Microphysics of diffusive shock acceleration: impact on the spectrum of accelerated particles

TL;DR

This paper explores how non-linear effects, magnetic field amplification, and streaming instabilities influence the energy spectrum of particles accelerated by collisionless shocks in astrophysical environments.

Contribution

It provides a detailed analysis of how non-resonant streaming instabilities affect the spectral shape and maximum energy of particles in diffusive shock acceleration.

Findings

Non-linear effects cause a concave spectrum at intermediate energies.

Magnetic field amplification increases the maximum particle momentum.

Streaming instabilities can steepen the particle spectrum depending on shock velocity.

Abstract

Diffusive shock acceleration at collisionless shocks remains the most likely process for accelerating particles in a variety of astrophysical sources. While the standard prediction for strong shocks is that the spectrum of accelerated particles is universal, $f(p)\propto p^{-4}$, numerous phenomena affect this simple conclusion. In general, the non-linear dynamical reaction of accelerated particles leads to a concave spectrum, steeper than $p^{-4}$ at momenta below a few tens of GeV/c and harder than the standard prediction at high energies. However, the non-linear effects become important in the presence of magnetic field amplification, which in turn leads to higher values of the maximum momentum $p_{max}$. It was recently discovered that the self-generated perturbations that enhance particle scattering, when advected downstream, move in the same direction as the background plasma, so that the effective compression factor at the shock decreases and the spectrum becomes steeper. We investigate the implications of the excitation of the non-resonant streaming instability on these spectral deformations, the dependence of the spectral steepening on the shock velocity and the role played by the injection momentum.