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arxiv: 2606.11294 · v1 · pith:X7DMMAQUnew · submitted 2026-06-09 · 🌌 astro-ph.HE · gr-qc

Intermediate States in Chaotic Triple Evolution and Applications to Black Hole Merger Statistics

Dina Meylakh , Nicholas C. Stone , Nathan W.C. Leigh This is my paper

Pith reviewed 2026-06-27 12:03 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords three-body interactionschaotic evolutionblack hole mergersgravitational wavesstar clusterseccentric mergersN-body simulationsMonte Carlo methods
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The pith

Three-body interactions in star clusters produce between 2.6 and 4.4 percent observably eccentric black hole mergers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that the outcomes of chaotic phases in triple systems can be described by an elliptic outcome distribution derived from equilibrium statistical mechanics. Comparison with N-body simulations shows this distribution reduces to a single free parameter while matching disintegration probabilities except at the lowest angular momenta. The resulting Monte Carlo model of repeated binary-single scatterings in clusters then predicts the fraction of gravitational-wave mergers that remain observably eccentric to detectors such as LIGO and Virgo. A reader would care because the calculation supplies a concrete, observationally testable fraction for one formation channel of merging black holes.

Core claim

We re-derive the elliptic outcome distribution using equilibrium statistical mechanics and explore it together with the hyperbolic distribution. When comparing to N-body simulations, we find that we can reduce the elliptic outcome model to one free parameter instead of the previously used two and that the predicted disintegration probabilities agree except for very low angular momentum triples. We then use both outcome distributions along with a star cluster model to design a Monte Carlo algorithm for repeated binary-single scatterings within dense star systems. Assuming an OEM detection sensitivity of f_min=10 Hz, e_min = 0.1, we find the elliptic OEMs are about ∼(32−63)% of the total ellip

What carries the argument

The elliptic outcome distribution derived from equilibrium statistical mechanics, which assigns probabilities to the hierarchical states that follow chaotic triple evolution and thereby governs the production of eccentric binaries.

If this is right

  • The reduced one-parameter elliptic model reproduces N-body disintegration probabilities except at very low angular momentum.
  • Elliptic observably eccentric mergers account for 32 to 63 percent of all elliptic mergers under the stated detector thresholds.
  • Higher total cluster mass increases the fraction of binaries ejected before merger.
  • Raising the minimum frequency to current detector values lowers the predicted OEM fraction to 1.6-3.1 percent.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same statistical-mechanics reduction might be tested against direct N-body runs that include post-Newtonian terms during the chaotic phase.
  • Varying the assumed cluster density or velocity dispersion would show how sensitive the OEM fraction is to environment.
  • The predicted eccentricity distribution could be folded into population-synthesis codes to assess overlap with other black-hole formation channels.

Load-bearing premise

The equilibrium statistical mechanics derivation of the elliptic outcome distribution remains valid across the full range of angular momenta encountered in realistic cluster scatterings.

What would settle it

A measured fraction of eccentric black hole mergers in LIGO-Virgo catalogs that lies well outside the 2.6-4.4 percent interval predicted for the star-cluster channel would falsify the model's applicability.

Figures

Figures reproduced from arXiv: 2606.11294 by Dina Meylakh, Nathan W.C. Leigh, Nicholas C. Stone.

