An external-shock origin of the E_p-E_gamma relation for Gamma-Ray Bursts

TL;DR

This paper explores how the observed E_p-E_gamma relation in long-duration gamma-ray bursts can be explained by external shocks interacting with a medium that has a specific radial density profile, suggesting a universal stratification.

Contribution

It demonstrates that the E_p-E_gamma relation can be derived from external shock models with a universal radial density profile of the ambient medium around GRBs.

Findings

The E_p-E_gamma relation can be explained by external shocks with a specific ambient medium density profile.

The circumburst medium must have a non-standard radial density distribution, different from R^{-2}.

The relation holds across different radiative and dissipation mechanisms.

Abstract

We investigate the possibility that the E_p propto E_gamma^{1/2} relation between the peak energy E_p of the nuF_nu spectrum and energy output E_gamma for long-duration GRBs arises from the external shock produced by the interaction of a relativistic outflow with the ambient medium. To that aim, we take into account the dependence of all parameters which determine E_p and E_gamma on the radial distribution of the ambient medium density and find that the E_p-E_gamma relation can be explained if the medium around GRBs has a universal radial stratification. For various combinations of GRB radiative process (synchrotron or inverse-Compton) and dissipation mechanism (reverse or forward shock), we find that the circumburst medium must have a particle density with a radial distribution different than the R^{-2} expected for constant mass-loss rate and terminal speed.