Secular Stellar Dynamics near a Massive Black Hole
  The angular momentum evolution of stars close to massive black holes (MBHs)
is driven by secular torques. In contrast to two-body relaxation, where
interactions between stars are incoherent, the resulting resonant relaxation
(RR) process is characterized by coherence times of hundreds of orbital
periods. In this paper, we show that all the statistical properties of RR can
be reproduced in an autoregressive moving average (ARMA) model. We use the ARMA
model, calibrated with extensive N-body simulations, to analyze the long-term
evolution of stellar systems around MBHs with Monte Carlo simulations.
  We show that for a single-mass system in steady-state, a depression is carved
out near an MBH as a result of tidal disruptions. Using Galactic center
parameters, the extent of the depression is about 0.1 pc, of similar order to
but less than the size of the observed "hole" in the distribution of bright
late-type stars. We also find that the velocity vectors of stars around an MBH
are locally not isotropic. In a second application, we evolve the highly
eccentric orbits that result from the tidal disruption of binary stars, which
are considered to be plausible precursors of the "S-stars" in the Galactic
center. We find that RR predicts more highly eccentric (e > 0.9) S-star orbits
than have been observed to date.