Figure 1
Figure 1. Figure 1: The marginal distribution of binary energy, d𝜎/d𝐸B for both hyperbolic (𝐸B/𝐸0 > 1) and elliptic (𝐸B/𝐸0 < 1) tertiary orbits, plotted against the dimensionless energy 𝐸B/𝐸0. The dotted lines correspond to the apocentric escape (AE) chaotic region, and filled lines to the simple escape (SE) chaotic region. The colors correspond to the systems different angular momenta 𝐿0 (here represented with 𝑒0), including… view at source ↗
Figure 2
Figure 2. Figure 2: The normalized marginal distribution of binary eccentricity, d𝜎/d𝑒𝐵 for both hyperbolic and elliptic tertiary orbits, plotted against ec￾centricity 𝑒𝐵. The dotted curves in both panels correspond to hyperbolic distributions while the filled curves correspond to elliptic distributions. The bottom panel corresponds to the apocentric escape (AE) chaotic region, and the top panel to the simple escape (SE) chao… view at source ↗
Figure 3
Figure 3. Figure 3: The normalized marginal distribution of binary orientation, d𝜎/d𝐶𝐵 for both hyperbolic and elliptic tertiary orbits, plotted against ori￾entation 𝐶𝐵. The dotted and filled lines and their colors are the same as [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Probability of an escape given any exit (either escape or excursion) from the chaotic region, taken with 𝑚1 = 𝑚2 and plotted against the 𝑚3/𝑚1 mass ratio. Colors denote the total angular momentum 𝐿0, varied from lowest (green) through intermediate (orange) to highest (blue). The top panel cor￾responds to the simple escape (SE) and the bottom panel to the apocentric escape (AE) definition of the chaotic reg… view at source ↗
Figure 6
Figure 6. Figure 6: Probability of a system to exhibit a certain number of scrambles, 𝑁scram, plotted against 𝑁scram. Calculations with the simple escape (SE) criteria are shown in blue, and for the apocentric escape (AE) in orange. Data gathered from the binary-single numerical scattering experiments of Stone & Leigh (2019) is shown in green. The four panels correspond to different total angular momenta of the 3-body system,… view at source ↗
Figure 7
Figure 7. Figure 7: Dynamical evolution of a BBH in a two-component cluster with 𝑀tot,★ = 106.33, 𝑐★ ≃ 6.3. The binary separation, measured in AU, is plotted against the triple state index of the DBS evolution, 𝑁 (e.g. 𝑁 = 20 represents the binary formed from the 20th metastable triple in the evolutionary se￾quence). Points with dark blue centers correspond to the binary’s semi-major axis 𝑎B; when circled in green, these are … view at source ↗
Figure 8
Figure 8. Figure 8: Branching ratios of sampled BBH outcomes plotted against varying star cluster total mass, 𝑀tot,★, for constant concentration parameter 𝑐★ = 6.3. The top panel corresponds to the equal mass BBH case, while the bottom panel corresponds to the unequal mass BBH case. For any given cluster mass 𝑀tot,★, the sum of all outcome ratios is 1. Different outcomes are color-coded as follows: ionization from three-body … view at source ↗
Figure 9
Figure 9. Figure 9: Branching ratios of sampled BBH outcomes plotted against varying star cluster concentration parameters 𝑐★, for fixed cluster total mass 𝑀tot,★ = 106.3𝑀⊙. The top panel corresponds to the equal mass BBH case while the bottom panel corresponds to the unequal mass BBH case. The colors of all data points are the same as in [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Ratios between the number of MC-sampled eccentric mergers (𝑁EOM) to the total number of sampled mergers (𝑁merger) as a function of eccentricity detection sensitivity. In the left panels, we plot 𝑁EOM/𝑁merge against a minimal eccentricity 𝑒f for detection at the fixed frequency 𝑓 = 10 Hz, while in the right panels, we vary the frequency 𝑓min for detection assuming a fixed minimal detectable eccentricity 𝑒m… view at source ↗
read the original abstract

Three-body interactions exhibit phases of strong chaotic evolution as well as hierarchical motion where one body separates from a binary and follows a hyperbolic or elliptic trajectory around it. The binaries produced during phases of hierarchical motion may lead to gravitational wave (GW) inspirals, but this depends on the outcomes of the chaotic states. In this paper we re-derive the elliptic outcome distribution using equilibrium statistical mechanics and explore it together with the hyperbolic distribution. When comparing to N-body simulations, we find that we can reduce the elliptic outcome model to one free parameter instead of the previously used two and that the predicted disintegration probabilities agree except for very low angular momentum triples. We then use both outcome distributions along with a star cluster model to design a Monte Carlo algorithm for repeated binary-single scatterings within dense star systems. We explore star cluster masses of $[10^5 - 10^7] M_{\odot}$, with the goal of quantifying observably eccentric merger (OEM) GWs, visible to instruments such as LIGO and Virgo. Assuming an OEM detection sensitivity of $f_{\rm min}=10 {\rm Hz}, e_{\rm min} = 0.1$, we find the elliptic OEMs are about $\sim (32 - 63)\%$ of the total elliptic mergers and that the total cluster mass greatly impacts the fraction of ejected binaries. The OEM to total merger fraction (OEM fraction) is found to be $(2.6 - 4.4)\%$. Considering the detection sensitivity that GW interferometers have today $(f_{\rm min} \simeq 34.4 {\rm Hz})$ we obtain the OEM fraction in the $(1.6 - 3.1)\%$ range.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper re-derives the elliptic outcome distribution for chaotic three-body interactions via equilibrium statistical mechanics, reduces the model to a single free parameter (with agreement to N-body simulations except at very low angular momentum), and applies the resulting hyperbolic and elliptic distributions in a Monte Carlo algorithm for repeated binary-single scatterings in star clusters of mass [10^5-10^7] M_⊙. It reports that elliptic OEMs comprise ~32-63% of total elliptic mergers and that the OEM-to-total-merger fraction is (2.6-4.4)% assuming f_min=10 Hz and e_min=0.1 (dropping to 1.6-3.1% at f_min~34.4 Hz).

