We present new dynamical models of weakly self-gravitating , finite dispersion eccentric stellar disks around central black holes for the double nucleus of M31 .
The disk is fixed in a frame rotating at constant precession speed , and is populated by stars on quasi-periodic orbits whose parents are numerically integrated periodic orbits in the total potential .
A distribution of quasi-periodic orbits about a given parent is approximated by a distribution of Kepler orbits dispersed in eccentricity and orientation , using an approximate phase-space distribution function written in terms of the integrals of motion in the Kepler problem .
We use these models , along with an optimization routine , to fit available published kinematics and photometry in the inner 2 \hbox { $ { } ^ { \prime \prime } $ } of the nucleus .
A grid of 24 best-fit models is computed to accurately constrain the mass of the central black hole and nuclear disk parameters .
We find that the supermassive black hole in M31 has mass M _ { BH } = 5.62 \pm 0.66 \times 10 ^ { 7 } \mbox { $ M _ { \odot } $ } , which is consistent with the observed correlation between the central black hole mass and the velocity dispersion of its host spheroid .
Our models precess rapidly , at \Omega = 36.5 \pm 4.2 \mbox { $ km s ^ { -1 } pc ^ { -1 } $ } , and possess a characteristic radial eccentricity distribution , which gives rise to multi-modal line of sight velocity distributions along lines of sight near the black hole .
These features can be used as sensitive discriminants of disk structure .