Orbit-superposition models of discrete, incomplete stellar kinematics: application to the Galactic centre

Abstract

We present a method for fitting orbit-superposition models to the kinematics of discrete stellar systems when the available stellar sample has been filtered by a known selection function. The fitting method can be applied to any model in which the distribution function is represented as a linear superposition of basis elements with unknown weights. As an example, we apply it to Fritz et al.'s kinematics of the innermost regions of the Milky Way's nuclear stellar cluster. Assuming spherical symmetry, our models fit a black hole of mass $M_{\bullet }=(3.76\pm 0.22)\times 10^6{M}_{\odot }$, surrounded by an extended mass $M_{\star }=(6.57\pm 0.54)\times 10^6{M}_{\odot }$ within 4 pc. Within 1 pc the best-fitting mass models have an approximate power-law density cusp $\rho \propto r^{-\gamma }$ with $\gamma =1.3\pm 0.3$. We carry out an extensive investigation of how our modelling assumptions might bias these estimates: $M_{\bullet }$ is the most robust parameter and $\gamma$ the least. Internally the best-fitting models have broadly isotropic orbit distributions, apart from a bias towards circular orbits between 0.1 and 0.3 parsec.

17 pages, MNRAS accepted

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• The Black Hole Mass of NGC 4151 from Stellar Dynamical Modeling
• Linking nearby stellar streams to more distant halo overdensities
• Minimal conditions for survival of technological civilizations in the face of stellar evolution
• Basis function expansions for galactic dynamics: Spherical versus cylindrical coordinates
• Dynamical mass distribution and velocity structure of the Galactic centre
• Self-consistent Solutions of Evolving Nuclear Star Clusters with Two-Dimensional Monte-Carlo Dynamical Simulations
• Co-evolution of Nuclear Star Clusters and Massive Black Holes: Extreme Mass-Ratio Inspirals