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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 speedv_A, as appropriate for realistic systems. The stability properties are chiefly determined by the angleψbetween the wavevector and the jet magnetic field. Forψ=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 ( $0<M_e\equiv \left(v/v_{\mathrm{A}}\right)\cos \theta <1$, wherevis the shear velocity andθthe angle between the velocity and the wavevector). Forψ= 0, the free energy in the velocity shear needs to overcome the magnetic tension, and only super-Alfvénic jets are unstable ( $1<M_e<\sqrt{{(1+{\mathrm{\Gamma }}_w^2)/[1+(v_{\mathrm{A}}/c)}^2{\mathrm{\Gamma }}_w^2]}$, with Γ_wthe wind adiabatic index). Our results have important implications for the propagation and emission of relativistic magnetized jets. 

ABSTRACT We study the linear stability of a planar interface separating two fluids in relative motion, focusing on the symmetric configuration where the two fluids have the same properties (density, temperature, magnetic field strength, and direction). We consider the most general case with arbitrary sound speed cs, Alfvén speed vA, and magnetic field orientation. For the instability associated with the fast mode, we find that the lower bound of unstable shear velocities is set by the requirement that the projection of the velocity on to the fluid-frame wavevector is larger than the projection of the Alfvén speed on to the same direction, i.e. shear should overcome the effect of magnetic tension. In the frame where the two fluids move in opposite directions with equal speed v, the upper bound of unstable velocities corresponds to an effective relativistic Mach number $$M_{\rm re}\equiv v/v_{\rm {f}\perp }\sqrt{(1-v_{\rm {f}\perp }^2)/(1-v^2)} \cos \theta =\sqrt{2}$$, where $$v_{\rm {f}\perp }=[v_{\rm {A}}^2+c_{\rm s}^2(1-v_{\rm {A}}^2)]^{1/2}$$ is the fast speed assuming a magnetic field perpendicular to the wavevector (here, all velocities are in units of the speed of light), and θ is the laboratory-frame angle between the flow velocity and the wavevector projection on to the shear interface. Our results have implications for shear flows in the magnetospheres of neutron stars and black holes – both for single objects and for merging binaries – where the Alfvén speed may approach the speed of light.