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arxiv: 2606.17344 · v1 · pith:YKDXRPSSnew · submitted 2026-06-15 · 🌌 astro-ph.EP

High-Eccentricity Tidal Migration Driven by Secular Chaos in Wide-Binary Systems

Yurou Liu , Hareesh Gautham Bhaskar , Xian-Yu Wang , Cristobal Petrovich This is my paper

Pith reviewed 2026-06-27 01:55 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords hot Jupiterstidal migrationsecular chaosZLK oscillationswide binarieshierarchical systemsstellar obliquityexoplanet formation
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The pith

Secular chaos in 3+1 systems drives high-eccentricity tidal migration even at modest inclinations when the ZLK timescale ratio is near unity.

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

The paper investigates how an additional companion in a wide stellar binary can excite extreme eccentricities in an inner planet through secular chaos, enabling tidal migration to form hot Jupiters. It shows that the ratio R of inner to outer ZLK timescales controls the onset of this chaos, allowing migration in most systems when R is between 0.5 and 2 even if mutual inclinations stay below the 39.2 degree threshold for standard ZLK oscillations. Diffusion times can reach thousands of inner-orbit ZLK periods. This expands migration pathways beyond idealized three-body setups and predicts hot Jupiters on nearly polar orbits relative to the host star and outer companions. Readers care because it ties observable multi-companion architectures to a testable formation channel for close-in giants.

Core claim

In hierarchical 3+1 systems, the onset of secular chaos is regulated by the ratio R of the von-Zeipel-Lidov-Kozai timescales of the inner and outer orbits. When R is approximately 0.5-2, most systems undergo high-eccentricity tidal migration even with mutual inclinations below 39.2 degrees, with diffusion timescales spanning a broad range up to thousands of inner-orbit ZLK timescales. At larger inclinations secular migration operates over R from 0.05-100 but most pathways become non-secular and potentially unstable.

What carries the argument

The ratio R of the von-Zeipel-Lidov-Kozai (ZLK) timescales of the inner and outer orbits, which sets the condition for secular chaos to excite eccentricity.

If this is right

  • Hot Jupiters form with stellar obliquities of 60-120 degrees relative to the host star's equator.
  • Migration occurs over a wide range of diffusion timescales up to thousands of inner ZLK periods when R is near 0.5-2.
  • At inclinations above the ZLK critical angle most pathways shift to non-secular and potentially unstable regimes.
  • Additional 3+1 systems discovered by Gaia and long-term radial velocity monitoring can test the predicted polar orbits.

Where Pith is reading between the lines

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

  • The mechanism suggests intermediate-mass companions may be common in systems that produce misaligned hot Jupiters.
  • It could be tested by checking whether known hot Jupiters with high obliquities show evidence of wide outer companions.
  • Secular chaos of this type might operate in other hierarchical exoplanet architectures beyond wide binaries.
  • Numerical N-body integrations of specific 3+1 systems could map the exact boundaries of the R~0.5-2 window.

Load-bearing premise

The hierarchical configuration and secular approximation remain valid throughout the evolution without close encounters or non-secular effects dominating before tidal migration finishes.

What would settle it

A survey of confirmed 3+1 systems that finds no hot Jupiters with stellar obliquities between 60 and 120 degrees or no outer companions around known polar hot Jupiters would contradict the predicted migration channel.

Figures

Figures reproduced from arXiv: 2606.17344 by Cristobal Petrovich, Hareesh Gautham Bhaskar, Xian-Yu Wang, Yurou Liu.

