  Over a two year period (1995-1997), we have conducted a diffraction-limited
imaging study at 2.2 microns of the inner 6"x6" of the Galaxy's central stellar
cluster using the Keck 10-m telescope. The K band images obtained reveal a
large population of faint stars. We use an unbiased approach for identifying
and selecting stars to be included in this proper motion study, which results
in a sample of 90 stars with brightness ranging from K=9-17 and velocities as
large as 1,400+-100 km/sec. Compared to earlier work (Eckart et al. 1997;
Genzel et al. 1997), the source confusion is reduced by a factor of 9, the
number of stars with proper motion measurement in the central 25 arcsec^2 of
our galaxy is doubled, and the accuracy of the velocity measurements in the
central 1 arcsec^2 is improved by a factor of 4. The peaks of both the stellar
surface density and the velocity dispersion are consistent with the position of
the unusual radio source and blackhole candidate, Sgr A*, suggesting that Sgr
A* is coincident (+-0."1) with the dynamical center of the Galaxy. As a
function of distance from Sgr A*, the velocity dispersion displays a falloff
well fit by Keplerian motion about a central dark mass of 2.6(+-0.2)x10^6 Mo
confined to a volume of at most 10^-6 pc^3, consistent with earlier results.
Although uncertainties in the measurements mathematically allow for the matter
to be distributed over this volume as a cluster, no realistic cluster is
physically tenable. Thus, independent of the presence of Sgr A*, the large
inferred central density of at least 10^12 Mo/pc^3, which exceeds the
volume-averaged mass densities found at the center of any other galaxy, leads
us to the conclusion that our Galaxy harbors a massive central black hole.
