A&A 409, 821-829 (2003)

DOI: 10.1051/0004-6361:20034038

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

**R. Vainio**

^{1}, J. J. P. Virtanen^{2}and R. Schlickeiser^{3}^{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

(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.

**Key words:**acceleration of particles

**--**ISM: cosmic rays

**--**galaxies: jets

**--**relativity

**--**shock waves

**--**waves

Offprint request: R. Vainio, rami.vainio@helsinki.fi

**©**

*ESO 2003*