Shocked relativistic magnetohydrodynamic flows with application to pulsar winds

Abstract

The time-dependent behavior of a shocked spherically symmetric relativistic fluid with tangential magnetic field is investigated, considering the case where the boundaries of the shocked fluid move at constant velocity so that self-similar solutions exist. The behavior of the fluid in the ultrarelativistic regime is compared to that in the nonrelativistic regime; there is a smooth transition between these limits. If a magnetic field is present, the magnetic pressure becomes increasingly important with distance from the shock wave; the gas pressure vanishes at the contact discontinuity that bounds the flow. Analytic expressions are given which describe the flow. The solutions can be applied to the evolution of shocked relativistic pulsar winds, which are probably observed as Crab-like supernova remnants. A model for the Crab Nebula, based on the steady-state model of Kennel and Coroniti (1984), indicates that sigma = 0.0016, where sigma is twice the ratio of magnetic to particle energy in the wind as measured in the fluid frame. This is about half the value suggested by Kennel and Coroniti and is much smaller than the value that might be expected for a pulsar wind.