The proper motion of Sagittarius A*. I. First VLBA results

We observed Sgr A* and two extragalactic radio sources nearby in angle with the VLBA over a period of 2 yr and measured relative positions with an acc uracy approaching 0.1 mas. The apparent proper motion of Sgr A* relative to J1745-283 is 5.90 +/- 0.4 mas yr(-1), almost entirely in the plane of the Galaxy. The effects of the orbit of the Sun around the Galactic center can account for this motion, and any residual proper motion of Sgr A*, with res pect to extragalactic sources, is less than about 20 km s(-1). Assuming tha t Sgr A* is at rest at the center of the Galaxy, we estimate that the circu lar rotation speed in the Galaxy at the position of the Sun, Theta(0) is 21 9 +/- 20 km s(-1), scaled by R-0/8.0 kpc. Current observations are consiste nt with Sgr A* containing all of the nearly 2.6 x 10(6) M-circle dot deduce d from stellar proper motions, in the form of a massive black hole. While t he low luminosity of Sgr A*, for example, might possibly have come from a c ontact binary containing of order 10 M-circle dot the lack of substantial m otion rules out a "stellar" origin for Sgr A*. The very slow speed of Sgr A * yields a lower limit to the mass of Sgr A* of about 1000 M-circle dot, Ev en for this mass, Sgr A* appears to be radiating at less than 0.1% of its E ddington limit.