Merger Timescales in Hierarchical Triple Black Hole Systems

Abstract

We examine the possibility that the three black holes in a hierarchical triple system all merge on a very small timescale with respect to the Hubble time. Hierarchical triples can be seen as an inner binary with a tertiary on a wide orbit around it. We find a formula that approximates the merger time of the inner binary. For certain initial conditions of the triple system this merger time can be strongly accelerated with respect to an isolated binary. This is caused by the Kozai effect: the tertiary induces oscillations in the eccentricity of the orbit of the inner binary. Using the approximation formula we examine the dependence of the Kozai effect on the initial conditions of the triple. When the inner binary merges, the remnant of the merger receives a kick due to conservation of linear momentum. We examine the influence of this kick on the merger time of the outer binary. A formula is derived for the changed merger time due to the kick in the limit that the tertiary is much more massive than the inner masses. We find distributions of the merger time assuming certain distributions for the initial parameters. It is found that it is possible that the merger time of the outer binary strongly decreases. Thus, it is possible that all three masses in a hierarchical triple black hole system merge on a small timescale.