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

TL;DR

This paper investigates how nonlinear effects and scattering models influence particle acceleration and gamma-ray emission in relativistic shocks, emphasizing the importance of momentum-dependent mean free paths in astrophysical phenomena.

Contribution

It introduces a generalized scattering mean free path in a nonlinear Monte Carlo model, highlighting the impact of turbulence and nonlinear effects on shock acceleration and emission spectra.

Findings

Short-scale turbulence dominates in unmagnetized shocks.

Momentum dependence of mfp affects acceleration efficiency.

Spectral shape and gamma-ray emission are sensitive to nonlinear effects.

Abstract

We include a general form for the scattering mean free path in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell (PIC) simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, self-generated magnetic turbulence that leads to a scattering mean free path (mfp) with a stronger momentum dependence than the mfp ~ 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 gamma-ray bursts (GRBs), pulsar winds, Type Ibc supernovae, and extra-galactic 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 the mfp has an important influence on the efficiency of cosmic-ray production as well as the accelerated particle spectral shape. These effects are absent in nonrelativistic 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 gamma-ray emission from proton-proton interactions and pion-decay radiation.