Significance. If the one-parameter reduction and its applicability hold, the work supplies a simplified statistical-mechanics framework for triple outcomes that can be embedded in cluster population synthesis, offering quantitative predictions for the contribution of observably eccentric black-hole mergers from dense environments to the LIGO/Virgo band.

major comments (3)
  1. [Abstract] Abstract: the reduction of the elliptic outcome model to a single free parameter is asserted on the basis of N-body agreement, yet no explicit derivation steps, choice criterion for the parameter value, or error budget across the full angular-momentum range are supplied; this choice directly determines the disintegration probabilities fed into the Monte Carlo and therefore the quoted OEM fractions.
  2. [Abstract] Abstract and Monte Carlo description: the model is stated to disagree with N-body results at very low angular momentum, but the Monte Carlo for [10^5-10^7] M_⊙ clusters necessarily samples encounter angular momenta that include this regime; no weighting, cutoff, or sensitivity test is reported to show that the discrepancy does not shift the OEM-to-total-merger fraction outside the quoted (2.6-4.4)% interval.
  3. [Abstract] Abstract: the elliptic distribution is re-derived from statistical mechanics and then tuned to match simulations; because the final OEM fractions inherit this fitted parameter, an independent test (e.g., against an orthogonal set of N-body runs or an analytic limit) is required to establish that the (2.6-4.4)% range is not an artifact of the tuning procedure.
minor comments (1)
  1. Notation for the single free parameter and its relation to the earlier two-parameter model should be defined once in a dedicated subsection rather than introduced only in the abstract.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and constructive comments. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reduction of the elliptic outcome model to a single free parameter is asserted on the basis of N-body agreement, yet no explicit derivation steps, choice criterion for the parameter value, or error budget across the full angular-momentum range are supplied; this choice directly determines the disintegration probabilities fed into the Monte Carlo and therefore the quoted OEM fractions.

    Authors: Section 2 of the manuscript presents the equilibrium statistical mechanics derivation of the elliptic outcome distribution. The reduction from two to one free parameter is obtained by direct comparison of predicted disintegration probabilities against N-body results, with the retained parameter chosen to minimize the mean absolute deviation over the sampled angular-momentum range. We will add an explicit error-budget figure and a short appendix describing the fitting criterion in the revised manuscript. revision: yes

  2. Referee: [Abstract] Abstract and Monte Carlo description: the model is stated to disagree with N-body results at very low angular momentum, but the Monte Carlo for [10^5-10^7] M_⊙ clusters necessarily samples encounter angular momenta that include this regime; no weighting, cutoff, or sensitivity test is reported to show that the discrepancy does not shift the OEM-to-total-merger fraction outside the quoted (2.6-4.4)% interval.

    Authors: The Monte Carlo does sample low-angular-momentum encounters. Because the cluster encounter-rate weighting strongly suppresses the lowest angular-momentum tail, the affected fraction of outcomes is small; however, no explicit sensitivity test was performed. We will add such a test (varying the low-L treatment and recomputing the OEM fraction) to the revised manuscript and confirm that the reported (2.6-4.4)% interval is robust. revision: yes

  3. Referee: [Abstract] Abstract: the elliptic distribution is re-derived from statistical mechanics and then tuned to match simulations; because the final OEM fractions inherit this fitted parameter, an independent test (e.g., against an orthogonal set of N-body runs or an analytic limit) is required to establish that the (2.6-4.4)% range is not an artifact of the tuning procedure.

    Authors: The statistical-mechanics derivation itself is independent of N-body data and supplies the functional form; the single-parameter adjustment is a calibration to compensate for the equilibrium approximation. The quoted OEM range already spans the full cluster-mass interval explored. While an additional orthogonal simulation suite would strengthen the claim, the existing validation against published N-body results in the dominant angular-momentum regime supports the fractions; we will clarify this distinction in the revised text. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper re-derives the elliptic outcome distribution from equilibrium statistical mechanics, compares it to N-body simulations to reduce the model from two free parameters to one (noting disagreement only at very low angular momentum), and then applies the resulting distributions in a separate Monte Carlo algorithm to compute OEM fractions for cluster masses in [10^5-10^7] M_⊙. This chain does not reduce any load-bearing prediction to its inputs by construction: the parameter reduction is an external calibration step against independent N-body data, the final OEM-to-total-merger fraction (2.6-4.4)% is generated by applying the calibrated model to a distinct cluster scattering simulation, and no self-citation, self-definition, or renaming of known results is invoked as the justification for the central result. The derivation is therefore independent of the target statistic.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central results rest on equilibrium statistical mechanics applied to chaotic triples, a single fitted parameter for the elliptic distribution, and an assumed star cluster model whose details are not specified in the abstract.

free parameters (1)
  • single free parameter for elliptic outcome distribution
    The paper states the model is reduced to one free parameter calibrated against N-body simulations.
axioms (1)
  • domain assumption Equilibrium statistical mechanics accurately describes the phase-space distribution of outcomes after chaotic triple evolution.
    Invoked to re-derive the elliptic outcome distribution.

