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 for radial anisotropy of the cluster of stars within $1''$ of Sgr A*. We find no evidence 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 the pericenter of their orbits during the observed time span. We calculated/constrained the orbital parameters of these stars. All orbits have moderate to high eccentricities. We discuss the possible bias in detecting preferentially orbits with high eccentricities. We find that the center of acceleration 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, we determine the mass of Sgr A* to be $3.3\pm0.7\times10^{6}$M$_{\odot}$ and its position to $2.0\pm2.4$ mas East and $2.7\pm4.5$ mas South of the nominal radio position. The mass estimate for the central dark mass from the orbit of S2 is fully 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 a Leonard-Merritt mass estimator. We find that radio astronomical observations of the proper motion of Sgr A* in combination with its intrinsic source size place at the moment the tightest constraints on the mass density of Sgr A*, which must exceed $\rho_{\mathrm{Sgr A*}}>3\times10^{19}\mathrm{M}_{\odot}\mathrm{pc}^{-3}$.