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

TL;DR

This paper investigates how Lidov-Kozai cycles in triple black hole systems can induce rapid mergers through gravitational radiation, estimating merger rates and eccentricities relevant for LIGO detections.

Contribution

It demonstrates that triple systems can significantly contribute to black hole mergers via Lidov-Kozai cycles, with estimated rates consistent with LIGO observations.

Findings

Estimated merger rate of about six per Gpc^3 per year.

A few percent of mergers have eccentricity > 0.999 at LIGO frequencies.

Merger rates are highly sensitive to natal kick velocities.

Abstract

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 mass comparable to the reduced mass of the binary and the companion orbit has semi-major axis within a factor of $\sim 10$ of the binary semi-major axis. Using a simple population-synthesis model and 3-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 $40\mbox{km s}^{-1}$ 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).