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Works this paper leans on

112 extracted references · 106 canonical work pages · 14 internal anchors

  1. [1]

    , keywords =

    The cosmic evolution of binary black holes in young, globular, and nuclear star clusters: rates, masses, spins, and mixing fractions. , keywords =. doi:10.1093/mnras/stac422 , archivePrefix =. 2109.06222 , primaryClass =

    work page doi:10.1093/mnras/stac422

  2. [2]

    , keywords =

    Population synthesis of black hole binary mergers from star clusters. , keywords =. doi:10.1093/mnras/stz3584 , archivePrefix =. 1906.11855 , primaryClass =

    work page doi:10.1093/mnras/stz3584 1906

  3. [3]

    , keywords =

    Dynamical formation of black hole binaries in dense star clusters: Rapid cluster evolution code. , keywords =. doi:10.1103/PhysRevD.110.043023 , archivePrefix =. 2210.10055 , primaryClass =

    work page doi:10.1103/physrevd.110.043023

  4. [4]

    The effect of Galactic tides

    Eccentricity dynamics of wide binaries - I. The effect of Galactic tides. , keywords =. doi:10.1093/mnras/stad2073 , archivePrefix =. 2303.15531 , primaryClass =

    work page doi:10.1093/mnras/stad2073

  5. [5]

    , keywords =

    How to Escape from a Trap: Outcomes of Repeated Black Hole Mergers in Active Galactic Nuclei. , keywords =. doi:10.3847/2041-8213/adb7dc , archivePrefix =. 2410.19904 , primaryClass =

    work page doi:10.3847/2041-8213/adb7dc 2041

  6. [6]

    Analytic computation of the secular effects of encounters on a binary: features arising from second-order perturbation theory

    Analytic computation of the secular effects of encounters on a binary: features arising from second-order perturbation theory. , keywords =. doi:10.1093/mnras/stz1646 , archivePrefix =. 1904.09624 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stz1646 1904

  7. [7]

    Nuclear star clusters in 228 spiral galaxies in the HST/WFPC2 archive: catalogue and comparison to other stellar systems

    Nuclear star clusters in 228 spiral galaxies in the HST/WFPC2 archive: catalogue and comparison to other stellar systems. , keywords =. doi:10.1093/mnras/stu797 , archivePrefix =. 1404.5956 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stu797

  8. [8]

    2020, MNRAS, 497, 536, doi: 10.1093/mnras/staa1915

    PETAR: a high-performance N-body code for modelling massive collisional stellar systems. , keywords =. doi:10.1093/mnras/staa1915 , archivePrefix =. 2006.16560 , primaryClass =

    work page doi:10.1093/mnras/staa1915 2006

  9. [9]

    , keywords =

    Remnant Black Hole Kicks and Implications for Hierarchical Mergers. , keywords =. doi:10.3847/2041-8213/ac20db , archivePrefix =. 2106.07179 , primaryClass =

    work page doi:10.3847/2041-8213/ac20db 2041

  10. [10]

    and Renzo, M

    Mind the Gap: The Location of the Lower Edge of the Pair-instability Supernova Black Hole Mass Gap. , keywords =. doi:10.3847/1538-4357/ab518b , archivePrefix =. 1910.12874 , primaryClass =

    work page doi:10.3847/1538-4357/ab518b 1910

  11. [11]

    MOCCA-SURVEY Database I: Coalescing Binary Black Holes Originating From Globular Clusters

    MOCCA-SURVEY Database - I. Coalescing binary black holes originating from globular clusters. , keywords =. doi:10.1093/mnrasl/slw177 , archivePrefix =. 1608.02520 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnrasl/slw177

  12. [12]

    , keywords =

    Two kinds of stellar collapse. , keywords =. doi:10.1038/253698a0 , adsurl =

    work page doi:10.1038/253698a0

  13. [13]

    Merging black hole binaries in galactic nuclei: implications for advanced-LIGO detections

    Merging Black Hole Binaries in Galactic Nuclei: Implications for Advanced-LIGO Detections. , keywords =. doi:10.3847/0004-637X/831/2/187 , archivePrefix =. 1606.04889 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/0004-637x/831/2/187

  14. [14]

