TY - JOUR

T1 - The chaotic four-body problem in Newtonian gravity -I. Identical point-particles

AU - Leigh, Nathan W.C.

AU - Stone, Nicholas C.

AU - Geller, Aaron M.

AU - Shara, Michael M.

AU - Muddu, Harsha

AU - Solano-Oropeza, Diana

AU - Thomas, Yancey

N1 - Publisher Copyright:
© 2016, Published by Oxford University Press on behalf of the Royal Astronomical Society.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2016/12/11

Y1 - 2016/12/11

N2 - 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.

AB - 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.

KW - Binaries: close

KW - Globular clusters: general

KW - Gravitation

KW - Methods: analytical

KW - Scattering

KW - Stars: kinematics and dynamics

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U2 - 10.1093/mnras/stw2178

DO - 10.1093/mnras/stw2178

M3 - Article

AN - SCOPUS:85014991691

VL - 463

SP - 3311

EP - 3325

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 3

ER -