Particle spectra and efficiency in nonlinear relativistic shock acceleration-survey of scattering models

Abstract

We include a general form for the scattering mean free path, λmfp(p), in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, selfgenerated magnetic turbulence that leads to a scattering mean free path with a stronger momentum dependence than the λmfp ∝ p dependence for Bohm diffusion. In unmagnetized shocks, this turbulence is strong enough to dominate the background magnetic field so the shock can be treated as parallel regardless of the initial magnetic field orientation, making application to γ-ray bursts, pulsar winds, type Ibc supernovae, and extragalactic radio sources more straightforward and realistic. In addition to changing the scale of the shock precursor, we show that, when nonlinear effects from efficient Fermi acceleration are taken into account, the momentum dependence of λmfp(p) has an important influence on the efficiency of cosmic ray production as well as the accelerated particle spectral shape. These effects are absent in non-relativistic shocks and do not appear in relativistic shock models unless nonlinear effects are self-consistently described. We show, for limited examples, how the changes in Fermi acceleration translate to changes in the intensity and spectral shape of γ-ray emission from proton-proton interactions and pion-decay radiation.