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

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.

12 pages, 1 figure, ApJL accepted

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• A Large Catalogue of Multi-wavelength GRB Afterglows I: Color Evolution And Its Physical Implication
• Probing Magnetic Fields of GRB X-ray Flares with Polarization Observations
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• GRB Timing: Decoding the Hidden Slow Jets in GRB 060729
• Predicting Multiwavelength Emission Associated with X-Ray Flares and Extended Emission of Gamma-Ray Bursts