THREE-DIMENSIONAL STELLAR KINEMATICS AT THE GALACTIC CENTER: MEASURING THE NUCLEAR STAR CLUSTER SPATIAL DENSITY PROFILE, BLACK HOLE MASS, AND DISTANCE

Abstract

We present 3D kinematic observations of stars within the central 0.5 pc of\nthe Milky Way nuclear star cluster using adaptive optics imaging and\nspectroscopy from the Keck telescopes. Recent observations have shown that the\ncluster has a shallower surface density profile than expected for a dynamically\nrelaxed cusp, leading to important implications for its formation and\nevolution. However, the true three dimensional profile of the cluster is\nunknown due to the difficulty in de-projecting the stellar number counts. Here,\nwe use spherical Jeans modeling of individual proper motions and radial\nvelocities to constrain for the first time, the de-projected spatial density\nprofile, cluster velocity anisotropy, black hole mass ($M_\\mathrm{BH}$), and\ndistance to the Galactic center ($R_0$) simultaneously. We find that the inner\nstellar density profile of the late-type stars, $\\rho(r)\\propto r^{-\\gamma}$ to\nhave a power law slope $\\gamma=0.05_{-0.60}^{+0.29}$, much more shallow than\nthe frequently assumed Bahcall $\\&$ Wolf slope of $\\gamma=7/4$. The measured\nslope will significantly affect dynamical predictions involving the cluster,\nsuch as the dynamical friction time scale. The cluster core must be larger than\n0.5 pc, which disfavors some scenarios for its origin. Our measurement of\n$M_\\mathrm{BH}=5.76_{-1.26}^{+1.76}\\times10^6$ $M_\\odot$ and\n$R_0=8.92_{-0.55}^{+0.58}$ kpc is consistent with that derived from stellar\norbits within 1$^{\\prime\\prime}$ of Sgr A*. When combined with the orbit of\nS0-2, the uncertainty on $R_0$ is reduced by 30% ($8.46_{-0.38}^{+0.42}$ kpc).\nWe suggest that the MW NSC can be used in the future in combination with\nstellar orbits to significantly improve constraints on $R_0$.\n