Numerical studies of the efficiency of resonant relaxation around a massive black hole

Resonant relaxation (RR) is a rapid relaxation process that operates in the nearly-Keplerian potential near a massive black hole (MBH). RR dominates the dynamics of compact remnants that inspiral into a MBH and emit gravitational waves (extreme mass ratio inspiral events, EMRIs). RR can either increase the EMRI rate, or strongly suppress it, depending on its still poorly-determined efficiency. We use small-scale Newtonian N-body simulations to measure the RR efficiency and to explore its possible dependence on the stellar number density profile around the MBH, and the mass-ratio between the MBH and a star (a single-mass stellar population is assumed). We present a suite of simulations with a range of stellar density profiles and mass-ratios, and measure the mean RR efficiency in the near-Keplerian limit. We do not find a strong dependence on the density profile or the mass-ratio. Our numerical determination of the RR efficiency in the Newtonian, single-mass population approximations, suggests that RR will likely enhance the EMRI rate by a factor of a few over the rates predicted assuming only slow stochastic two-body relaxation.