Cosmic ray acceleration at perpendicular shocks in supernova remnants

TL;DR

This paper investigates cosmic ray acceleration at perpendicular shocks in supernova remnants using a realistic diffusion model, revealing how the maximum particle energy and spectral shape depend on diffusion parameters and aligning with recent observations.

Contribution

It introduces a realistic perpendicular diffusion coefficient with a high-momentum plateau and analyzes its impact on particle acceleration and spectra in supernova remnants.

Findings

Shock modifications are similar across different high-momentum cutoffs.

Low cutoff momenta lead to steeper spectra, removing non-linear DSA concavity.

Results align with high-energy observations of Galactic SNRs.

Abstract

Supernova remnants (SNRs) are believed to accelerate particles up to high energies through the mechanism of diffusive shock acceleration (DSA). Except for direct plasma simulations, all modeling efforts must rely on a given form of the diffusion coefficient, a key parameter that embodies the interactions of energetic charged particles with the magnetic turbulence. The so-called Bohm limit is commonly employed. In this paper we revisit the question of acceleration at perpendicular shocks, by employing a realistic model of perpendicular diffusion. Our coefficient reduces to a power-law in momentum for low momenta (of index $\alpha$), but becomes independent of the particle momentum at high momenta (reaching a constant value $\kappa_{\infty}$ above some characteristic momentum $p_{\rm c}$). We first provide simple analytical expressions of the maximum momentum that can be reached at a given time with this coefficient. Then we perform time-dependent numerical simulations to investigate the shape of the particle distribution that can be obtained when the particle pressure back-reacts on the flow. We observe that, for a given index $\alpha$ and injection level, the shock modifications are similar for different possible values of $p_{\rm c}$, whereas the particle spectra differ markedly. Of particular interest, low values of $p_{\rm c}$ tend to remove the concavity once thought to be typical of non-linear DSA, and result in steep spectra, as required by recent high-energy observations of Galactic SNRs.