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 σ l and σ 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 ∼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 v l -histograms. (ii) This requires an axial ratio near q 1 = 0.7 consistent with our determination from star counts, q 1 = 0.73 ± 0.04 for r