Astrometry in the Galactic Center with the Thirty Meter Telescope

We report on the expected astrometric performance of the Thirty Meter Telescope's InfraRed Imaging Spectrometer (IRIS) as determined using simulated images of the Galactic center. This region of the Galaxy harbors a supermassive black hole and a dense nuclear stellar cluster, thus providing an ideal laboratory for testing crowded-field astrometry with the IRIS imager. Understanding the sources of astrometric error is also important for making precision measurements of the short-period stars orbiting the supermassive black hole in order to probe the curvature of space-time as predicted by General Relativity. Various sources of error are investigated, including read-out and photon noise, spatially variable point spread functions, confusion, static distortion for the IRIS imager, and the quadratic probe arm distortion. Optical distortion is the limiting source of error for bright stars (K < 15), while fainter sources will be limited by the effects of source confusion. A detailed astrometric error budget for the Galactic center science case is provided.