The efficiency of resonant relaxation around a massive black hole

Abstract

Resonant relaxation (RR) is a rapid relaxation process that operates in the nearly Keplerian potential near massive black holes (MBHs). RR dominates the dynamics of compact remnants that inspiral into an MBH and emit gravitational waves (extreme mass ratio inspiral (EMRI) events), and can either increase the EMRI rate, or strongly suppress it, depending on its still poorly determined efficiency. We use 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 develop an efficient and robust procedure for detecting and measuring RR in N-body simulations. 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, and explore its long-term behavior. 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. © 2009. The American Astronomical Society. All rights reserved.