    , keywords =

    Binary Black Hole Mergers from Young Massive and Open Clusters: Comparison to GWTC-2 Gravitational Wave Data. , keywords =. doi:10.3847/2041-8213/ac00a7 , archivePrefix =. 2103.10447 , primaryClass =

    work page doi:10.3847/2041-8213/ac00a7 2041

  15. [15]

    , keywords =

    Merger rate density of binary black holes formed in open clusters. , keywords =. doi:10.1093/mnras/staa1440 , archivePrefix =. 2001.10690 , primaryClass =

    work page doi:10.1093/mnras/staa1440 2001

  16. [16]

    , keywords =

    Nuclear star clusters. , keywords =. doi:10.1007/s00159-020-00125-0 , archivePrefix =. 2001.03626 , primaryClass =

    work page doi:10.1007/s00159-020-00125-0 2001

  17. [18]

    Binary black hole mergers from field triples: properties, rates and the impact of stellar evolution

    Binary Black Hole Mergers from Field Triples: Properties, Rates, and the Impact of Stellar Evolution. , keywords =. doi:10.3847/1538-4357/aa6f5e , archivePrefix =. 1703.06614 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/aa6f5e

  18. [19]

    , keywords =

    Gravitational waves from scattering of stellar-mass black holes in galactic nuclei. , keywords =. doi:10.1111/j.1365-2966.2009.14653.x , archivePrefix =. 0807.2638 , primaryClass =

    work page doi:10.1111/j.1365-2966.2009.14653.x 2009

  19. [20]

    Mind your Ps and Qs: the Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars

    Mind Your Ps and Qs: The Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars. , keywords =. doi:10.3847/1538-4365/aa6fb6 , archivePrefix =. 1606.05347 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4365/aa6fb6

  20. [21]

    , keywords =

    What is a globular cluster? An observational perspective. , keywords =. doi:10.1007/s00159-019-0119-3 , archivePrefix =. 1911.02835 , primaryClass =

    work page doi:10.1007/s00159-019-0119-3 1911

  21. [22]

    Encyclopedia of Astrophysics, Volume 4 , year = 2026, volume =

    The formation of globular clusters. Encyclopedia of Astrophysics, Volume 4 , year = 2026, volume =. doi:10.1016/B978-0-443-21439-4.00078-X , archivePrefix =. 2501.16438 , primaryClass =

    work page doi:10.1016/b978-0-443-21439-4.00078-x 2026

  22. [23]

    Binary Black Hole Mergers from Globular Clusters: Masses, Merger Rates, and the Impact of Stellar Evolution

    Binary black hole mergers from globular clusters: Masses, merger rates, and the impact of stellar evolution. , keywords =. doi:10.1103/PhysRevD.93.084029 , archivePrefix =. 1602.02444 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.93.084029

  23. [24]

    , keywords =

    Modeling Dense Star Clusters in the Milky Way and Beyond with the CMC Cluster Catalog. , keywords =. doi:10.3847/1538-4365/ab7919 , archivePrefix =. 1911.00018 , primaryClass =

    work page doi:10.3847/1538-4365/ab7919 1911

  24. [25]

    , year = 1967, month = jan, volume =

    A Study of the Dynamics of Triple Systems by Means of Statistical Sampling. , year = 1967, month = jan, volume =

    1967

  25. [26]

    On the Astrophysical Origin of Binary Black Hole Subpopulations: A Tale of Three Channels?, 2026

    On the Astrophysical Origin of Binary Black Hole Subpopulations: A Tale of Three Channels?. arXiv e-prints , keywords =. doi:10.48550/arXiv.2603.17987 , archivePrefix =. 2603.17987 , primaryClass =

    work page doi:10.48550/arxiv.2603.17987

  26. [27]

    Assisted Inspirals of Stellar Mass Black Holes Embedded in AGN Disks: Solving the "Final AU Problem"

    Assisted inspirals of stellar mass black holes embedded in AGN discs: solving the `final au problem'. , keywords =. doi:10.1093/mnras/stw2260 , archivePrefix =. 1602.04226 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stw2260

  27. [28]

    GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run

    GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run. arXiv e-prints , keywords =. doi:10.48550/arXiv.2508.18082 , archivePrefix =. 2508.18082 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2508.18082

  28. [29]

    D., & Dermott, S

    Solar System Dynamics. doi:10.1017/CBO9781139174817 , adsurl =

    work page doi:10.1017/cbo9781139174817

  29. [30]

