Gravitational Encounters and the Evolution of Galactic Nuclei. III.
  Anomalous Relaxation
  This paper is the third in a series presenting the results of direct
numerical integrations of the Fokker-Planck equation for stars orbiting a
supermassive black hole (SBH) at the center of a galaxy. The algorithm of Paper
II included diffusion coefficients that described the effects of random
("classical") and correlated ("resonant") relaxation. In this paper, the
diffusion coefficients of Paper II have been generalized to account for the
effects of "anomalous relaxation," the qualitatively different way in which
eccentric orbits evolve in the regime of rapid relativistic precession. Two
functional forms for the anomalous diffusion coefficients are investigated,
based on power-law or exponential modifications of the resonant diffusion
coefficients. The parameters defining the modified coefficients are first
constrained by comparing the results of Fokker-Planck integrations with
previously-published N-body integrations. Steady-state solutions are then
obtained via the Fokker-Planck equation for models with properties similar to
those of the Milky Way nucleus. Inclusion of anomalous relaxation leads to the
formation of less prominent cores than in the case of resonant relaxation
alone, due to the lengthening of diffusion timescales for eccentric orbits.
Steady-state capture rates of stars by the SBH are found to always be less, by
as much as an order of magnitude, than capture rates in the presence of
resonant relaxation alone.