Figure 1
Figure 1. Figure 1: Initial configuration of “3+1” hierarchical quadruple systems in the frame of Star 0 (not to scale). The central star is part of a stellar binary and is orbited by the planet of interest, as well as an intermediate perturber, which can be a giant planet, brown dwarf, or low-mass star. As shown in this figure, and throughout most of our analysis, the planet and the intermediate perturber are coplanar, and t… view at source ↗
Figure 2
Figure 2. Figure 2: Example of a hot Jupiter forming through high- -eccentricity migration triggered by secular chaos. The sys￾tem parameters are shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Surface of sections in ω-j space of the rotating frame Hamiltonian in Equation 7. These figures are created by integrating equations of motion in Equations y-z. The Hamiltonian and the system parameters are fixed as H = 0.1, I23 = 20◦ , Ω23 = 0◦ . The completely empty regions in the figures are the prohibited region by conservation of H. When R = 0.05, there is only a small band of chaos; most trajectories… view at source ↗
Figure 4
Figure 4. Figure 4: The fraction of simulations where the planet’s eccentricity reaches 0.99 from an initial eccentricity of 0.05 as a function of normalized time. We set I1 = I2 = 20◦ , I3 = 0◦ , and randomly sample ω1, Ω1. All other system parameters are shown in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The fraction of simulations in which the planet reaches near-unity eccentricity (e1 > 1 − 10−2 ) as a function of R. The fraction increases with R in the low R regime, plateaus around R = 0.6 − 1.0, and decreases with R in the high R regime. critical ZLK limit of 40◦ , and the planet’s eccentricity cannot be excited to near-unity. 4.2. Varying mutual inclination Next, we explore how lifting the I23 = 20◦ c… view at source ↗
Figure 7
Figure 7. Figure 7: The R parameter space in which planet eccen￾tricity can be excited with varying initial I23. The color bar shows the extent to which eccentricity is excited. The square dots indicate runs that are unstable according to the M. Tory et al. (2022) criteria for instability. All system parameters are taken from [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The distribution of final stellar obliquity obtained by the planet and mutual inclinations in the system after the planet evolves into a hot Jupiter. We set I1 = I2 ≈ 0 ◦ and isotropically sample I3 below 39.2 ◦ . ω1 and Ω1 are randomly sampled. All other system parameters are taken from [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The eccentricity and semimajor axis evolution of a simulation of HD 4113 b and HD 4113 C that matches the observed values. The system parameters are shown in [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Joint two-companion orbit fit of HD 4113 with orvara. Panel (a): Radial-velocity time series with the best-fit model overlaid, colored by instrument (red: CORALIE-98, before the 2007 upgrade; green: CORALIE-07, after the 2007 upgrade; blue: HIRES; yellow: MIKE; cyan: PFS); the lower subpanel shows the residuals. Panels (b) and (c): Hipparcos–Gaia proper motions in µα∗ and µδ, respectively. The dense teal … view at source ↗
read the original abstract

High-eccentricity tidal migration driven by a distant stellar companion offers a natural pathway for producing some hot Jupiters; yet, most theoretical work has relied on an idealized three-body configuration whose simplicity makes the problem especially tractable. In reality, many cold-Jupiter systems may host additional planets or substellar objects, whose interactions can dramatically alter the pathways to secularly excite extreme eccentricities. We investigate how secular chaos can drive high-eccentricity tidal migration in hierarchical ``3+1'' systems--stellar binaries hosting a planet and an additional intermediate companion orbiting the primary star. We show that the onset of secular chaos is regulated by the ratio of the von-Zeipel-Lidov-Kozai (ZLK) timescales of the inner and outer orbits $\mathcal{R}$. When $\mathcal{R}\sim 0.5-2$, most systems can undergo migration even when their mutual inclinations remain modest--below the $39.2^\circ$ critical angle for ZLK oscillations--with diffusion timescales spanning a broad range, up to thousands of inner orbit ZLK timescales. For larger mutual inclinations, secular migration operates over a much broader region of parameter space with $\mathcal{R} \sim 0.05-100$, but most evolutionary pathways become non-secular and potentially unstable--behavior recently identified as an alternative pathway to tidal migration. Our model predicts hot Jupiters in nearly polar orbits relative to both the host star's stellar equator (stellar obliquities $\sim 60^\circ-120^\circ$) and the orbits of the outer two companions. Future Gaia releases and long-term radial velocity campaigns are likely to uncover additional ``3+1'' systems, providing valuable opportunities to test this migration pathway.

