Steep Decay of GRB X-Ray Flares: The Results of Anisotropic Synchrotron Radiation

Abstract

When an emitting spherical shell with a constant Lorentz factor turns off emission abruptly at some radii, its high-latitude emission would obey the relation of (the temporal index) =  (the spectral index). However, this relation is violated by the X-ray fares in some gamma-ray bursts (GRBs), whose is much more steeper. We show that the synchrotron radiation should be anisotropic when the angular distribution of accelerated electrons has a preferable orientation, and this anisotropy would naturally lead to a steeper decay for the high-latitude emission if the intrinsic emission is limb-brightened. We use this simple toy model to reproduce the temporal and spectral evolution of 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 an 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 provide meaningful clues to the details of electron acceleration in the emitting region.