Scalar Resonant Relaxation of Stars Around a Massive Black Hole
  In nuclear star clusters, the potential is governed by the central massive
black hole, so that stars move on nearly Keplerian orbits and the total
potential is almost stationary in time. Yet, the deviations of the potential
from the Keplerian one, due to the enclosed stellar mass and general
relativity, will cause the stellar orbits to precess. Moreover, as a result of
the finite number of stars, small deviations of the potential from spherical
symmetry induce residual torques that can change the stars' angular momentum
faster than the standard two-body relaxation. The combination of these two
effects drives a stochastic evolution of orbital angular momentum, a process
named "resonant relaxation". Owing to recent developments in the description of
the relaxation of self-gravitating systems, we can now fully describe scalar
resonant relaxation (relaxation of the magnitude of the angular momentum) as a
diffusion process. In this framework, the potential fluctuations due to the
complex orbital motion of the stars are described by a random correlated noise,
whose statistical properties are fully characterized by the stars' mean field
motion. On long timescales, the cluster can be regarded as a diffusive system,
whose diffusion coefficients depend explicitly on the mean field stellar
distribution through the properties of the noise. We show here, for the first
time, how the diffusion coefficients of scalar resonant relaxation, for a
spherically symmetric system, can be fully calculated from first principles,
without any free parameters. We also provide an open source code that evaluates
these diffusion coefficients numerically.
