Stellar Orbits around the Galactic Center Black Hole

We present new proper motion measurements and simultaneous orbital solutions for three newly identified (S0-16, S0-19, and S0-20) and five previously known (S0-1, S0-2, S0-3, S0-4, and S0-5) stars at the Galactic Center. This analysis pinpoints the Galaxy's central dark mass to within +-1 milli-arcsec and, for the first time from orbital dynamics, limits its proper motion to 0. 8+-0. 7 mas/y. The estimated central dark mass from orbital motions is (4. 0+-0. 3) x10⁶ (Ro/8kpc) ³ Mo; this is a more direct measure of mass than those obtained from velocity dispersion measurements, which are as much as a factor of two smaller. The smallest closest approach is achieved by S0-16, which confines the mass to within a radius of a mere 90 AU and increases the inferred dark mass density by four orders of magnitude compared to earlier analyses based on velocity and acceleration vectors, making the Milky Way the strongest existing case by far for a supermassive black hole at the center of any normal type galaxy. The stellar orbital properties suggest that while the distributions of eccentricities and the directions of the angular momentum vectors are consistent with those of an isotropic system, the distribution of the apoapse directions is not, at the 2 sigma level. Furthermore, there appears to be an inner cutoff in the distribution of apoapse distances for stars brighter than K=15. 5, with a minimum value around 1800 AU. If the bias in the distribution of apoapse directions is indeed real, this would favor a formation scenario in which the Sgr A* cluster stars are young stars that have been tidally stripped from a dense in-spiraling cluster near the cluster's periapse passage (>1800 AU) and subsequently scattered inward.