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

2 major / 1 minor

Summary. The manuscript claims that in hierarchical 3+1 systems (star + planet + intermediate companion + distant binary), secular chaos regulated by the ratio R of inner-to-outer ZLK timescales enables high-eccentricity tidal migration for R ∼ 0.5–2 even at modest inclinations below the 39.2° ZLK critical angle, with diffusion timescales ranging up to thousands of inner-orbit ZLK periods. For larger inclinations the accessible parameter space widens to R ∼ 0.05–100 but most pathways become non-secular. The model predicts hot Jupiters on nearly polar orbits relative to both the stellar equator and the outer companions.

Significance. If the central results hold, the work identifies a new secular-chaos pathway for hot-Jupiter formation that operates at modest inclinations in systems with additional companions, extending beyond the classical three-body ZLK mechanism. The regulating parameter is the timescale ratio R with no additional free parameters, yielding falsifiable predictions for stellar obliquities of ∼60°–120° that can be tested with future Gaia releases and long-term RV monitoring. This strengthens the dynamical inventory of migration channels in multi-body exoplanet systems.

major comments (2)
  1. [Abstract and §3 (model and diffusion timescale derivation)] The claim that secular chaos drives migration for R ∼ 0.5–2 at inclinations < 39.2° (abstract) is load-bearing and rests on the assumption that the secular averaging over ZLK timescales remains valid throughout the diffusion process. When inner and outer ZLK timescales are comparable, chaotic eccentricity excursions can produce pericenter distances small enough for close encounters or mean-motion resonance overlap to dominate before tidal migration completes; the manuscript provides no explicit N-body validation or analytic estimate showing that the reported diffusion timescales (up to thousands of inner ZLK periods) are reached while the hierarchical secular regime still holds.
  2. [Results section on R regimes] Table or figure presenting the R–inclination regimes (presumably in the results section) reports that most systems undergo migration for R ∼ 0.5–2 at modest inclinations, yet the boundary between secular and non-secular evolution is stated only qualitatively. A quantitative criterion (e.g., minimum pericenter distance or resonance overlap condition) is needed to demarcate where the secular diffusion calculation ceases to apply.
minor comments (1)
  1. [Abstract] The symbol ℛ for the ZLK timescale ratio is introduced in the abstract without an explicit definition; a parenthetical definition on first use would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us identify areas where the assumptions and boundaries of our secular model require further clarification. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and §3 (model and diffusion timescale derivation)] The claim that secular chaos drives migration for R ∼ 0.5–2 at inclinations < 39.2° (abstract) is load-bearing and rests on the assumption that the secular averaging over ZLK timescales remains valid throughout the diffusion process. When inner and outer ZLK timescales are comparable, chaotic eccentricity excursions can produce pericenter distances small enough for close encounters or mean-motion resonance overlap to dominate before tidal migration completes; the manuscript provides no explicit N-body validation or analytic estimate showing that the reported diffusion timescales (up to thousands of inner-orbit ZLK periods) are reached while the hierarchical secular regime still holds.

    Authors: We agree that the validity of the secular approximation during diffusion is central to the claims for R ∼ 0.5–2. The diffusion timescales reported in §3 are obtained by direct integration of the secular equations under the hierarchical assumption. In the revised manuscript we will add an analytic estimate of the minimum pericenter distance reached during the diffusion process (based on the random-walk scaling of eccentricity) to show that, for the parameter range and timescales considered, close encounters or resonance overlap are not expected to intervene before the secular diffusion completes. We will also add an explicit statement that full N-body validation lies beyond the scope of this secular study but is a natural direction for future work. revision: partial

  2. Referee: [Results section on R regimes] Table or figure presenting the R–inclination regimes (presumably in the results section) reports that most systems undergo migration for R ∼ 0.5–2 at modest inclinations, yet the boundary between secular and non-secular evolution is stated only qualitatively. A quantitative criterion (e.g., minimum pericenter distance or resonance overlap condition) is needed to demarcate where the secular diffusion calculation ceases to apply.

