Auroral images of Jupiter reveal a distinctive signature of the downstream corotational wake of Io, as well as of Io itself. The wake signature can be understood as a product of the plasma current that accelerates Io's mass-loaded flux tube up to (almost) corotation with Jupiter. The radially directed acceleration current in the magnetosphere is linked by Birkeland (magnetic field aligned) currents to Jupiter's ionosphere where closure is provided by a meridional Pedersen current. The Pedersen current is proportional to the velocity of the plasma relative to the corotating frame, while the acceleration current is proportional to (minus) the time rate of change of that velocity. Thus the requirement of current closure implies a simple exponential decay of the relative velocity, with a time constant that is proportional to the ratio of flux-tube mass content to ionospheric Pedersen conductance. For expected values of these parameters, the time constant is ~ 0.5 hours, implying a length scale ~ 1 RJ (= Jupiter's radius) for the variation of velocity with downstream distance in the wake, or ~12¿ of longitude. This length scale is remarkably close to that of the observed brightness of the wake auroral signature.