Deus Ex Statistica: A Statistical Solution to the binary-binary Outcome of the Chaotic, Non-Hierarchical Four-Body Problem

Abstract: We present an analytical, statistical solution to the binary-binary (2+2) outcome of the chaotic non-hierarchical four-body problem. The solution is based on the density-of-states formulation pioneered by J. J. Monaghan. The method skips the computationally expensive integration of the equations of motion, and instead samples the outcome from the chaotic phase-space, subject to conservation of energy, momentum, and angular momentum. From the joint distribution, we extract marginal distributions of several key parameters using Monte-Carlo integration, and numerically verify them by comparing to an identical ensemble of scattering experiments produced by the FEWBODY code. From the comparison, we identify a regime not represented by the density-of-states formulation: the hard binary regime, where one binary is much harder then the four-body energy scale, and the system acts as an effective three-body system. We hypothesize that at this regime the system's probability distribution spreads over an effective reduced three-body chaotic phase space. The process of transfer from four-body to three-body phase-space is still not understood, and represents the next natural extension of density-of-states methods.