2014ApJ...789...74Z

Gamma-ray bursts (GRBs) usually occur in a dense star-forming region with a massive circumburst medium. The small-angle scattering of intense prompt X-ray emission off the surrounding dust grains will have observable consequences and sometimes can dominate the X-ray afterglow. In most of the previous studies, only the Rayleigh-Gans (RG) approximation is employed for describing the scattering process, which works accurately for the typical size of grains (with radius of a ≤ 0.1 µm) in the diffuse interstellar medium. When the size of the grains may significantly increase, as in a more dense region where GRBs would occur, the RG approximation may not be valid enough for modeling detailed observational data. In order to study the temporal and spectral properties of the scattered X-ray emission more accurately with potentially larger dust grains, we provide a practical approach using the series expansions of anomalous diffraction (AD) approximation based on the complicated Mie theory. We apply our calculations to understand the puzzling X-ray afterglow of recently observed GRB 130925A that showed a significant spectral softening. We find that the X-ray scattering scenarios with either AD or RG approximation adopted could well reproduce both the temporal and spectral profile simultaneously. Given the plateau present in the early X-ray light curve, a typical distribution of smaller grains as in the interstellar medium would be suggested for GRB 130925A.