On the tidal radius of satellites on prograde and retrograde orbits

Abstract: A tidal radius is a distance from a satellite orbiting in a host potential beyond which its material is stripped by the tidal force. We derive a revised expression for the tidal radius of a rotating satellite which properly takes into account the possibility of prograde and retrograde orbits of stars. Besides the eccentricity of the satellite orbit, the tidal radius depends also on the ratio of the satellite internal angular velocity to the orbital angular velocity. We compare our formula to the results of two $N$-body simulations of dwarf galaxies orbiting a Milky Way-like host on a prograde and retrograde orbit. The tidal radius for the retrograde case is larger than for the prograde. We introduce a kinematic radius separating stars still orbiting the dwarf galaxy from those already stripped and following the potential of the host galaxy. We find that the tidal radius matches very well the kinematic radius. Our results provide a connection between the formalism of the tidal radius derivation and the theory of resonant stripping.