Comparing Observed Stellar Kinematics and Surface Densities in a Low-latitude Bulge Field to Galactic Population Synthesis Models

We present an analysis of Galactic bulge stars from Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations of the Stanek window (l,b=[0.25,-2.15]) from two epochs approximately two years apart. This dataset is adjacent to the provisional Wide-field Infrared Survey Telescope (WFIRST) microlensing field. Proper motions are measured for approximately 115,000 stars down to 28th mag in V band and 25th mag in I band, with accuracies of 0.5 mas yr$^{-1}$ (20 km s$^{-1}$) at I $\approx$ 21. A cut on the longitudinal proper motion $\mu_l$ allows us to separate disk and bulge populations and produce bulge-only star counts that are corrected for photometric completeness and efficiency of the proper-motion cut. The kinematic dispersions and surface density in the field are compared to the nearby SWEEPS sight-line, finding a marginally larger than expected gradient in stellar density. The observed bulge star counts and kinematics are further compared to the Besancon, Galaxia, and GalMod Galactic population synthesis models. We find that most of the models underpredict low-mass bulge stars by $\sim$33% below the main-sequence turnoff, and upwards of $\sim$70% at redder J and H wavebands. While considering inaccuracies in the Galactic models, we give implications for the exoplanet yield from the WFIRST microlensing mission.