Production of trans-Neptunian binaries through chaos-assisted capture

The recent discovery of binary objects in the Kuiper Belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary object formation model based on the notion of chaos-assisted capture (CAC). In this model two potential binary partners may become trapped for long times inside chaotic layers within their mutual Hill sphere. The binary may then be captured permanently through gravitational scattering with a third 'intruder' body. The creation of binaries having similarly sized partners is an ab initio prediction of the model which also predicts large binary semimajor axes and moderately eccentric mutual orbits similar to those observed. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity and orbital element distributions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering to the circular Hill four-body problem and find that the CAC mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the 'fine-tuning' problem recently identified by Noll et al. is also addressed.