Topology of Black Hole Binary-Single Interactions

Abstract

We present a study on how the outcomes of co-planar binary-single black hole (BH) interactions distribute as a function of the orbital initial conditions. We refer to this distribution as the topology. Using an $N$-body code that includes BH finite sizes and gravitational wave (GW) emission in the equation-of-motion (EOM), we perform more than a million three-body scatterings to explore the topology of both the classical and the relativistic limit. We further describe how the inclusion of GW emission in the EOM naturally leads to scenarios where the binary-single system undergoes two successive GW mergers. The time span from the first to the second GW merger is shortest in co-planar interactions, and are for some configurations even short enough for LIGO to observe both events. We note that co-planar interactions could be frequent in environments such as active galactic nuclei discs.