    Authors: We concur that a quantitative demarcation would strengthen the presentation of the R regimes. In the revised manuscript we will introduce an explicit criterion based on the minimum pericenter distance q_min remaining above a threshold (e.g., q_min > 0.05 AU, chosen so that mean-motion resonance overlap or close encounters remain negligible) and will apply this threshold to delineate the secular versus non-secular regions in the relevant figure and accompanying table. This will replace the current qualitative description. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper defines migration regimes via the dynamical ratio R of inner/outer ZLK timescales and analyzes secular chaos diffusion of eccentricity. These regimes and the claim of migration at modest inclinations for R~0.5-2 emerge from the secular model equations rather than being fitted to the target outcome or defined in terms of the result itself. No load-bearing self-citations, uniqueness theorems from the same authors, or ansatzes smuggled via prior work are visible in the abstract or described structure that would reduce the central prediction to its inputs by construction. The derivation remains self-contained against external dynamical benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on standard celestial-mechanics assumptions without introducing new free parameters or entities; R is a derived diagnostic ratio.

axioms (2)
  • standard math Newtonian gravity and hierarchical orbital separation
    Required for secular perturbation theory and ZLK timescale definitions.
  • domain assumption Secular approximation remains valid until tidal migration occurs
    Central to the chaos and diffusion analysis described.

pith-pipeline@v0.9.1-grok · 5862 in / 1337 out tokens · 43079 ms · 2026-06-27T01:55:23.523159+00:00 · methodology

discussion (0)

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Works this paper leans on

114 extracted references · 96 canonical work pages · 5 internal anchors

  1. [1]

    H., Marcussen, M

    Albrecht, S. H., Marcussen, M. L., Winn, J. N., Dawson, R. I., & Knudstrup, E. 2021, ApJL, 916, L1, doi: 10.3847/2041-8213/ac0f03 Ávila-Bravo, M., Charalambous, C., & Aguilera-Gómez, C. 2025, arXiv e-prints, arXiv:2511.09676. https://arxiv.org/abs/2511.09676

    work page doi:10.3847/2041-8213/ac0f03 2021

  2. [2]

    2012, Nature, 491, 418, doi: 10.1038/nature11560

    Batygin, K. 2012, Nature, 491, 418, doi: 10.1038/nature11560

    work page doi:10.1038/nature11560 2012

  3. [3]

    2011, A&A, 533, A7, doi: 10.1051/0004-6361/201117193

    Batygin, K., Morbidelli, A., & Tsiganis, K. 2011, A&A, 533, A7, doi: 10.1051/0004-6361/201117193

    work page doi:10.1051/0004-6361/201117193 2011

  4. [4]

    A., Gunnels, S

    Bernstein, R., Shectman, S. A., Gunnels, S. M., Mochnacki, S., & Athey, A. E. 2003, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 4841, Instrument Design and Performance for Optical/Infrared Ground-based Telescopes, ed. M. Iye & A. F. M. Moorwood, 1694–1704, doi: 10.1117/12.461502

    work page doi:10.1117/12.461502 2003

  5. [5]

    2013, in European Planetary Science

    Beuzit, J.-L. 2013, in European Planetary Science

    2013

  6. [6]

    G., & Perets, H

    Bhaskar, H. G., & Perets, H. 2024, ApJ, 973, 108, doi: 10.3847/1538-4357/ad62f9

    work page doi:10.3847/1538-4357/ad62f9 2024

  7. [7]

    2025, Nature, 644, 356, doi: 10.1038/s41586-025-09324-0

    Wu, Y.-L. 2025, Nature, 644, 356, doi: 10.1038/s41586-025-09324-0

    work page doi:10.1038/s41586-025-09324-0 2025

  8. [8]

    Boekholt, T. C. N., & Correia, A. C. M. 2023, MNRAS, 522, 2885, doi: 10.1093/mnras/stad1133

    work page doi:10.1093/mnras/stad1133 2023

  9. [9]

