The Proper Motion of Sagittarius A*. III. The Case for a Supermassive Black Hole

We report measurements with the Very Long Baseline Array of the proper motion of Sgr.A* relative to two extragalactic radio sources spanning 18 yr. The apparent motion of Sgr.A* is -6.411.+/-.0.008.mas.yr-1 along the Galactic plane and -0.219.+/-.0.007.mas.yr-1 toward the North Galactic Pole. This apparent motion can almost entirely be attributed to the effects of the Sun's orbit about the Galactic center. Removing these effects yields residuals of -0.58. +/-.2.23 km s-1 in the direction of Galactic rotation and -0.85.+/-.0.75 km s-1 toward the North Galactic Pole. A maximum-likelihood analysis of the motion, both in the Galactic plane and perpendicular to it, expected for a massive object within the Galactic center stellar cluster indicates that the radiative source, Sgr.A*, contains more than about 25% of the gravitational mass of 4.x.106 M. deduced from stellar orbits. The intrinsic size of Sgr.A* is comparable to its Schwarzschild radius, and the implied mass density of.4 1023 M. pc-3 is very close to that expected for a black hole, providing overwhelming evidence that it is indeed a supermassive black hole. Finally, intermediate mass black holes more massive than 3. x.104 M. between approximately 0.003 and 0.1.pc from Sgr.A*. are excluded.