Hard electron energy distribution in the relativistic shocks of gamma-ray burst afterglows

Particle acceleration in relativistic shocks is not a very well understood subject. Owing to that difficulty, radiation spectra from relativistic shocks, such as those in gamma-ray burst (GRB) afterglows, have been often modelled by making assumptions about the underlying electron distribution. One such assumption is a relatively soft distribution of the particle energy, which need not be true always, as is obvious from observations of several GRB afterglows. In this paper, we describe modifications to the afterglow standard model to accommodate energy spectra which are 'hard'. We calculate the overall evolution of the synchrotron and Compton flux arising from such a distribution. We also model two afterglows, GRB010222 and GRB020813, under this assumption and estimate the physical parameters.