Abstract

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 degrees), 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 similar to 10 for the lower end of assumed MBH masses (M-center dot = 10(4) M-circle dot) and decreases sharply with increasing M-center dot. 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 LKVRR-enhanced rate is similar to 100 times lower than the LIGO/VIRGO limit, and for M-center dot = 10(4) M-circle dot, the rate barely reaches 12 Gpc(-3) yr(-1).