Stellar Dynamics in the Central Arcsecond of Our Galaxy

We present proper motions for $>$40 stars at projected distances $\leq1.2''$from Sagittarius A* (Sgr A*). We find evidence on a $\geq2\sigma$ level forradial anisotropy of the cluster of stars within $1''$ of Sgr A*. We find noevidence for a stationary source or variable source at the position of Sgr A*.We confirm/find accelerated motion for 6 stars, with 4 stars having passed thepericenter of their orbits during the observed time span. Wecalculated/constrained the orbital parameters of these stars. All orbits havemoderate to high eccentricities. We discuss the possible bias in detectingpreferentially orbits with high eccentricities. We find that the center ofacceleration for all the orbits coincides with the radio position of Sgr A*. From the orbit of the star S2, the currently most tightly constrained one, wedetermine the mass of Sgr A* to be $3.3\pm0.7\times10^{6}$M$_{\odot}$ and itsposition to $2.0\pm2.4$ mas East and $2.7\pm4.5$ mas South of the nominal radioposition. The mass estimate for the central dark mass from the orbit of S2 isfully consistent with the mass estimate of $3.4\pm0.5\times10^{6}$M$_{\odot}$obtained from stellar proper motions within $1.2''$ of Sgr A* using aLeonard-Merritt mass estimator. We find that radio astronomical observations ofthe proper motion of Sgr A* in combination with its intrinsic source size placeat the moment the tightest constraints on the mass density of Sgr A*, whichmust exceed $\rho_{\mathrm{SgrA*}}>3\times10^{19}\mathrm{M}_{\odot}\mathrm{pc}^{-3}$.Comment: 51 pages, 16 Figures, reviewed ms submitted to ap