# Resonant relaxation near a massive black hole: the stellar distribution and gravitational wave sources

## Clovis Hopman and Tal Alexander

Faculty of Physics, Weizmann Institute of Science, POB 26, Rehovot 76100, Israel

### Paper: ApJ, submitted

**Abstract:**
Resonant relaxation (RR) of orbital angular momenta occurs near massive
black holes (MBHs) where the stellar orbits are nearly Keplerian and
so do not precess significantly. The resulting coherent torques
efficiently change the magnitude of the angular momenta and rotate
the orbital inclination in all directions. As a result, many of the
tightly bound stars very near the MBH are rapidly destroyed by falling
into the MBH on low-angular momentum orbits, while the orbits of the
remaining stars are efficiently randomized. We solve numerically the
Fokker-Planck equation in energy for the steady state distribution
of a single mass population with a RR sink term. We find that the
steady state current of stars, which sustains the accelerated drainage
close to the MBH, can be <= than 10 times larger than that due to
non-coherent
2-body relaxation alone. RR mostly affects tightly bound stars, and
so it increases only moderately the total tidal disruption rate, which
is dominated by stars originating from less bound orbits farther away.
We show that the event rate of gravitational wave (GW) emission from
inspiraling stars, originating much closer to the MBH, is dominated
by RR dynamics. The GW event rate depends on the uncertain efficiency
of RR. The efficiency indicated by the few available simulations implies
rates <= 10 times higher than those predicted by 2-body
relaxation, which would improve the prospects of detecting such events
by future GW detectors, such as LISA. However, a higher,
but still plausible RR efficiency can lead to the drainage of all
tightly bound stars and strong suppression of GW events from inspiraling
stars. We apply our results to the Galactic MBH, and show that the
observed dynamical properties of stars there are consistent with RR.

Preprints available from the authors at tal.alexander@weizmann.ac.il
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