Lidov-Kozai Cycles with Gravitational Radiation: Merging Black Holes in Isolated Triple Systems

We show that a black-hole binary with an external companion can undergo Lidov-Kozai cycles that cause a close pericenter passage, leading to a rapid merger due to gravitational-wave emission. This scenario occurs most often for systems in which the companion has a. mass comparable to the reduced mass of the binary and the companion orbit has a. semimajor axis within a factor of similar to 10 of the binary semimajor axis. Using a simple population-synthesis model and three-body simulations, we estimate the rate of mergers in triple black-hole systems in the field to be about six per Gpc(3) per year in the absence of natal kicks during black-hole formation. This value is within the low end of the 90% credible interval for the total black hole-black hole merger rate inferred from the current LIGO results. There are many uncertainties in these calculations, the largest of which is the unknown distribution of natal kicks. Even modest natal kicks of 40 km s(-1) will reduce the merger rate by a factor of 40. A few percent of these systems will have eccentricity greater than 0.999 when they first enter the frequency band detectable by aLIGO (above 10 Hz).