Stochastic Acceleration Model of Gamma-Ray Burst with Decaying Turbulence

TL;DR

This paper explores a stochastic acceleration model with decaying turbulence to explain the spectral shape of gamma-ray burst prompt emissions, aiming to reproduce the observed Band function through evolving electron energy distributions.

Contribution

It introduces a model where turbulence decay over time shapes the GRB spectra, providing a potential explanation for the Band function's origin.

Findings

The model produces a power-law high-energy spectrum through turbulence decay.

Decaying turbulence can reconcile the narrow electron distribution with observed spectra.

Shorter acceleration timescales are necessary for the model to match observations.

Abstract

The spectral shape of the prompt emissions of gamma-ray bursts (GRBs) is typically expressed by the Band function: smooth joining of two power-law functions for high-energy and low-energy regions. To reveal the origin of the Band function, we revisit the stochastic acceleration model, in which electrons are accelerated via scattering with turbulent waves in the GRB outflow. The balance between the acceleration and synchrotron cooling yields a narrow energy-distribution similar to the Maxwellian distribution. The synchrotron spectrum becomes consistent with the observed hard photon index for the low-energy region. On the other hand, the narrow electron energy distribution contradicts the power-law spectrum for the high-energy region. We consider an evolution of the electron energy distribution to solve this problem. The turbulence and magnetic field induced by a certain hydrodynamical instability gradually decay. According to this evolution, the typical synchrotron photon energy also decreases with time. The time-integrated spectrum forms the power-law shape for the high-energy region. We discuss the required evolutions of the turbulence and magnetic field to produce a typical Band function. Although the decay of the turbulence is highly uncertain, recent numerical simulations for decaying turbulence seem comparatively positive for the stochastic acceleration model. Another condition required to reconcile observations is a much shorter duration of the stochastic acceleration than the dynamical timescale.