On the synchrotron spectrum of GRB prompt emission

TL;DR

This paper explores how the interplay of stochastic acceleration, injection, and cooling processes shapes the synchrotron spectrum of GRB prompt emission, explaining the observed spectral indices.

Contribution

It presents a model combining adiabatic stochastic acceleration and synchrotron cooling to explain the GRB prompt emission spectrum.

Findings

The low-energy photon index approaches -1 due to ASA.

High-energy electrons undergo fast synchrotron cooling, softening the spectrum.

The break energy is around 100 keV, influenced by turbulence.

Abstract

The prompt emission spectrum of Gamma-ray bursts (GRB) is characterized by a smoothly joint broken power-law spectrum known as the Band function. The typical low-energy photon index is $\sim -1$, which poses challenge to the standard synchrotron radiation models. We investigate the electron energy spectrum as a result of the interplay among adiabatic stochastic acceleration (ASA), particle injection, and synchrotron cooling. In the ASA-dominated low-energy range, ASA enables an efficient hardening of the injected energy spectrum to approach a spectral index $-1$. In the synchrotron cooling-dominated high-energy range, the injected high-energy electrons undergo fast synchrotron cooling and have a softer photon spectrum. With the energy range of the injected electrons broadly covering both the ASA- and synchrotron cooling-dominated ranges, the resulting photon number spectrum has the low- and high-energy indices as $\alpha_s \sim -1$ and $\beta_s \sim -p/2-1$, respectively. The break energy is of the order of $\sim 100 $ keV, depending on the turbulence properties.