On the Consistency of Gamma-Ray Burst Spectral Indices with the Synchrotron Shock Model

The current scenario for gamma-ray bursts (GRBs) involves internal shocks for the prompt GRB emission phase and external shocks for the afterglow phase. Assuming optically thin synchrotron emission from isotropically distributed energetic shocked electrons, GRB spectra observed with a low-energy power-law spectral index greater than - (for positive photon number indices E^α) indicate a problem with this model. For spectra that do not violate this condition, additional tests of the shock model can be made by comparing the low- and high-energy spectral indices, on the basis of the model's assertion that synchrotron emission from a single power-law distribution of electrons is responsible for both the low-energy and the high-energy power-law portions of the spectra. We find in most cases that the inferred relationship between the two spectral indices of observed GRB spectra is inconsistent with the constraints from the simple optically thin synchrotron shock emission model. In this sense, the prompt burst phase is different from the afterglow phase, and this difference may be related to anisotropic distributions of particles or to their continual acceleration in shocks during the prompt phase.