Rapid cosmic-ray acceleration at perpendicular shocks in supernova remnants

TL;DR

This paper demonstrates that perpendicular shocks in supernova remnants are highly efficient at accelerating cosmic rays, especially when specific shock and scattering conditions are met, potentially explaining ultra-high-energy cosmic ray origins.

Contribution

It provides analytical and simulation-based evidence that perpendicular shocks can accelerate particles rapidly under certain conditions, extending standard shock acceleration theory.

Findings

Spectral index softens by unity at optimal conditions.

Acceleration time doubles compared to standard theory.

Supports supernovae in Wolf-Rayet winds as sources of >10^{15} eV protons.

Abstract

Perpendicular shocks are shown to be rapid particle accelerators that perform optimally when the ratio $u_{\rm s}$ of the shock speed to the particle speed roughly equals the ratio $1/\eta$ of the scattering rate to the gyro frequency. We use analytical methods and Monte-Carlo simulations to solve the kinetic equation that governs the anisotropy generated at these shocks, and find, for $\eta u_{\rm s}\approx1$, that the spectral index softens by unity and the acceleration time increases by a factor of two compared to the standard result of diffusive shock acceleration theory. These results provide a theoretical basis for the thirty-year-old conjecture that a supernova exploding into the wind of a Wolf-Rayet star may accelerate protons to an energy exceeding $10^{15}\,$eV.