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
\nimprovements are made possible by refining our astrometric reference frame with a new geometric optical distortion
\nmodel for the W. M. Keck II 10 m telescope’s adaptive optics camera (NIRC2) in its narrow field mode. For the
\nfirst time, this distortion model is constructed from on-sky measurements and is made available to the public in the
\nform of FITS files.When applied to widely dithered images, it produces residuals in the separations of stars that are
\na factor of ~3 smaller compared with the outcome using previous models. By applying this new model, along with
\ncorrections for differential atmospheric refraction, to widely dithered images of SiO masers at the Galactic center
\n(GC), we improve our ability to tie into the precisely measured radio Sgr A*-rest frame. The resulting infrared
\nreference frame is ~2–3 times more accurate and stable than earlier published efforts. In this reference frame,
\nSgr A* is localized to within a position of 0.6 mas and a velocity of 0.09 mas yr^(−1), or ~3.4 km s^(−1) at 8 kpc (1σ).
\nAlso, proper motions for members of the central stellar cluster are more accurate, although less precise, due to the
\nlimited number of these wide field measurements. These proper motion measurements show that, with respect to
\nSgr A*, the central stellar cluster has no rotation in the plane of the sky to within 0.3 mas yr^(−1) arcsec^(−1), has no
\nnet translational motion with respect to Sgr A* to within 0.1 mas yr^(−1), and has net rotation perpendicular to the
\nplane of the sky along the Galactic plane, as has previously been observed. While earlier proper motion studies
\ndefined a reference frame by assuming no net motion of the stellar cluster, this approach is fundamentally limited
\nby the cluster’s intrinsic dispersion and therefore will not improve with time.We define a reference frame with SiO
\nmasers and this reference frame’s stability should improve steadily with future measurements of the SiO masers in
\nthis region (∝t^(−3/2)). This is essential for achieving the necessary reference frame stability required to detect the
\neffects of general relativity and extended mass on short-period stars at the GC.