Stellar Orbits around the Galactic Center Black Hole

We present new proper motion measurements and simultaneous orbital solutionsfor three newly identified (S0-16, S0-19, and S0-20) and four previously known(S0-1, S0-2, S0-4, and S0-5) stars at the Galactic Center. This analysispinpoints the Galaxy's central dark mass to within +-1 milli-arcsec and, forthe first time from orbital dynamics, limits its proper motion to 1.5+-0.5mas/y, which is consistent with our derivation of the position of Sgr A* in theinfrared reference frame (+-10 mas). The estimated central dark mass fromorbital motions is 3.7 (+-0.2) x 10^6 (Ro/8kpc)^3 Mo; this is a more directmeasure of mass than those obtained from velocity dispersion measurements,which are as much as a factor of two smaller. The smallest closest approach isachieved by S0-16, which confines the mass to within a radius of a mere 45 AUand increases the inferred dark mass density by four orders of magnitudecompared to earlier analyses based on velocity and acceleration vectors, makingthe Milky Way the strongest existing case by far for a supermassive black holeat the center of any normal type galaxy. The stellar orbital properties suggestthat the distributions of eccentricities and angular momentum vector andapoapse directions are consistent with those of an isotropic system. Thereforemany of the mechanisms proposed for the formation of young stars in thevicinity of a supermassive black hole, such as formation from a pre-existingdisk, are unlikely solutions for the Sgr A* cluster stars. Unfortunately, allexisting alternative theories are also somewhat problematic. Understanding theapparent youth of stars in the Sgr A* cluster, as well as the more distant He Iemission line stars, has now become one of the major outstanding issues in thestudy of the Galactic Center.Comment: Abridged abstract, 38 pages, 5 figures, ApJ accepte