On Binary Formation from Three Initially Unbound Bodies

We explore three-body binary formation (3BBF), the formation of a bound system via gravitational scattering of three initially unbound bodies (3UB), using direct numerical integrations. For the first time, we consider systems with unequal masses, as well as finite-size and post-Newtonian effects. Our analytically derived encounter rates and numerical scattering results reproduce the 3BBF rate predicted by Goodman & Hut for hard binaries in dense star clusters. We find that 3BBF occurs overwhelmingly through nonresonant encounters and that the two most-massive bodies are never the most likely to bind. Instead, 3BBF favors pairing the two least-massive bodies (for wide binaries) or the most- plus least-massive bodies (for hard binaries). 3BBF overwhelmingly favors wide-binary formation with superthermal eccentricities, perhaps helping to explain the eccentric wide binaries observed by Gaia. Hard-binary formation is far rarer, but with a thermal eccentricity distribution. The semimajor axis distribution scales cumulatively as a ³ for hard and slightly wider binaries. Although mergers are rare between black holes when including relativistic effects, direct collisions occur frequently between main-sequence stars—more often than hard 3BBF. Yet, these collisions do not significantly suppress hard 3BBF at the low-velocity dispersions typical of open or globular clusters. Energy dissipation through gravitational radiation leads to a small probability of a bound, hierarchical triple system forming directly from 3UB.