Linear analysis of the Kelvin-Helmholtz instability for relativistic magnetohydrodynamics

Abstract: A linear analysis of the Kelvin Helmholtz instability (KHI) in a two di-mensional relativistic magneto-hydrodynamics is considered. As appropriate for astrophysical conditions, we neglect gravity, surface tension and viscosity, so that the relevant equations are those given by particle number and energy-momentum density conservation of a relativistic perfect fluid in flat Minkowskian metric, added by the induction equation. In a vortex sheet approximation an equation governing the dispersion relation is derived and numerically solved. Based on physical parameters, regimes of the KHI are studied and corresponding ranges of parameters are analyzed