly used power-law relation in the fireshell model of GRBs, showing it is only approximately valid under limited conditions and for short durations.

Contribution

It clarifies the conditions under which the constant-index power-law relation in the fireshell model holds, challenging its widespread use in GRB studies.

Findings

The power-law relation is only approximately valid in limited parameter ranges.

The asymptotic regime where the relation holds is reached only briefly, if at all.

The validity of the relation depends on specific physical and astrophysical parameters.

Abstract

We here re-examine the validity of the constant-index power-law relation between the fireshell Lorentz gamma factor and its radial coordinate, usually adopted in the current Gamma-Ray Burst (GRB) literature on the grounds of an "ultrarelativistic" approximation. Such expressions are found to be mathematically correct but only approximately valid in a very limited range of the physical and astrophysical parameters and in an asymptotic regime which is reached only for a very short time, if any.