    Braak, C. J. T. 2006, Statistics and Computing, 16, 239

    2006

  10. [10]

    Brandt, T. D. 2018, ApJS, 239, 31, doi: 10.3847/1538-4365/aaec06

    work page doi:10.3847/1538-4365/aaec06 2018

  11. [11]

    D., Dupuy, T

    Brandt, T. D., Dupuy, T. J., Li, Y., et al. 2021, AJ, 162, 186, doi: 10.3847/1538-3881/ac042e

    work page doi:10.3847/1538-3881/ac042e 2021

  12. [12]

    P., Wright, J

    Butler, R. P., Wright, J. T., Marcy, G. W., et al. 2006, ApJ, 646, 505, doi: 10.1086/504701

    work page doi:10.1086/504701 2006

  13. [13]

    2022, MNRAS, 511, 457, doi: 10.1093/mnras/stac033

    Cadman, J., Hall, C., Fontanive, C., & Rice, K. 2022, MNRAS, 511, 457, doi: 10.1093/mnras/stac033

    work page doi:10.1093/mnras/stac033 2022

  14. [15]

    2018b, A&A, 614, A16, doi: 10.1051/0004-6361/201630136

    Cheetham, A., Ségransan, D., Peretti, S., et al. 2018b, A&A, 614, A16, doi: 10.1051/0004-6361/201630136

    work page doi:10.1051/0004-6361/201630136

  15. [16]

    MESA Isochrones and Stellar Tracks (MIST). I: Solar-Scaled Models

    Choi, J., Dotter, A., Conroy, C., et al. 2016, ApJ, 823, 102, doi: 10.3847/0004-637X/823/2/102

    work page internal anchor Pith review doi:10.3847/0004-637x/823/2/102 2016

  16. [17]

    2022, AJ, 163, 207

    Christian, S., Vanderburg, A., Becker, J., et al. 2022, AJ, 163, 207

    2022

  17. [18]

    D., Hatzes, A

    Cochran, W. D., Hatzes, A. P., Butler, R. P., & Marcy, G. W. 1997, ApJ, 483, 457, doi: 10.1086/304245

    work page doi:10.1086/304245 1997

  18. [19]

    D., Shectman, S

    Crane, J. D., Shectman, S. A., & Butler, R. P. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6269, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, ed. I. S. McLean & M. Iye, 626931, doi: 10.1117/12.672339

    work page doi:10.1117/12.672339 2006

  19. [20]

    D., Shectman, S

    Crane, J. D., Shectman, S. A., Butler, R. P., et al. 2010, in Ground-based and Airborne Instrumentation for Astronomy III, Vol. 7735, SPIE, 1909–1923

    2010

  20. [21]

    D., Shectman, S

    Crane, J. D., Shectman, S. A., Butler, R. P., Thompson, I. B., & Burley, G. S. 2008, in Ground-based and Airborne Instrumentation for Astronomy II, Vol. 7014, SPIE, 2484–2493

    2008

  21. [22]

    I., & Johnson, J

    Dawson, R. I., & Johnson, J. A. 2018, ARA&A, 56, 175

    2018

  22. [23]

    2023, A&A, 675, A158, doi: 10.1051/0004-6361/202244611

    Desidera, S., Damasso, M., Gratton, R., et al. 2023, A&A, 675, A158, doi: 10.1051/0004-6361/202244611

    work page doi:10.1051/0004-6361/202244611 2023

  23. [24]

    2023, AJ, 166, 112, doi: 10.3847/1538-3881/ace105

    Dong, J., & Foreman-Mackey, D. 2023, AJ, 166, 112, doi: 10.3847/1538-3881/ace105

    work page doi:10.3847/1538-3881/ace105 2023

  24. [25]

    MESA Isochrones and Stellar Tracks (MIST) 0: Methods for the construction of stellar isochrones

    Dotter, A. 2016, ApJS, 222, 8, doi: 10.3847/0067-0049/222/1/8

    work page internal anchor Pith review doi:10.3847/0067-0049/222/1/8 2016

  25. [26]