    , keywords =

    Predicting the Stability of Hierarchical Triple Systems with Convolutional Neural Networks. , keywords =. doi:10.3847/1538-4357/ac8eab , archivePrefix =. 2206.12402 , primaryClass =

    work page doi:10.3847/1538-4357/ac8eab

  30. [31]

    doi:10.1046/j.1365-8711.2001.04719.x , eprint =

    Tidal interactions in star cluster simulations. , keywords =. doi:10.1046/j.1365-8711.2001.03974.x , adsurl =

    work page doi:10.1046/j.1365-8711.2001.03974.x 2001

  31. [32]

    , eprint =

    Dynamics of rotating triple systems: statistical escape theory versus numerical simulations. , keywords =. doi:10.1111/j.1365-2966.2005.09540.x , adsurl =

    work page doi:10.1111/j.1365-2966.2005.09540.x 2005

  32. [33]

    The Formation of Eccentric Compact Binary Inspirals and the Role of Gravitational Wave Emission in Binary-Single Stellar Encounters

    The Formation of Eccentric Compact Binary Inspirals and the Role of Gravitational Wave Emission in Binary-Single Stellar Encounters. , keywords =. doi:10.1088/0004-637X/784/1/71 , archivePrefix =. 1308.2964 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/784/1/71

  33. [34]

    Eccentric Black Hole Mergers Forming in Globular Clusters

    Eccentric black hole mergers forming in globular clusters. , keywords =. doi:10.1103/PhysRevD.97.103014 , archivePrefix =. 1711.07452 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.97.103014

  34. [35]

    , keywords =

    A statistical solution to the chaotic, non-hierarchical three-body problem. , keywords =. doi:10.1038/s41586-019-1833-8 , archivePrefix =. 1909.05272 , primaryClass =

    work page doi:10.1038/s41586-019-1833-8 1909

  35. [36]

    Physical Review X , keywords =

    Analytical, Statistical Approximate Solution of Dissipative and Nondissipative Binary-Single Stellar Encounters. Physical Review X , keywords =. doi:10.1103/PhysRevX.11.031020 , archivePrefix =. 2011.00010 , primaryClass =

    work page doi:10.1103/physrevx.11.031020 2011

  36. [37]

    Gravitational Radiation and the Motion of Two Point Masses , author =. Phys. Rev. , volume =. 1964 , month =. doi:10.1103/PhysRev.136.B1224 , url =

    work page doi:10.1103/physrev.136.b1224 1964

  37. [38]

    Research Notes of the American Astronomical Society , keywords =

    An Accurate Analytical Fit to the Gravitational-wave Inspiral Duration for Eccentric Binaries. Research Notes of the American Astronomical Society , keywords =. doi:10.3847/2515-5172/ac2d35 , archivePrefix =. 2110.09254 , primaryClass =

    work page doi:10.3847/2515-5172/ac2d35

  38. [39]

    The Astrophysical Journal , author =

    A. The Astrophysical Journal , author =. 2015 , note =. doi:10.1088/2041-8205/806/2/L28 , language =

    work page doi:10.1088/2041-8205/806/2/l28 2015

  39. [40]

    Monthly Notices of the Royal Astronomical Society , author =

    Binary. Monthly Notices of the Royal Astronomical Society , author =. 1975 , pages =. doi:10.1093/mnras/173.3.729 , abstract =

    work page doi:10.1093/mnras/173.3.729 1975

  40. [41]

    Formation mechanisms, mass, and spin of intermediate-mass black holes in star clusters with up to 1 million stars

    The DRAGON-II simulations - II. Formation mechanisms, mass, and spin of intermediate-mass black holes in star clusters with up to 1 million stars. , keywords =. doi:10.1093/mnras/stad2292 , archivePrefix =. 2307.04806 , primaryClass =

    work page doi:10.1093/mnras/stad2292

  41. [42]

    , keywords =

    Stellar-mass black holes in star clusters: implications for gravitational wave radiation , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2010 , pages =. doi:10.1111/j.1365-2966.2009.15880.x , abstract =

    work page doi:10.1111/j.1365-2966.2009.15880.x 2010

  42. [43]

    Interpretation of high-resolution spectroscopic observations with asymptotic giant branch models

    Compact binaries in star clusters –. Monthly Notices of the Royal Astronomical Society , author =. 2011 , pages =. doi:10.1111/j.1365-2966.2011.19023.x , abstract =

    work page doi:10.1111/j.1365-2966.2011.19023.x 2011

  43. [45]

    2018 , note =

    Monthly Notices of the Royal Astronomical Society , author =. 2018 , note =. doi:10.1093/mnras/sty1859 , abstract =

    work page doi:10.1093/mnras/sty1859 2018

  44. [46]

    Proceedings of the International Astronomical Union , author =

    The. Proceedings of the International Astronomical Union , author =. 2019 , note =. doi:10.1017/S1743921319007269 , abstract =

    work page doi:10.1017/s1743921319007269 2019

  45. [47]

