First-order Fermi acceleration at oblique relativistic magnetohydrodynamic shocks

Abstract

In this paper we investigate first-order Fermi acceleration at oblique relativistic magnetohydrodynamic (MHD) shock fronts. The jump conditions at the shock are solved using a full relativistic equation of state and allowing for various possible downstream conditions. Having obtained solutions to the jump conditions, the spectral indices of electrons accelerated by the shock front through the first-order Fermi mechanism are obtained by employing two methods: a Monte Carlo simulation and the semi-analytic theory of Kirk & Heavens. Good agreement is found for the case where irregularities in the magnetic field are assumed to be small. We find that synchrotron spectral indices in the range of 0 to 0.5 are expected for oblique relativistic MHD shocks, unless the Alfven Mach number is not much greater than unity.