Efficiency of CR acceleration in supernova remnants

Abstract

Cosmic ray (CR) acceleration in supernova remnants (SNRs) has been studied for a wide range of interstellar medium (ISM) parameters. The CR transport equation with Bohm diffusion coefficient has been numerically solved self-consistently with gas dynamic equations for the underlying flow. It is shown that CRs are accelerated in SNRs very efficiently, up to 90% of the explosion energy can be absorbed by CRs. At the same time, contrary to the plane-wave and simplified model prediction, the SN shock cannot be completely modified: together with a smooth precursor, the shock front always includes a sufficiently strong subshock. The shock compression ratio σ ∼- M3/4 is an increasing function of the shock Mach number M, it can be much greater than 4, the compression ratio of strong classical shocks. Alfven wave dissipation restricts the shock compression ratio to about 7.3. Acceleration efficiency remains high, about 50% of the explosion energy is absorbed by CRs. The result fits very well with the requirements for the energy density of galactic CRs, and also with their spectral shape in the energy range up to 1015 eV.