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

Resonant relaxation (RR) of orbital angular momenta occurs near massive black holes (MBHs) where the potential is spherical and 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 an RR sink term. We find that the steady state current of stars, which sustains the accelerated drainage close to the MBH, can be less than or similar to 10 larger than that due to noncoherent two-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 less than or similar to 10 times higher than those predicted by two-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.