Resonant Tidal Disruption in Galactic Nuclei

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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), who also argued 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. 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>8*10^7 solar masses. 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.

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