Acceleration at Relativistic Shocks in Gamma-Ray Bursts

Most recent extragalactic models of gamma-ray bursts consider the expansion of a relativistic blast wave, emanating from a solar-mass type progenitor, into the surrounding interstellar medium as the site for their activity. The popular perception is that the optical afterglows result from the external shock interface, while the prompt transient gamma-ray signal arises from multiple shocks internal to the expansion. This paper illustrates a number of acceleration properties of relativistic and ultrarelativistic shocks that pertain to GRB models, by way of a standard Monte Carlo simulation. Computations of the spectral shape, the range of spectral indices, and the energy gain per shock crossing are presented, as functions of the shock speed and the type of particle scattering.