Early Afterglows of Gamma-Ray Bursts in a Stratified Medium with a Power-Law Density Distribution

TL;DR

This paper models early gamma-ray burst afterglows in stratified media with power-law density profiles, revealing that many GRBs occur in environments with intermediate density gradients, suggesting complex progenitor mass-loss histories.

Contribution

It introduces a comprehensive model for GRB afterglows in stratified media with variable density profiles, enabling better interpretation of early optical light curves and environmental properties.

Findings

Most GRBs have density profile index k around 1

The environment is neither uniform nor wind-like, indicating complex progenitor evolution

The model fits well with 19 observed GRBs

Abstract

A long-duration gamma-ray burst (GRB) has been widely thought to arise from the collapse of a massive star, and it has been suggested that its ambient medium is a homogenous interstellar medium (ISM) or a stellar wind. There are two shocks when an ultra-relativistic fireball that has been ejected during the prompt gamma-ray emission phase sweeps up the circumburst medium: a reverse shock that propagates into the fireball, and a forward shock that propagates into the ambient medium. In this paper, we investigate the temporal evolution of the dynamics and emission of these two shocks in an environment with a general density distribution of $n\propto R^{-k}$ (where $R$ is the radius) by considering thick-shell and thin-shell cases. A GRB afterglow with one smooth onset peak at early times is understood to result from such external shocks. Thus, we can determine the medium density distribution by fitting the onset peak appearing in the light curve of an early optical afterglow. We apply our model to 19 GRBs, and find that their $k$ values are in the range of 0.4 - 1.4, with a typical value of $k\sim1$, implying that this environment is neither a homogenous interstellar medium with $k=0$ nor a typical stellar wind with $k=2$. This shows that the progenitors of these GRBs might have undergone a new mass-loss evolution.