A Non-Parametric Estimate of the Mass of the Central Black Hole in the Galaxy

We estimate the mass of the central black hole in our Galaxy from stellar kinematical data published by Ghez et al. (1998) and Genzel et al. (2000). For this we develop a method, related to Merritt (1993), for non-parametrically reconstructing the mass profile and the stellar distribution function in the central region of the Galaxy from discrete kinematic data, including velocity errors. Models are searched using the Metropolis algorithm. We assume that the mass distribution is spherical and the stellar velocity distribution is isotropic, and devise a test of this assumption. From proper motions we obtain an enclosed mass of $2.0\pm{0.7}\times10^6{\rm M}_{\odot}$ within the inner $0.0044\rm pc$, from radial velocities we obtain a mass of $2.2^{+1.6}_{-1.0}\times10^6{\rm M}_{\odot}$ within 0.046pc and from three-dimensional velocities we obtain $1.8^{+0.4}_{-0.3}\times10^6{\rm M}_{\odot}$ within 0.046pc.