# Steep Decay of GRB X-ray Flares: the Result of Anisotropic Synchrotron Radiation

## TL;DR

This paper proposes that anisotropic synchrotron radiation explains the steep decay of X-ray flares in GRBs, challenging the standard high-latitude emission model and linking electron acceleration details to observed emission decay.

## Contribution

It introduces a model where anisotropic synchrotron radiation accounts for steeper X-ray flare decay, supported by simulations and observations, providing new insights into electron acceleration in GRBs.

## Key findings

- The anisotropic synchrotron model reproduces observed flare decay and spectral evolution.
- The model explains deviations from the standard high-latitude emission relation.
- Simulations support the proposed anisotropic electron distribution.

## Abstract

When an emitting spherical shell with a constant Lorentz factor turns off emission abruptly at some radius, its high-latitude emission would obey the relation of $\hat{\alpha}$ (the temporal index) = $2 + \hat{\beta}$ (the spectral index). However, this relation is violated by the X-ray fares in some gamma-ray bursts (GRBs), whose $\hat{\alpha}$ is much more steeper. We show that the synchrotron radiation should be anisotropic when the angular distribution of accelerated electrons has preferable orientation, and this anisotropy would naturally lead to the steeper decay for the high-latitude emission if the the intrinsic emission is limb-brightened. We use our simple toy model to reproduce the temporal and the spectral evolution of the X-ray flares. We show that our model can well interpret the steep decay of the X-ray flares in the three GRBs selected as example. Recent simulations on particle acceleration may support the specific anisotropic distribution of the electrons adopted in our work. Reversely, confirmation of the anisotropy in the radiation would give meaningful clues to the details of electron acceleration in the emitting region.