Modeling the Multi-band Afterglows of GRB 060614 and GRB 060908: Further Evidence for a Double Power-Law Hard Electron Energy Spectrum

TL;DR

This paper presents evidence that some gamma-ray burst afterglows are best explained by a double power-law electron energy spectrum, challenging the common assumption of a single power-law distribution.

Contribution

It provides further observational support for the double power-law hard electron energy spectrum model in GRB afterglows, extending previous findings to two additional bursts.

Findings

GRB 060614's afterglow fits the DPLH model with energy injection.

GRB 060908's afterglow supports a wind-like circumburst environment.

The injection break evolution appears consistent across multiple GRBs.

Abstract

Electrons accelerated in relativistic collisionless shocks are usually assumed to follow a power-law energy distribution with an index of $p$. Observationally, although most gamma-ray bursts (GRBs) have afterglows that are consistent with $p>2$, there are still a few GRBs suggestive of a hard ($p<2$) electron energy spectrum. Our previous work showed that GRB 091127 gave strong evidence for a double power-law hard electron energy (DPLH) spectrum with $1<p_1<2$, $p_2>2$ and an "injection break" assumed as $\gamma_{\rm b}\propto \gamma^q$ in the highly relativistic regime, where $\gamma$ is the bulk Lorentz factor of the jet. In this paper, we show that GRB 060614 and GRB 060908 provide further evidence for such a DPLH spectrum. We interpret the multi-band afterglow of GRB 060614 with the DPLH model in an homogeneous interstellar medium by taking into account a continuous energy injection process, while for GRB 060908, a wind-like circumburst density profile is used. The two bursts, along with GRB 091127, suggest a similar behavior in the evolution of the injection break, with $q\sim0.5$. Whether this represents a universal law of the injection break remains uncertain and more such afterglow observations are needed to test this conjecture.