    2025, arXiv e-prints, arXiv:2510.20740, doi: 10.48550/arXiv.2510.20740

    Dugan, E., Wang, X.-Y., Heron, A., et al. 2025, arXiv e-prints, arXiv:2510.20740, doi: 10.48550/arXiv.2510.20740

    work page doi:10.48550/arxiv.2510.20740 2025

  26. [27]

    J., Kraus, A

    Dupuy, T. J., Kraus, A. L., Kratter, K. M., et al. 2022, MNRAS, 512, 648

    2022

  27. [28]

    2017, http://ascl.net/1710.003

    Eastman, J. 2017, http://ascl.net/1710.003

    2017

  28. [29]

    D., Rodriguez, J

    Eastman, J. D., Rodriguez, J. E., Agol, E., et al. 2019, arXiv e-prints, arXiv:1907.09480. https://arxiv.org/abs/1907.09480

    Pith/arXiv arXiv 2019

  29. [30]

    P., Kiseleva, L

    Eggleton, P. P., Kiseleva, L. G., & Hut, P. 1998, ApJ, 499, 853, doi: 10.1086/305670 17

    work page doi:10.1086/305670 1998

  30. [31]

    P., & Kiseleva-Eggleton, L

    Eggleton, P. P., & Kiseleva-Eggleton, L. 2001, ApJ, 562, 1012, doi: 10.1086/323843

    work page doi:10.1086/323843 2001

  31. [32]

    I., Brahm, R., Petrovich, C., et al

    Espinoza-Retamal, J. I., Brahm, R., Petrovich, C., et al. 2023, ApJL, 958, L20, doi: 10.3847/2041-8213/ad096d

    work page doi:10.3847/2041-8213/ad096d 2023

  32. [33]

    I., Stefánsson, G., Petrovich, C., et al

    Espinoza-Retamal, J. I., Stefánsson, G., Petrovich, C., et al. 2024, AJ, 168, 185, doi: 10.3847/1538-3881/ad70b8

    work page doi:10.3847/1538-3881/ad70b8 2024

  33. [34]

    2007, ApJ, 669, 1298, doi: 10.1086/521702

    Fabrycky, D., & Tremaine, S. 2007, ApJ, 669, 1298, doi: 10.1086/521702

    work page doi:10.1086/521702 2007

  34. [35]

    2007, ApJ, 669, 1298

    Fabrycky, D., & Tremaine, S. 2007, ApJ, 669, 1298

    2007

  35. [36]

    2026, The Astrophysical Journal Letters, 1003, L7, doi: 10.3847/2041-8213/ae6659

    Fan, Q., & Liu, S.-F. 2026, The Astrophysical Journal Letters, 1003, L7, doi: 10.3847/2041-8213/ae6659

    work page doi:10.3847/2041-8213/ae6659 2026

  36. [37]

    P., Vogt, S

    Feng, F., Butler, R. P., Vogt, S. S., et al. 2022, ApJS, 262, 21, doi: 10.3847/1538-4365/ac7e57

    work page doi:10.3847/1538-4365/ac7e57 2022

  37. [38]

    B., McKee, C

    Fielding, D. B., McKee, C. F., Socrates, A., Cunningham, A. J., & Klein, R. I. 2015, MNRAS, 450, 3306, doi: 10.1093/mnras/stv836

    work page doi:10.1093/mnras/stv836 2015

  38. [39]

    2021, Frontiers in Astronomy and Space Sciences, 8, 16, doi: 10.3389/fspas.2021.625250 Gaia Collaboration, Vallenari, A., Brown, A

    Fontanive, C., & Bardalez Gagliuffi, D. 2021, Frontiers in Astronomy and Space Sciences, 8, 16, doi: 10.3389/fspas.2021.625250 Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1, doi: 10.1051/0004-6361/202243940

    work page doi:10.3389/fspas.2021.625250 2021

  39. [40]

