Oblique magnetohydrodynamic shocks: Space-like and time-like characteristics

Abstract

Shock waves constitute discontinuities in matter which are relevant in the study of plasma behavior in astrophysical scenarios and in heavy-ion collision. They can produce conical emission in relativistic collisions and are also thought to be the mechanism behind the acceleration of energetic particles in active galactic nuclei and $\ensuremath{\gamma}$-ray bursts. The shocks are mostly hydrodynamic shocks. In a magnetic background they become magnetohydrodynamic (MHD) shocks. For that reason we study the space-like and time-like shock discontinuity in a magnetic plasma. The shocks induce a phase transition in the plasma, here assuming a transition from hadron to quarks. The MHD conservation conditions are derived across the shock. The conservation conditions are solved for downstream velocities and flow angles for given upstream variables. The shock conditions are solved at different baryon densities. For the space-like shocks the anisotropy in the downstream velocity arises due to the magnetic field. The downstream velocity vector always points downward with respect to the shock normal. With the increase in density the anisotropy is somewhat reduced. The magnetic field has effectively no impact on time-like shocks. The slight anisotropy in the downstream flow velocities is caused by the boosting that brings the quantities from the fluid frame to a normal incidence frame.