Spot-like Proton Acceleration in SNR Shocks: Implications for the Energy Spectra

Cosmic ray (CR) spectra, both measured upon their arrival at the Earth atmosphere and inferred from the emission in supernova remnants (SNR), appear to be significantly steeper than the "standard" diffusive shock acceleration (DSA) theory predicts. Although the CR spectra steepen due to propagation losses, this steepening falls short to explain the data. We investigate whether the variable acceleration conditions on the SNR shock suffice to produce the necessary extra steepening. To this end, we perform two-dimensional hybrid simulations of a shock propagating into a SNR shock environment where the magnetic field inclination to the shock front varies. The rationale behind this approach is the strong dependence of the DSA efficiency upon the field angle. We find that the variation of shock obliquity along its face results in a noticeable steepening of the DSA spectrum: as compared to simulations of quasi-parallel shocks, we observe an increase of the spectral index by $\Delta q = 0.1-0.15$.