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

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.

20 pages and 11 figures

References in corpus (4)

• An online repository of Swift/XRT light curves of GRBs
• Ultrahigh-Energy Cosmic Ray Production by Turbulence in Gamma-Ray Burst Jets and Cosmogenic Neutrinos
• The truncated lognormal distribution as a luminosity function for SWIFT-BAT gamma-ray bursts
• Relativistic scaling laws for the light curve in supernovae