Gamma-Ray Burst Spectral Indices: Evidence for Deceleration of Synchrotron Shocks

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 synchrotron emission from energetic shocked electrons. GRB spectra observed with a low-energy power-law spectral index greater than -2/3 (for positive photon number indices E(sup alpha) indicate a problem with this model. The remaining spectra can test the synchrotron shock model prediction that the emission from a single distribution of electrons, cooling rapidly, is responsible for both the low-energy and high-energy power-low portions of the spectra. We find that the inferred relationship between the two spectral indices of observed GRB spectra is inconsistent with the constraints from the model, posing another problem for the synchrotron shock emission model. To overcome this problem, we describe a model where the average of -1, rather than the value of -3/2 predicted for cooling electrons. Situations where this might arise have been discussed in other contexts, and involve deceleration of the internal shocks during the GRB phase.