Triple-induced mergers of black hole binaries

Context. Through observations of gravitational waves, mergers of black holes (BHs) have been shown to be a ubiquitous phenomenon in the Universe. However, uncertainties remain in our theoretical understanding of the evolution of the BHs prior to their merger. Black hole progenitors are seemingly born primarily in triples or higher-order multiples, and the presence of a tertiary object can perturb a black hole binary (BHB) enough to precipitate a merger. Aims. We aim to provide a detailed overview of BH mergers in wide triples by evolving systems from stellar birth to BH merger, using non-orbit-averaged methods for both the dynamics and BH spins from the point of BHB formation, and including triples that become dynamically unstable due to stellar evolution. This allows us to obtain a more complete picture of BH mergers in triples, shedding light on the initial orbital properties required to produce a merger in a triple, as well as the final properties of the merging BHBs. Methods. We used population synthesis coupled with orbit-averaged descriptions of triple dynamics to evolve a population of triples with initially wide orbits and massive progenitors. Wide orbits were chosen to avoid stellar interaction prior to BH formation. Systems that remain bound and form an inner BHB were evolved using a direct n-body code with post-Newtonian terms up to an order of 2.5. We also simulated the precession of the BH spin vectors by coupling the n-body solver with the differential equations for the spins. Results. Forming a wide, bound BHB with a tertiary companion requires the system to survive pre-BH stellar evolution and at least two supernovae in the inner binary. Consequently, only a small fraction of the massive triple population are born with the parameters required to achieve this configuration. For the dynamically stable triples with inner BHBs, only the systems with inclinations close to 90° can excite the eccentricity in the inner binary to values high enough for gravitational waves (GWs) to dissipate sufficient energy to merge the system with an estimated merger rate density of ∼5 Gpc−3 yr−1. Mergers also occur in triples that become dynamically unstable at a rate of ∼1.4 Gpc−3 yr−1. At the point of entering the 10 Hz gravitational wave frequency band, the merging inner binaries exhibit eccentricities between 10−4 and 10−2. Finally, we find that the final effective spin of a BHB that merges through this channel can display a wide range of values between −1 and 1, with a slight tendency towards χeff ≈ 0. This is a result of the strong three-body dynamics experienced by the merging triples before the inner binary begins to shrink due to GW emission. The inner angular momentum can explore the full phase space before the binary rapidly shrinks and decouples from the tertiary, effectively freezing out the effective spin to its value at the time of the highest inner eccentricity.