We systematically investigate the error sources for high-precision astrometry from adaptive optics based near-infrared imaging data. We focus on the application in the crowded stellar field in the Galactic Center. We show that at the level of <=100 micro-arcseconds a number of effects are limiting the accuracy. Most important are the imperfectly subtracted seeing halos of neighboring stars, residual image distortions and unrecognized confusion of the target source with fainter sources in the background. Further contributors to the error budget are the uncertainty in estimating the point spread function, the signal-to-noise ratio induced statistical uncertainty, coordinate transformation errors, the chromaticity of refraction in Earth's atmosphere, the post adaptive optics differential tilt jitter and anisoplanatism. For stars as bright as mK=14, residual image distortions limit the astrometry, for fainter stars the limitation is set by the seeing halos of the surrounding stars. In order to improve the astrometry substantially at the current generation of telescopes, an adaptive optics system with high performance and weak seeing halos over a relatively small field (r<=3") is suited best. Furthermore, techniques to estimate or reconstruct the seeing halo could be promising.
We derive new constraints on the mass, rotation, orbit structure and statistical parallax of the Galactic old nuclear star cluster (NSC) and the mass of the supermassive black hole. We combine star counts and kinematic data from Fritz et al (2014), including 2'500 line-of-sight velocities and 10'000 proper motions. We show that the difference between the proper motion dispersions sigma_l and sigma_b cannot be explained by rotation, but is a consequence of the flattening of the NSC. We fit the surface density distribution of stars in the central 1000" by a spheroidal cluster with scale ~100" and a much larger nuclear disk component. We compute the two-integral distribution function f(E,Lz) for this density model, and add rotation self-consistently. We find that: (i) The orbit structure of the f(E,Lz) gives an excellent match to the observed velocity dispersion profiles as well as the proper motion and line-of-sight velocity histograms, including the double-peak in the v_l-histograms. (ii) This requires an axial ratio of q= 0.73+-0.04 for r<70" consistent with our determination from star counts. (iii) The NSC is approximately described by an isotropic rotator model. (iv) Using the corresponding Jeans equations to fit the proper motion and line-of-sight velocity dispersions, we obtain best estimates for the NSC mass, black hole mass, and distance M*(r<100")=(8.94+-0.31|stat+-0.9|syst)x10^6Msun, Mbh=(3.86+-0.14|stat+-0.4|syst)x10^6Msun, and R0=8.27+-0.09|stat+-0.1|syst kpc, where the systematic errors estimate additional uncertainties in the dynamical modeling. (v) The combination of the cluster dynamics with the S-star orbits around Sgr A* strongly reduces the degeneracy between black hole mass and Galactic centre distance present in previous S-star studies. A joint statistical analysis with the results of Gillessen et al (2009) gives Mbh=(4.23+-0.14)x10^6Msun and R0=8.33+-0.11kpc.
