Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

Shock jump conditions are obtained for steady-state, plane shocks withoblique magnetic fields and arbitrary flow speeds. For ultrarelativistic andnonrelativistic shocks, the jump conditions may be solved analytically. Formildly relativistic shocks, analytic solutions are obtained for isotropicpressure using an approximation for the adiabatic index that is valid in highsonic Mach number cases. In the more general case of gyrotropic pressure, thejump conditions cannot be solved analytically without additional assumptions,and the effects of gyrotropic pressure are investigated by parameterizing thedistribution of pressure parallel and perpendicular to the magnetic field. Ournumerical solutions reveal that relatively small departures from isotropy(e.g., about 20%) produce significant changes in the shock compression ratio,r, at all shock Lorentz factors, including ultrarelativistic ones, where ananalytic solution with gyrotropic pressure is obtained. In particular, eitherdynamically important fields or significant pressure anisotropies can incurmarked departures from the canonical gas dynamic value of r=3 for a shockedultrarelativistic flow and this may impact models of particle acceleration ingamma-ray bursts and other environments where relativistic shocks are inferred.The jump conditions presented apply directly to test-particle acceleration, andwill facilitate future self-consistent numerical modeling of particleacceleration at oblique, relativistic shocks.Comment: 26 pages with 7 figures, submitted to Ap. J. April 200