Self‐Gravitating Eccentric Disk Models for the Double Nucleus of M31

We present new dynamical models of weakly self-gravitating, finite dispersioneccentric stellar disks around central black holes for the double nucleus ofM31. The disk is fixed in a frame rotating at constant precession speed, and ispopulated by stars on quasi-periodic orbits whose parents are numericallyintegrated periodic orbits in the total potential. A distribution ofquasi-periodic orbits about a given parent is approximated by a distribution ofKepler orbits dispersed in eccentricity and orientation, using an approximatephase-space distribution function written in terms of the integrals of motionin the Kepler problem. We use these models, along with an optimization routine,to fit available published kinematics and photometry in the inner 2 arcsecondsof the nucleus. A grid of 24 best-fit models is computed to accuratelyconstrain the mass of the central black hole and nuclear disk parameters. Wefind that the supermassive black hole in M31 has mass $M_{BH} = 5.62 \pm 0.66\times 10^7 \msun$, which is consistent with the observed correlation betweenthe central black hole mass and the velocity dispersion of its host spheroid.Our models precess rapidly, at $\Omega = 36.5 \pm 4.2 \kmspc$, and possess acharacteristic radial eccentricity distribution, which gives rise tomulti-modal line of sight velocity distributions along lines of sight near theblack hole. These features can be used as sensitive discriminants of diskstructure.Comment: 54 pages, submitted to The Astrophysical Journa