    Grishin, E., Lai, D., & Perets, H. B. 2018, MNRAS, 474, 3547, doi: 10.1093/mnras/stx3005

    work page doi:10.1093/mnras/stx3005 2018

  40. [41]

    F., Millholland, S

    Gupta, A. F., Millholland, S. C., Im, H., et al. 2024, Nature, 632, 50, doi: 10.1038/s41586-024-07688-3

    work page doi:10.1038/s41586-024-07688-3 2024

  41. [42]

    2018, AJ, 156, 95, doi: 10.3847/1538-3881/aad32c

    Hadden, S., & Lithwick, Y. 2018, AJ, 156, 95, doi: 10.3847/1538-3881/aad32c

    work page doi:10.3847/1538-3881/aad32c 2018

  42. [43]

    S., & Lai, D

    Hamers, A. S., & Lai, D. 2017, MNRAS, 470, 1657, doi: 10.1093/mnras/stx1319

    work page doi:10.1093/mnras/stx1319 2017

  43. [44]

    Zwart, S. F. 2015, MNRAS, 449, 4221, doi: 10.1093/mnras/stv452

    work page doi:10.1093/mnras/stv452 2015

  44. [45]

    1997, Nature, 386, 254, doi: 10.1038/386254a0

    Holman, M., Touma, J., & Tremaine, S. 1997, Nature, 386, 254, doi: 10.1038/386254a0

    work page doi:10.1038/386254a0 1997

  45. [46]

    Hwang, H.-C., Ting, Y.-S., & Zakamska, N. L. 2022, MNRAS, 512, 3383, doi: 10.1093/mnras/stac675

    work page doi:10.1093/mnras/stac675 2022

  46. [47]

    Ida, S., Lin, D. N. C., & Nagasawa, M. 2013, ApJ, 775, 42, doi: 10.1088/0004-637X/775/1/42

    work page doi:10.1088/0004-637x/775/1/42 2013

  47. [48]

    A., Zheng, J

    Innanen, K. A., Zheng, J. Q., Mikkola, S., & Valtonen, M. J. 1997, AJ, 113, 1915, doi: 10.1086/118405 Jurić, M., & Tremaine, S. 2008, ApJ, 686, 603, doi: 10.1086/590047

    work page doi:10.1086/118405 1997

  48. [49]

    2012, MNRAS, 427, 1266, doi: 10.1111/j.1365-2966.2012.22060.x

    Kane, S. R., Ciardi, D. R., Gelino, D. M., & von Braun, K. 2012, MNRAS, 425, 757, doi: 10.1111/j.1365-2966.2012.21627.x

    work page doi:10.1111/j.1365-2966.2012.21627.x 2012

  49. [50]

    R., & Wittenmyer, R

    Kane, S. R., & Wittenmyer, R. A. 2024, ApJL, 962, L21, doi: 10.3847/2041-8213/ad2463

    work page doi:10.3847/2041-8213/ad2463 2024

  50. [51]

    Y., & Katz, B

    Klein, Y. Y., & Katz, B. 2023, ApJL, 953, L10, doi: 10.3847/2041-8213/aceae7

    work page doi:10.3847/2041-8213/aceae7 2023

  51. [52]

    Y., & Katz, B

    Klein, Y. Y., & Katz, B. 2024, AJ, 167, 80, doi: 10.3847/1538-3881/ad18b6

    work page doi:10.3847/1538-3881/ad18b6 2024

  52. [53]

    Y., & Katz, B

    Klein, Y. Y., & Katz, B. 2025, MNRAS, 539, L7, doi: 10.1093/mnrasl/slaf017

    work page doi:10.1093/mnrasl/slaf017 2025

  53. [54]

    H., Winn, J

    Knudstrup, E., Albrecht, S. H., Winn, J. N., et al. 2024, A&A, 690, A379, doi: 10.1051/0004-6361/202450627

    work page doi:10.1051/0004-6361/202450627 2024

  54. [55]

