The Proper Motion of Sagittarius A*. II. The Mass of Sagittarius A*

We report measurements with the VLBA of the position of Sgr A* with respect to two extragalactic radio sources over a period of eight years. The apparent proper motion of relative to J1745-283 is 6. 379 +/- 0. 024 mas/y along a position angle of 209. 60 +/- 0. 18 degrees, 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 the residual proper motion of Sgr A* perpendicular to the plane of the Galaxy is -0. 4 +/- 0. 9 km/s. A maximum-likelihood analysis of the motion expected for a massive object within the observed Galactic center stellar cluster indicates that Sgr A* contains more than about 10% of the approximately 4 x 10⁶ Msun deduced from stellar orbits. The intrinsic size of Sgr A*, as measured by several investigators, is less than 1 AU, and the implied mass density of ~10²2 Msun/pc³ is within about three orders of magnitude of a comparable super-massive black hole within its Schwarzschild radius. Our observations provide the first direct evidence that a compact radiative source at the center of a galaxy contains of order 10⁶ Msun and provides overwhelming evidence that it is in the form of a super-massive black hole. Finally, the existence of "intermediate mass" black holes more massive than ~10⁴ Msun between roughly 10³ and 10⁵ AU from Sgr A* are excluded.