Stellar orbits around the Galactic center black hole

We present new diffraction-limited images of the Galactic center, obtained with the W. M. Keck I 10m telescope. Within 0.4 of the Galaxy's central dark mass, 17 proper-motion stars, with K magnitudes ranging from 14.0 to 16.8, are identified, and 10 of these are new detections ( six were also independently discovered by others). In this sample, three newly identified (S0-16, S0-19, and S0-20) and four previously known ( S0-1, S0-2, S0-4, and S0-5) sources have measured proper motions that reveal orbital solutions. Orbits are derived simultaneously so that they jointly constrain the central dark object's properties: its mass, its position, and, for the first time using orbits, its motion on the plane of the sky. This analysis pinpoints the Galaxy's central dark mass to within 1.3 mas ( 10 AU) and limits its propermotion to 1.5 +/- 0.5 mas yr(-1) (or equivalently 60 +/- 20 km s(-1)) with respect to the central stellar cluster. This localization of the central darkmass is consistent with our derivation of the position of the radio source SgrA* in the infrared reference frame ( +/- 10 mas) but with an uncertainty that is a factor of 8 times smaller, which greatly facilitates searches for near- infrared counterparts to the central black hole. Consequently, one previous claim for such a counterpart can now be ascribed to a close stellar passage in 1996. Furthermore, we can place a conservative upper limit of 15.5 mag on any steady state counterpart emission. The estimated central dark mass from orbital motions is 3.7(+/- 0.2) x 10(6) R-0/(8 kpc)](3) M-.; this is a more direct measure of mass than those obtained from velocity dispersion measurements, which are as much as a factor of 2 smaller. The Galactic center's distance, which adds an additional 19% uncertainty in the estimated mass, is now the limiting source of uncertainty in the absolute mass. For stars in this sample, the closest approach is achieved by S0-16, which came within a mere 45 AU (= 0.0002 pc = 600R(s)) at a velocity of 12,000 km s(-1). This increases the inferred dark mass density by 4 orders of magnitude compared to earlier analyses based on velocity and acceleration vectors, making the Milky Way the strongest existing case for a supermassive black hole at the center of a normal-type galaxy. Well-determined orbital parameters for these seven Sgr A* cluster stars also provide new constraints on how these apparently massive, young (< 10 Myr) stars formed in a region that seems to be hostile to star formation. Unlike the more distant He I emission line stars - another population of young stars in the Galactic center - that appear to have coplanar orbits, the Sgr A* cluster stars have orbital properties ( eccentricities, angular momentum vectors, and apoapse directions) that are consistent with an isotropic distribution. Therefore, many of the mechanisms proposed for the formation of the He I stars, such as formation from a preexisting disk, are unlikely solutions for the Sgr A* cluster stars. Unfortunately, alternative theories for producing young stars, or old stars that look young, in close proximity to a central supermassive black hole are all also somewhat problematic. Understanding the apparent youth of stars in the Sgr A* cluster, as well as the more distant He I emission line stars, has now become one of the major outstanding issues in the study of the Galactic center.