Improving Galactic Center Astrometry by Reducing the Effects of
  Geometric Distortion
  We present significantly improved proper motion measurements of the Milky
Way's central stellar cluster. These improvements are made possible by refining
our astrometric reference frame with a new geometric optical distortion model
for the W. M. Keck II 10 m telescope's Adaptive Optics camera (NIRC2) in its
narrow field mode. For the first time, this distortion model is constructed
from on-sky measurements, and is made available to the public. When applied to
widely dithered images, it produces residuals in the separations of stars that
are a factor of ~3 smaller compared to the outcome using previous models. By
applying this new model, along with corrections for differential atmospheric
refraction, to widely dithered images of SiO masers at the Galactic center, we
improve our ability to tie into the precisely measured radio Sgr A*-rest frame.
The resulting infrared reference frame is ~2-3 times more accurate and stable
than earlier published efforts. In this reference frame, Sgr A* is localized to
within a position of 0.6 mas and a velocity of 0.09 mas/yr, or ~3.4 km/s at 8
kpc (1 sigma). While earlier proper motion studies defined a reference frame by
assuming no net motion of the stellar cluster, this approach is fundamentally
limited by the cluster's intrinsic dispersion and therefore will not improve
with time. We define a reference frame with SiO masers and this reference
frame's stability should improve steadily with future measurements of the SiO
masers in this region. This is essential for achieving the necessary reference
frame stability required to detect the effects of general relativity and
extended mass on short-period stars at the Galactic center.
