On the linear theory of Kelvin-Helmholtz instabilities of relativistic magnetohydrodynamic planar flows

TL;DR

This paper analyzes the linear stability of relativistic magnetized flow interfaces, revealing conditions for instability related to magnetosonic modes and flow parameters, with implications for astrophysical jet stability.

Contribution

It provides a detailed linear stability analysis of relativistic MHD shear flows using the vortex-sheet approximation, deriving dispersion relations and identifying instability regimes.

Findings

Two separate instability regions linked to slow and fast magnetosonic modes.

Destabilization occurs for modes parallel to flow velocity at low magnetization.

High relativistic velocities can stabilize the interface.

Abstract

We investigate the linear stability properties of the plane interface separating two relativistic magnetized flows in relative motion. The two flows are governed by the (special) relativistic equations for a magnetized perfect gas in the infinite conductivity approximation. By adopting the vortex-sheet approximation, the relativistic magnetohydrodynamics equations are linearized around the equilibrium state and the corresponding dispersion relation is derived and discussed. The behavior of the configuration and the regimes of instability are investigated following the effects of four physical parameters, namely: the flow velocity, the relativistic and Alfv\'enic Mach numbers and the inclination of the wave vector on the plane of the interface. From the numerical solution of the dispersion relation, we find in general two separate regions of instability, associated respectively with the slow and fast magnetosonic modes. Modes parallel to the flow velocity are destabilized only for sufficiently low magnetization. For the latter case, stabilization is attained, additionally, at sufficiently large relativistic velocities between the two flows in relative motion. The relevance of these results to the study of the stability of astrophysical jets is briefly commented.