Proper Motion of Milky Way Dwarf Spheroidals from Line-of-Sight Velocities

Proper motions for several Milky Way dwarf spheroidal (dSph) galaxies have been determined using both ground and space-based imaging. These measurements require long baselines and repeat observations and typical errors are of order ten milli-arcseconds per century. In this paper, we utilize the effect of "perspective rotation" to show that systematic proper motion of some dSphs can be determined to a similar precision using only stellar line-of-sight velocities. We show that including the effects of small intrinsic rotation in dSphs increases the proper motion errors by about a factor of two. We provide error projections for future data sets, and show that proposed thirty meter class telescopes will measure the proper motion of a few dSphs with milli-arcsecond per century precision.