    Galactic Dynamics: Second Edition

  46. [48]

    Dynamical evolution of black hole sub-systems in idealised star clusters

    Dynamical evolution of black hole subsystems in idealized star clusters. , keywords =. doi:10.1093/mnras/stt628 , archivePrefix =. 1304.3401 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stt628

  47. [49]

    Formation of Massive Black Holes in Galactic Nuclei: Runaway Tidal Encounters

    Formation of massive black holes in galactic nuclei: runaway tidal encounters. , keywords =. doi:10.1093/mnras/stx097 , archivePrefix =. 1606.01909 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stx097

  48. [50]

    Kippenhahn, Rudolf and Weigert, Alfred , year =. Stellar. doi:10.1007/978-3-642-61523-8 , keywords =

    work page doi:10.1007/978-3-642-61523-8

  49. [51]

    , keywords =

    Tidal disruption of stars by black holes of 106–108 solar masses in nearby galaxies , volume =. Nature , author =. 1988 , note =. doi:10.1038/333523a0 , abstract =

    work page doi:10.1038/333523a0 1988

  50. [52]

    2023 , note =

    Physical Review X , author =. 2023 , note =. doi:10.1103/PhysRevX.13.041039 , abstract =

    work page doi:10.1103/physrevx.13.041039 2023

  51. [53]

    , keywords =

    Search for Eccentric Black Hole Coalescences during the Third Observing Run of LIGO and Virgo. , keywords =. doi:10.3847/1538-4357/ad65ce , archivePrefix =. 2308.03822 , primaryClass =

    work page doi:10.3847/1538-4357/ad65ce

  52. [54]

    The Astrophysical Journal , author =

    Search for. The Astrophysical Journal , author =. 2019 , note =. doi:10.3847/1538-4357/ab3c2d , abstract =

    work page doi:10.3847/1538-4357/ab3c2d 2019

  53. [55]

    The Astrophysical Journal , author =

    Four. The Astrophysical Journal , author =. 2022 , note =. doi:10.3847/1538-4357/ac9798 , abstract =

    work page doi:10.3847/1538-4357/ac9798 2022

  54. [56]

    , month = jul, year =

    Grishin, Evgeni and Gilbaum, Shmuel and Stone, Nicholas C. , month = jul, year =. The. doi:10.48550/arXiv.2307.07546 , abstract =

    work page doi:10.48550/arxiv.2307.07546

  55. [57]

    Astronomy and Astrophysics , author =

    Impact of common envelope development criteria on the formation of. Astronomy and Astrophysics , author =. 2021 , note =. doi:10.1051/0004-6361/202140520 , abstract =

    work page doi:10.1051/0004-6361/202140520 2021

  56. [58]

    The Astrophysical Journal , author =

    Binary. The Astrophysical Journal , author =. 2021 , note =. doi:10.3847/1538-4357/ac2610 , abstract =

    work page doi:10.3847/1538-4357/ac2610 2021

  57. [59]

    Astronomy and Astrophysics , author =

    Common-envelope ejection in massive binary stars. Astronomy and Astrophysics , author =. 2016 , note =. doi:10.1051/0004-6361/201629420 , abstract =

    work page doi:10.1051/0004-6361/201629420 2016

  58. [60]

    The Astrophysical Journal , author =

    On the. The Astrophysical Journal , author =. 2020 , note =. doi:10.3847/2041-8213/abbc0a , abstract =

    work page doi:10.3847/2041-8213/abbc0a 2020

  59. [61]

    Monthly Notices of the Royal Astronomical Society , author =

    A. Monthly Notices of the Royal Astronomical Society , author =. 1976 , pages =. doi:10.1093/mnras/176.1.63 , abstract =

    work page doi:10.1093/mnras/176.1.63 1976

  60. [62]

    Valtonen, Mauri and Karttunen, Hannu , month = mar, year =. The

  61. [63]

    Monthly Notices of the Royal Astronomical Society , author =

    A. Monthly Notices of the Royal Astronomical Society , author =. 1976 , pages =. doi:10.1093/mnras/177.3.583 , abstract =

    work page doi:10.1093/mnras/177.3.583 1976

  62. [64]

    Monthly Notices of the Royal Astronomical Society , author =

    A statistical theory of the disruption of three-body systems –. Monthly Notices of the Royal Astronomical Society , author =. 1978 , pages =. doi:10.1093/mnras/184.1.119 , abstract =

    work page doi:10.1093/mnras/184.1.119 1978

  63. [65]

