The impact of vector resonant relaxation on the evolution of binaries near a massive black hole: implications for gravitational wave sources

Binaries within the sphere of influence of a massive black hole (MBH) in galactic nuclei are susceptible to the Lidov-Kozai (LK) mechanism, which can drive orbits to high eccentricities and trigger strong interactions within the binary such as the emission of gravitational waves (GWs), and mergers of compact objects. These events are potential sources for GW detectors such as Advanced LIGO and VIRGO. The LK mechanism is only effective if the binary is highly inclined with respect to its orbit around the MBH (within a few degrees of 90 deg), implying low rates. However, close to an MBH, torques from the stellar cluster give rise to the process of vector resonant relaxation (VRR). VRR can bring a low-inclination binary into an `active' LK regime in which high eccentricities and strong interactions are triggered in the binary. Here, we study the coupled LK-VRR dynamics, with implications for LIGO and VIRGO GW sources. We carry out Monte Carlo simulations and find that the merger fraction enhancement due to LK-VRR dynamics is up to a factor of ~10 for the lower end of assumed MBH masses (M_MBH = 1e4 MSun), and decreases sharply with increasing M_MBH. We find that, even in our most optimistic scenario, the baseline BH-BH merger rate is small, and the enhancement by LK-VRR coupling is not large enough to increase the rate to well above the LIGO/VIRGO lower limit, 12 Gpc^{-3} yr^{-1}. For the Galactic Center, the LK-VRR-enhanced rate is ~100 times lower than the LIGO/VIRGO limit, and for M_MBH = 1e4 MSun, the rate barely reaches 12 Gpc^{-3} yr^{-1}.