Relativistic oblique shocks with ordered or random magnetic fields: tangential field governs

TL;DR

This paper demonstrates that in relativistic magnetohydrodynamic shocks, the jump conditions are primarily determined by the tangential magnetic field component, regardless of the overall field geometry or inclination, simplifying theoretical modeling.

Contribution

It introduces the concept of tangential magnetization $\sigma_ot$ and shows it governs shock jump conditions across various magnetic field configurations.

Findings

Jump conditions depend on $\sigma_ot$, not total magnetization.

Analytical solutions are provided for arbitrary field inclinations and anisotropies.

Results simplify modeling of shocks in GRBs and FRBs.

Abstract

Relativistic magnetohydrodynamic shocks are efficient particle accelerators, often invoked in the models of gamma-ray bursts (GRBs) and shock-powered fast radio bursts (FRBs). Most theoretical studies assume a perpendicular shock with an ordered magnetic field perpendicular to the shock normal. However, the degree of magnetization $\sigma$ and the magnetic field geometry in shock-powered GRB/FRB scenarios are still poorly constrained by observations. Analogous to the magnetization $\sigma$ associated with the total field strength, we define a tangential magnetization $\sigma_\perp$ associated with the tangential field component. We explore the jump conditions of magnetized relativistic shocks, either with an ordered field of arbitrary inclination angle or with a random field of arbitrary anisotropy. In either case, we find that the jump conditions of relativistic shocks are governed by the tangential magnetization $\sigma_\perp$ instead of the total magnetization $\sigma$, insensitive to the inclination angles or the anisotropy of the pre-shock magnetic field. The approximated analytical solution developed in this work could serve as a quick check for numerical simulations and apply to theoretical studies of GRBs/FRBs with a more general field geometry.