    Celestial Mechanics and Dynamical Astronomy , author =

    Flux-based statistical prediction of three-body outcomes , volume =. Celestial Mechanics and Dynamical Astronomy , author =. 2021 , note =. doi:10.1007/s10569-021-10015-x , abstract =

    work page doi:10.1007/s10569-021-10015-x 2021

  64. [66]

    Natural dynamical reduction of the three-body problem , url =

    Kol, Barak , month = jul, year =. Natural dynamical reduction of the three-body problem , url =. doi:10.48550/arXiv.2107.12372 , abstract =

    work page doi:10.48550/arxiv.2107.12372

  65. [67]

    Monthly Notices of the Royal Astronomical Society , author =

    Testing the flux-based statistical prediction of the three-body problem , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2021 , note =. doi:10.1093/mnras/stab1689 , abstract =

    work page doi:10.1093/mnras/stab1689 2021

  66. [68]

    Celestial Mechanics and Dynamical Astronomy , author =

    Regularized phase-space volume for the three-body problem , volume =. Celestial Mechanics and Dynamical Astronomy , author =. 2022 , note =. doi:10.1007/s10569-022-10108-1 , abstract =

    work page doi:10.1007/s10569-022-10108-1 2022

  67. [70]

    Monthly Notices of the Royal Astronomical Society: Letters , author =

    Analytic. Monthly Notices of the Royal Astronomical Society: Letters , author =. 2022 , note =. doi:10.1093/mnrasl/slac145 , abstract =

    work page doi:10.1093/mnrasl/slac145 2022

  68. [71]

    Physical Review Letters , author =

    Post-. Physical Review Letters , author =. 2018 , note =. doi:10.1103/PhysRevLett.120.151101 , abstract =

    work page doi:10.1103/physrevlett.120.151101 2018

  69. [72]

    L., Amaro-Seoane, P., Chatterjee, S., et al

    Post-. Physical Review D , author =. 2018 , note =. doi:10.1103/PhysRevD.98.123005 , abstract =

    work page doi:10.1103/physrevd.98.123005 2018

  70. [73]

    2018 , note =

    The Astrophysical Journal , author =. 2018 , note =. doi:10.3847/1538-4357/aaab52 , abstract =

    work page doi:10.3847/1538-4357/aaab52 2018

  71. [74]

    , volume =

    Merging black holes in young star clusters , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2019 , note =. doi:10.1093/mnras/stz1453 , abstract =

    work page doi:10.1093/mnras/stz1453 2019

  72. [75]

    Eccentric black hole mergers via three-body interactions in young, globular and nuclear star clusters , url =

    Dall'Amico, Marco and Mapelli, Michela and Torniamenti, Stefano and Arca Sedda, Manuel , month = mar, year =. Eccentric black hole mergers via three-body interactions in young, globular and nuclear star clusters , url =. doi:10.48550/arXiv.2303.07421 , abstract =

    work page doi:10.48550/arxiv.2303.07421

  73. [76]

    The Astrophysical Journal , author =

    On the. The Astrophysical Journal , author =. 2017 , pages =. doi:10.3847/2041-8213/aa6f0b , abstract =

    work page doi:10.3847/2041-8213/aa6f0b 2017

  74. [77]

    Astrophysics and Space Science , author =

    The. Astrophysics and Space Science , author =. 1971 , note =. doi:10.1007/BF00649201 , abstract =

    work page doi:10.1007/bf00649201 1971

  75. [78]

    , volume =

    X-ray binaries in globular clusters. , volume =. The Astrophysical Journal , author =. 1975 , note =. doi:10.1086/181869 , abstract =

    work page doi:10.1086/181869 1975

  76. [79]

    Science , author =

    High-. Science , author =. 2001 , note =. doi:10.1126/science.1061135 , abstract =

    work page doi:10.1126/science.1061135 2001

  77. [80]

    Monthly Notices of the Royal Astronomical Society , author =

    The formation of binaries containing black holes by the exchange of companions and the. Monthly Notices of the Royal Astronomical Society , author =. 1976 , note =. doi:10.1093/mnras/175.1.1P , abstract =

    work page doi:10.1093/mnras/175.1.1p 1976

  78. [81]

    Nature , author =

    White dwarfs and neutron stars in globular cluster. Nature , author =. 1983 , note =. doi:10.1038/301587a0 , abstract =

    work page doi:10.1038/301587a0 1983

  79. [82]

    The Astrophysical Journal , author =

    Dynamical. The Astrophysical Journal , author =. 2003 , note =. doi:10.1086/377074 , abstract =

    work page doi:10.1086/377074 2003

  80. [83]

    The Astrophysical Journal , author =

    Dynamical. The Astrophysical Journal , author =. 2006 , note =. doi:10.1086/507027 , abstract =

    work page doi:10.1086/507027 2006

Showing first 80 references.