Eccentric Nuclear Disks with Self-Gravity: Predictions for the Double Nucleus of M31

We present a method for constructing models of weakly self-gravitating, finite dispersion eccentric stellar disks around central black holes. The disk is stationary in a frame rotating at a constant precession speed. The stars populate quasi-periodic orbits whose parents are numerically integrated periodic orbits in the total potential. We approximate the quasi-periodic orbits by distributions of Kepler orbits dispersed in eccentricity and orientation, using an approximate phase-space distribution function written in terms of the Kepler integrals of motion. We show an example of a model with properties similar to those of the double nucleus of M31. The properties of our models are primarily determined by the behavior of the periodic orbits. Self-gravity in the disk causes these orbits to assume a characteristic radial eccentricity profile, which gives rise to distinctive multipeaked line-of-sight velocity distributions along lines of sight near the black hole. The multipeaked features should be observable in M31 at the resolution of the Space Telecope Imaging Spectrograph. These features provide the best means of identifying an eccentric nuclear disk in M31 and can be used to constrain the disk properties and black hole mass.