Spectral curvature and breaks from Fermi acceleration at oblique shocks

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.