Rarefaction wave in relativistic steady magnetohydrodynamic flows

TL;DR

This paper develops a self-similar model of relativistic steady-state MHD rarefaction waves, analyzing how magnetic fields and flow speed influence the dynamics under external pressure drops.

Contribution

It introduces a new relativistic MHD rarefaction model using self-similarity, extending previous Newtonian and hydrodynamic solutions to include magnetic fields and relativistic effects.

Findings

Derived a system of ODEs describing flow dynamics.

Provided analytical results and scaling laws for homogeneous flows.

Explored the role of magnetic fields and flow speed through parametric study.

Abstract

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic (MHD) rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.