The Kelvin–Helmholtz Instability at the Boundary of Relativistic Magnetized Jets

Abstract

Abstract We study the linear stability of a planar interface separating two fluids in relative motion, focusing on conditions appropriate for the boundaries of relativistic jets. The jet is magnetically dominated, whereas the ambient wind is gas-pressure-dominated. We derive the most general form of the dispersion relation and provide an analytical approximation of its solution for an ambient sound speed much smaller than the jet Alfvén speed v A, as appropriate for realistic systems. The stability properties are chiefly determined by the angle ψ between the wavevector and the jet magnetic field. For ψ = π/2, magnetic tension plays no role, and our solution resembles the one of a gas-pressure-dominated jet. Here, only sub-Alfvénic jets are unstable ( 0 < M e ≡ ( v / v A ) cos θ < 1 , where v is the shear velocity and θ the angle between the velocity and the wavevector). For ψ = 0, the free energy in the velocity shear needs to overcome the magnetic tension, and only super-Alfvénic jets are unstable ( 1 < M e < ( 1 + Γ w 2 ) / [ 1 + ( v A / c ) 2 Γ w 2 ] , with Γ w the wind adiabatic index). Our results have important implications for the propagation and emission of relativistic magnetized jets.