Kelvin-Helmholtz instabilities of relativistic magnetohydrodynamic planar flows

Aims. We investigate the stability properties of the interface separating two relativistic magnetized fluids in relative motion. The two fluids are governed by the (special) relativistic equations for a perfect magnetized gas in the infinite conductivity approximation. Methods. 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 by adopting four physical parameters, namely: the flow velocity, the relativistic and Alfvénic Mach numbers and the inclination of the wave vector’s projection on the plane of the interface. Results. From the numerical solution of the dispersion relation, we find in general two separate regions of instability, associated respectively with slow and fast magnetosonic modes. Modes parallel to the flow velocity are destabilized only for sufficiently low magnetization. For the latter case, flow stabilization can be attained, additionally, sufficiently large relativistic relative motions between the two fluids. Conclusions.