The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal Shocks

Abstract

The prompt emission of most gamma-ray bursts (GRBs) typically exhibits a non-thermal Band component. The synchrotron radiation in the popular internal shock model is generally put forward to explain such a non-thermal component. However, the low-energy photon index α∼−1.5 predicted by the synchrotron radiation is inconsistent with the observed value α∼−1. Here, we investigate the evolution of a magnetic field during propagation of internal shocks within an ultrarelativistic outflow, and revisit the fast cooling of shock-accelerated electrons via synchrotron radiation for this evolutional magnetic field. We find that the magnetic field is first nearly constant and then decays as B′∝t−1, which leads to a reasonable range of the low-energy photon index, −3/2<α<−2/3. In addition, if a rising electron injection rate during a GRB is introduced, we find that α reaches −2/3 more easily. We thus fit the prompt emission spectra of GRB 080916c and GRB 080825c.