Alfvén-wave transmission and test-particle acceleration in parallel relativistic shocks

¹ Department of Physical Sciences, P O Box 64, 00014 University of Helsinki, Finland
² Tuorla Observatory (Tuorla Observatory is part of the Väisälä Institute for Space Physics & Astronomy, University of Turku, Finland.) , University of Turku, 21500 Piikkiö, Finland
³ Institut für Theoretische Physik IV, Ruhr-Universität Bochum, 44780 Bochum, Germany

Corresponding author: R. Vainio, rami.vainio@helsinki.fi

Received: 2 July 2003
Accepted: 28 July 2003

Abstract

Alfvén-wave transmission through super-Alfvénic parallel relativistic shock waves is studied. We calculate the wave transmission coefficients for given shock properties. We show (i) that the Alfvén waves downstream the shock wave are propagating predominantly anti-parallel to the flow direction for low-Mach-number shocks, as in the case of non-relativistic shocks; and (ii) that for high-Mach-number ultra-relativistic shocks the forward and backward downstream waves are in equipartition. For low Alfvénic Mach numbers, the scattering center compression ratio of the shock, thus, becomes large and the spectral index of accelerated test particles approaches the limit at shock waves approaching the critical value of the quasi-Newtonian Alfvénic Mach number (i.e., the ratio of upstream fluid and Alfvén proper speeds), which depends on the shock properties, and equals the square root of the compression ratio at the test-wave limit. Although the inclusion of the wave electromagnetic and velocity fields to the shock jump conditions is likely to decrease the scattering-center compression ratio for shocks with critical Mach numbers, values significantly above the gas compression ratio can be expected for such shocks. Particle acceleration in weak relativistic shocks propagating in magnetized astrophysical jets may, therefore, be substantially more efficient than predicted by models neglecting turbulent electric fields.