Steep Cosmic Ray Spectra with Revised Diffusive Shock Acceleration

Abstract: Galactic cosmic rays (CRs) are accelerated at the forward shocks of supernova remnants (SNRs) via diffusive shock acceleration (DSA), an efficient acceleration mechanism that predicts power-law energy distributions of CRs. However, observations of nonthermal SNR emission imply CR energy distributions that are generally steeper than $E^{-2}$, the standard DSA prediction. Recent results from kinetic hybrid simulations suggest that such steep spectra may arise from the drift of magnetic structures with respect to the thermal plasma downstream of the shock. Using a semi-analytic model of non-linear DSA, we investigate the implications that these results have on the phenomenology of a wide range of SNRs. By accounting for the motion of magnetic structures in the downstream, we produce CR energy distributions that are substantially steeper than $E^{-2}$ and consistent with observations. Our formalism reproduces both modestly steep spectra of Galactic supernova remnants ($\propto E^{-2.2}$) and the very steep spectra of young radio supernovae ($\propto E^{-3}$).