Classical and relativistic models for time duration of gamma-ray bursts

TL;DR

This paper develops classical and relativistic models to analytically and numerically estimate gamma-ray burst durations based on supernova expansion dynamics and statistical luminosity distributions, considering different cosmologies.

Contribution

It introduces a combined classical and relativistic framework for modeling GRB durations, incorporating statistical distributions and different cosmological models.

Findings

Classical model yields an analytical expression for GRB duration.

Relativistic model provides a numerical approach for high-velocity phases.

Analysis of two cosmologies shows their impact on GRB duration estimates.

Abstract

A classical model based on a power law assumption for the radius-time relationship in the expansion of a Supernova (SN) allows to derive an analytical expression for the flow of mechanical kinetic energy and the time duration of Gamma-ray burst (GRB). A random process based on the ratio of two truncated lognormal distributions for luminosity and luminosity distance allows to derive the statistical distribution for time duration of GRBs. The high velocities involved in the first phase of expansion of a SN requires a relativistic treatment. The circumstellar medium is assumed to follow a density profile of Plummer type with eta=6. A series solution for the relativistic flow of kinetic energy allows to derive in a numerical way the duration time for GRBs. Here we analyse two cosmologies: the standard cosmology and the plasma cosmology.