Particle acceleration at oblique shocks and discontinuities of the density profile

TL;DR

This paper investigates whether energetic particle densities exhibit discontinuities at oblique shock fronts, combining analytical, semi-analytical, and simulation methods to explore conditions leading to such jumps.

Contribution

It demonstrates that anisotropy caused by shock obliquity can produce a density jump, advancing understanding of particle acceleration at shocks.

Findings

An isotropic particle distribution implies continuous density at shocks.

Anisotropy from obliquity can cause a density discontinuity.

Particles tend to concentrate in a precursor ahead of the shock.

Abstract

In the theory of diffusive acceleration at oblique shock fronts the question of the existence of a discontinuity of energetic particle density is contentious. The resolution of this problem is interesting from a theoretical point of view, and potentially for the interpretation of observations of particle densities at heliospheric shocks and of high-resolution radio observations of the rims of supernova remnants. It can be shown analytically that an isotropic particle distribution at a shock front implies continuity of the particle density -- whether or not the shock is oblique. However, if the obliquity of the shock induces an anisotropy, a jump is permitted. Both semi-analytic computations and Monte-Carlo simulations are used to show that, for interesting parameter ranges, a jump is indeed produced, with accelerated particles concentrated in a precursor ahead of the shock front.