Spectral curvature and breaks from Fermi acceleration at oblique shocks

TL;DR

This paper investigates how spectral shapes of energetic particles at oblique shocks depend on scattering conditions, showing that deviations from Bohm scaling lead to curved spectra and breaks, especially in astrophysical shock environments.

Contribution

It demonstrates that power-law spectra at oblique shocks require Bohm scaling and uniform scattering, and explores how deviations cause spectral curvature and breaks using numerical simulations.

Findings

Non-Bohm scaling results in curved spectra.

Spectral breaks occur with non-uniform scattering profiles.

Effects are significant at fast shocks in astrophysical sources.

Abstract

A major attraction of diffusive shock acceleration is the prediction of power-law spectra for energetic particle distributions. However, this property is not fundamental to the theory. We demonstrate that for planar shocks with an oblique magnetic field the generation of power-law spectra critically requires the particles' scattering rate to be both directly proportional to their gyro radius (Bohm scaling) and spatially uniform. Non-Bohm scaling results in curved spectra at oblique shocks, while abrupt changes in the spatial profile of the scattering upstream introduces spectral breaks. Using the publicly available code Sapphire++, we numerically explore the magnitude of these effects, which are particularly pronounced at fast shocks, as expected in active galactic nuclei and microquasar jets, or young supernova remnants.