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 .
( 29 ) , including 2 ’ 500 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 } can not 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 ^ { \prime \prime } by a superposition of a spheroidal cluster with scale \sim 100 ^ { \prime \prime } and a much larger nuclear disk 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 \pm 0.04 for r < 70 ^ { \prime \prime } .
( 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 ^ { \prime \prime } ) = ( 8.94 \pm 0.31 { | _ { stat } } \pm 0.9 % { | _ { syst } } ) \times { 10 ^ { 6 } } { M _ { \odot } } , { M _ { \bullet } } = ( 3.86 \pm 0.14 { | _ { stat } \pm 0.4 { | _ { syst } } } ) % \times { 10 ^ { 6 } } { M _ { \odot } } , and { R _ { 0 } } = 8.27 \pm 0.09 { | _ { stat } } \pm 0.1 { | _ { syst } } kpc , where the estimated systematic errors account for 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 .
( 35 ) gives { M _ { \bullet } } = ( 4.23 \pm 0.14 ) \times { 10 ^ { 6 } } { M _ { \odot } } and { R _ { 0 } } = 8.33 \pm 0.11 kpc .