HST/WFPC2 proper motions in two bulge fields: kinematics and stellar population of the Galactic bulge

We report proper motion dispersions for stars in the direction of two fields of the Galactic bulge, using HST/WFPC2 images taken six years apart. Our two fields are Baade's Window (l,b)=(1.13,-3.77) and Sgr I (l,b)=(1.25 ,-2.65). Our proper motion dispersions are in good agreement with prior ground- and space-based proper motion studies in bulge fields, but in contrast to some prior studies, we do not exclude any subset of stars from our studies. In Baade's Window, we find the $l$ and $b$ proper motion dispersions are 2.9 and 2.5 mas/yr, while in Sgr I, they are 3.3 and 2.7 mas/yr, respectively. For the first time, we can clearly separate the foreground disk stars out from the bulge because of their large mean apparent proper motion. The population with non-disk kinematics (which we conclude to be the bulge) has an old main sequence turnoff point, similar to those found in old, metal rich bulge globular clusters while those stars selected to have disk kinematics lie on a fully populated main sequence. Separating main sequence stars by luminosity, we find strong evidence that the bulge population is rotating, largely explaining observations of proper motion anisotropy in bulge fields. Because we have isolated such a pure sample of stars in the bulge, we have one of the clearest demonstrations that the old stellar population of the inner bulge/bar is in fact rotating.