The old nuclear star cluster in the Milky Way: dynamics, mass, statistical parallax, and black hole mass

We derive new constraints on the mass, rotation, orbit structure, and statistical parallax of the Galactic old nuclear star cluster and the mass of the supermassive black hole. We combine star counts and kinematic data from Fritz et al., including 2500 line-of-sight velocities and 10 000 proper motions obtained with VLT instruments. 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 nuclear cluster. We fit the surface density distribution of stars in the central 1000 arcsec by a superposition of a spheroidal cluster with scale similar to 100 arcsec and a much larger nuclear disc component. We compute the self-consistent two-integral distribution function f(E, L-z) for this density model, and add rotation self-consistently. We find that (i) the orbit structure of the f(E, L-z) 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 vl-histograms. (ii) This requires an axial ratio near q1 = 0.7 consistent with our determination from star counts, q1 = 0.73 +/- 0.04 for r < 70 arcsec. (iii) The nuclear star cluster 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 nuclear star cluster mass, black hole mass, and distance M-*(r < 100 arcsec) = (8.94 +/- 0.31 vertical bar(stat) +/- 0.9 vertical bar(syst)) x 10(6)M(circle dot), M-center dot =(3.86 +/- 0.14 vertical bar(stat) +/- 0.4 vertical bar(syst)) x10(6) M-circle dot, and R-0 = 8.27 +/- 0.09 vertical bar(stat) +/- 0.1 vertical bar(syst) kpc, where the estimated systematic errors account for additional uncertainties in the dynamical modelling. (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., gives M-center dot = (4.23 +/- 0.14) x 10(6)M(circle dot) and R-0 = 8.33 +/- 0.11 kpc.