  The nuclear rotation curve of M31, as observed by the Hubble Space Telescope
Faint Object Camera Spectrograph, shows a significant disturbance coinciding
with the off-center brightness peak, P1. This +/- 60 km/s feature is
distinguished by a local velocity maximum centered on P1 and a local minimum
approxmately 0.08" closer to P2. If the M31 double nucleus is an eccentric disk
with an off-center density concentration, as suggested by Tremaine, then the
self-gravity of the disk can produce just such a disturbance. The expected
kinematic signature is calculated approximately by examining sequences of
closed periodic orbits in a Kepler potential perturbed by a model disk
potential that precesses at constant frequency. The perturbation forces a steep
negative eccentricity gradient in the sequence of closed orbits through the
densest part of the disk, which reverses the arrangement of periapsis and
apoapsis with respect to the central mass. Stars making up the inner part of
the density concentration are at apoapsis, while stars making up the outer part
are at periapsis, producing a steep local velocity gradient. This result is
independent of the details of the mass distribution. The projected rotation
curve of the model is shown to closely resemble that of M31, giving strong
support to the eccentric disk picture.
