We present 3D kinematic observations of stars within the central 0.5 pc of the Milky Way nuclear star cluster using adaptive optics imaging and spectroscopy from the Keck telescopes .
Recent observations have shown that the cluster has a shallower surface density profile than expected for a dynamically relaxed cusp , leading to important implications for its formation and evolution .
However , the true three dimensional profile of the cluster is unknown due to the difficulty in de-projecting the stellar number counts .
Here , we use spherical Jeans modeling of individual proper motions and radial velocities to constrain for the first time , the de-projected spatial density profile , cluster velocity anisotropy , black hole mass ( M _ { \mathrm { BH } } ) , and distance to the Galactic center ( R _ { 0 } ) simultaneously .
We find that the inner stellar density profile of the late-type stars , \rho ( r ) \propto r ^ { - \gamma } to have a power law slope \gamma = 0.05 _ { -0.60 } ^ { +0.29 } , much more shallow than the frequently assumed Bahcall \& Wolf slope of \gamma = 7 / 4 .
The measured slope will significantly affect dynamical predictions involving the cluster , such as the dynamical friction time scale .
The cluster core must be larger than 0.5 pc , which disfavors some scenarios for its origin .
Our measurement of M _ { \mathrm { BH } } = 5.76 _ { -1.26 } ^ { +1.76 } \times 10 ^ { 6 } M _ { \odot } and R _ { 0 } = 8.92 _ { -0.55 } ^ { +0.58 } kpc is consistent with that derived from stellar orbits within 1 \arcsec of Sgr A* .
When combined with the orbit of S0-2 , the uncertainty on R _ { 0 } is reduced by 30 % ( 8.46 _ { -0.38 } ^ { +0.42 } kpc ) .
We suggest that the MW NSC can be used in the future in combination with stellar orbits to significantly improve constraints on R _ { 0 } .