Three-dimensional Keplerian orbit-superposition models of the nucleus of
  M31
  We present three-dimensional eccentric disc models of the nucleus of M31,
modelling the disc as a linear combination of thick rings of massless stars
orbiting in the potential of a central black hole. Our models are nonparametric
generalisations of the parametric models of Peiris & Tremaine. The models
reproduce well the observed WFPC2 photometry, the detailed line-of-sight
velocity distributions from STIS observations along P1 and P2, together with
the qualitative features of the OASIS kinematic maps. We confirm Peiris &
Tremaine's finding that nuclear discs aligned with the larger disc of M31 are
strongly ruled out. Our optimal model is inclined at 57 degrees with respect to
the line of sight of M31 and has a position angle of 55 degrees. It has a
central black hole of mass 10^8 solar masses, and, when viewed in three
dimensions, shows a clear enhancement in the density of stars around the black
hole. The distribution of orbit eccentricities in our models is similar to
Peiris & Tremaine's model, but we find significantly different inclination
distributions, which might provide valuable clues to the origin of the disc.
