2016/08/25 by Nathan W. C. Leigh, Nicholas C. Stone, Aaron M. Geller +4 · 31 citations
Physics and Astronomy · #Astrophysics #Binary number #Binary star #Chaotic #Classical mechanics #Cluster (spacecraft) #Formalism (music) #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gamma-ray bursts and supernovae #Gravitation #Gravitational potential #Many-body problem #Newtonian fluid #Newtonian potential #Physics #Quantum mechanics #Series (stratigraphy) #Star cluster #Stars #Statistical physics #Stellar, planetary, and galactic studies #Virial theorem #astro-ph.SR #physics.class-ph #physics.data-an
paper · pdf · doi:10.1093/mnras/stw2178
published in Monthly Notices of the Royal Astronomical Society 463(3), 3311-3325 (Oxford University Press) · 18 pages, 12 figures; accepted for publication in MNRAS
arxiv created 2016/08/25 · openalex publication_date 2016/08/30 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we study the chaotic four-body problem in Newtonian gravity. Assuming point particles and total encounter energies ≤0, the problem has three possible outcomes. We describe each outcome as a series of discrete transformations in energy space, using the diagrams first presented in Leigh & Geller (see the appendix). Furthermore, we develop a formalism for calculating probabilities for these outcomes to occur, expressed using the density of escape configurations per unit energy, and based on the Monaghan description originally developed for the three-body problem. We compare this analytic formalism to results from a series of binary–binary encounters with identical point particles, simulated using the fewbody code. Each of our three encounter outcomes produces a unique velocity distribution for the escaping star(s). Thus, these distributions can potentially be used to constrain the origins of dynamically formed populations, via a direct comparison between the predicted and observed velocity distributions. Finally, we show that, for encounters that form stable triples, the simulated single star escape velocity distributions are the same as for the three-body problem. This is also the case for the other two encounter outcomes, but only at low virial ratios. This suggests that single and binary stars processed via single–binary and binary–binary encounters in dense star clusters should have a unique velocity distribution relative to the underlying Maxwellian distribution (provided the relaxation time is sufficiently long) or if ejected from the cluster, which can be calculated analytically.