#
Resonant Tidal Disruption in Galactic Nuclei

*Kevin P. Rauch and Brian Ingalls*

Canadian Institute for Theoretical Astrophysics,

University of Toronto,

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

## Abstract

It has recently been shown that the rate of angular momentum relaxation
in nearly-Keplerian star clusters is greatly increased by a process
termed resonant relaxation (Rauch & Tremaine 1996);
it was also argued,
via a series of scaling arguments, that tidal disruption of stars in
galactic nuclei containing massive black holes could be noticeably
enhanced by this process. We describe here the results of numerical
simulations of resonant tidal disruption which quantitatively test
the predictions made by Rauch & Tremaine.
The simulation method is based on an *N*-body routine incorporating
cloning of stars near the loss cone and a semi-relativistic symplectic
integration scheme. Normalized disruption rates for resonant and
non-resonant nuclei are derived at orbital energies both above
and below the critical energy, and the corresponding angular momentum
distribution functions are found. The black hole mass above which
resonant tidal disruption is quenched by relativistic precession is
determined. We also briefly describe the discovery of chaos in the
Wisdom-Holman symplectic integrator applied to highly
eccentric orbits and propose a modified
integration scheme that remains robust under these conditions.

We find that resonant disruption rates exceed their non-resonant
counterparts by an amount consistent with the predictions;
in particular, we estimate the
net tidal disruption rate for a fully resonant cluster to be about twice
that of its non-resonant counterpart. No significant
enhancement in rates is observed outside the critical radius.
Relativistic quenching of the effect
is found to occur for hole masses
*M>M*_{Q}*= (8 ± 3) ×
10*^{7}M_{Sun}. The numerical results combined
with the observed properties of galactic nuclei indicate
that for most galaxies
the resonant enhancement to tidal disruption rates will be very small.

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

**Status:** Appeared in *MNRAS*, **299**, 1231 (1998).