#
Resonant Relaxation in Stellar Systems

*Kevin P. Rauch and Scott Tremaine*

Canadian Institute for Theoretical Astrophysics,

University of Toronto,

60 St. George St., Toronto, On M5S 3H8, Canada.

## Abstract

We demonstrate the existence of an enhanced rate of angular momentum
relaxation in nearly Keplerian star clusters, such as those found in the
centers of galactic nuclei containing massive black holes. The enhanced
relaxation arises because the radial and azimuthal orbital frequencies
in a Keplerian potential are equal, and hence may be termed *resonant
relaxation*. We explore the dynamics of resonant relaxation using
both numerical simulations and order-of-magnitude analytic calculations.
We find
that the resonant angular momentum relaxation time is shorter than the
non-resonant relaxation time by of order *M*_{*}/M,
where *M*_{*} is the mass in stars and *M*
is the mass of the central object. Resonance does not
enhance the energy relaxation rate. We examine the effect of resonant
relaxation on the rate of tidal disruption of stars by the central mass;
we find that the flux of stars into the loss cone is enhanced when the
loss cone
is empty, but that the disruption rate averaged over the entire cluster
is not strongly affected. We show that relativistic precession can
disable resonant relaxation near the main-sequence loss cone for black
hole masses comparable
to those in galactic nuclei. Resonant dynamical friction leads to growth
or decay of the eccentricity of the orbit of a massive body, depending on
whether the distribution function of the stars is predominantly radial or
tangential. The accelerated relaxation implies that there are regions
in nuclear star
clusters that are relaxed in angular momentum but not in energy;
unfortunately, these regions are not well-resolved in most nearby
galaxies by the Hubble Space Telescope.

**Keywords:**
black hole physics --- galaxies: active --- galaxies: kinematics and
dynamics --- galaxies: nuclei --- stellar dynamics

**Status:** Appeared in *NewA*, **1**, 149 (1996).