Near-Infrared Astrometry of Star Clusters with Different Flavors of Adaptive Optics and HST

High-precision infrared astrometry is a powerful tool for the study of resolved stellar populations throughout our Galaxy. We highlight two particular science cases that require precise infrared astrometry: (1) measuring the initial mass function in massive young clusters throughout the Milky Way and (2) finding isolated black holes that photometrically and astrometrically lens background bulge stars. Using astrometric results from these science cases, we perform a comparative analysis of the infrared astrometric capabilities from the Keck single-conjugate adaptive optics (AO) system, the Gemini multi-conjugate AO system, and the Hubble WFC3IR instrument. For the most crowded fields and a small region of interest, we show that Keck's single-conjugate AO system and the well-characterized NIRC2 instrument produce the highest astrometric precision at similar to 150 mu as. However, for targets that cover a wider field of view, both the Gemini South AO Imager (GSAOI) and HST WFC3IR should be considered carefully. GSAOI currently delivers lower astrometric precision than HST WFC3IR for a given integration time; but, programs that require more frequent astrometric measurements over longer periods of time may benefit from the higher availability and possibly longer lifetime of GSAOI.