Nonacceleration of Sagittarius A*: Implications for galactic structure

We estimate that observations by Backer and collaborators over the past two decades constrain the time derivative of the proper motion of Sgr A* to be less than 0.14 mas yr(-2). Using this result and a measurement by Eckart & Genzel of sigma similar to 560 km s(-1) for the velocity dispersion of the star cluster within 0." 13 of Sgr A*, we derive the following implications. First, if the nuclear star cluster is dominated by a massive black hole, then either Sgr AY: is directly associated with that black hole or it orbits the black hole with a radius less than or similar to 40 AU. Under this assumption, and adopting upsilon(LSR) = 220 +/- 10 km s(-1), the Galacto-centric distance is therefore R-0 = 7.5 +/- 0.4 kpc. If the star cluster is not assumed to contain a massive black hole, Sgr A* is constrained to move slower than 55 km s(-1) (1 sigma) relative to the center of mass of the cluster. This is too weak a limit to provide useful constraints on Galactic structure, but we show that it could be improved by more than one order of magnitude over the next decade. Such an improvement would eliminate the need to make any assumption about a black hole in the derivation of R-0.