    A., Fulton, B

    Knutson, H. A., Fulton, B. J., Montet, B. T., et al. 2014, ApJ, 785, 126, doi: 10.1088/0004-637X/785/2/126

    work page doi:10.1088/0004-637x/785/2/126 2014

  55. [56]

    2012, ApJ, 745, 19, doi: 10.1088/0004-637X/745/1/19

    Martinache, F. 2012, ApJ, 745, 19, doi: 10.1088/0004-637X/745/1/19

    work page doi:10.1088/0004-637x/745/1/19 2012

  56. [57]

    2012, MNRAS, 427, 1266, doi: 10.1111/j.1365-2966.2012.22060.x

    Lai, D. 2012, MNRAS, 423, 486, doi: 10.1111/j.1365-2966.2012.20893.x

    work page doi:10.1111/j.1365-2966.2012.20893.x 2012

  57. [58]

    2014, MNRAS, 440, 3532, doi: 10.1093/mnras/stu485

    Lai, D. 2014, MNRAS, 440, 3532, doi: 10.1093/mnras/stu485

    work page doi:10.1093/mnras/stu485 2014

  58. [59]

    Lai, D., Foucart, F., & Lin, D. N. C. 2011, MNRAS, 412, 2790, doi: 10.1111/j.1365-2966.2010.18127.x

    work page doi:10.1111/j.1365-2966.2010.18127.x 2011

  59. [60]

    V., Matson, R

    Lester, K. V., Matson, R. A., Howell, S. B., et al. 2021, AJ, 162, 75, doi: 10.3847/1538-3881/ac0d06

    work page doi:10.3847/1538-3881/ac0d06 2021

  60. [61]

    V., Howell, S

    Lester, K. V., Howell, S. B., Matson, R. A., et al. 2023, AJ, 166, 166, doi: 10.3847/1538-3881/acf563

    work page doi:10.3847/1538-3881/acf563 2023

  61. [62]

    Lidov, M. L. 1962, Planetary and Space Science, 9, 719

    1962

  62. [63]

    2021, A&A, 649, A4, doi: 10.1051/0004-6361/202039653

    Lindegren, L., Bastian, U., Biermann, M., et al. 2021, A&A, 649, A4, doi: 10.1051/0004-6361/202039653

    work page doi:10.1051/0004-6361/202039653 2021

  63. [64]

    J., & Lai, D

    Liu, B., Muñoz, D. J., & Lai, D. 2015, MNRAS, 447, 747, doi: 10.1093/mnras/stu2396

    work page doi:10.1093/mnras/stu2396 2015

  64. [65]

    C., Vick, M., & Tamayo, D

    Liveoak, D., Millholland, S. C., Vick, M., & Tamayo, D. 2025, ApJ, 989, 35, doi: 10.3847/1538-4357/adefe7

    work page doi:10.3847/1538-4357/adefe7 2025

  65. [66]

    M., & Millholland, S

    Louden, E. M., & Millholland, S. C. 2024, ApJ, 974, 304, doi: 10.3847/1538-4357/ad74ff

    work page doi:10.3847/1538-4357/ad74ff 2024

  66. [67]

    2025, ApJ, 979, 218, doi: 10.3847/1538-4357/ad9b79

    Lu, T., An, Q., Li, G., et al. 2025, ApJ, 979, 218, doi: 10.3847/1538-4357/ad9b79

    work page doi:10.3847/1538-4357/ad9b79 2025

  67. [68]

    2023, ApJ, 948, 41, doi: 10.3847/1538-4357/acc06d

    Lu, T., Rein, H., Tamayo, D., et al. 2023, ApJ, 948, 41, doi: 10.3847/1538-4357/acc06d

    work page doi:10.3847/1538-4357/acc06d 2023

  68. [69]

    2022, MNRAS, 510, 5050, doi: 10.1093/mnras/stab3602

    Marzari, F., Nagasawa, M., & Goździewski, K. 2022, MNRAS, 510, 5050, doi: 10.1093/mnras/stab3602

    work page doi:10.1093/mnras/stab3602 2022

  69. [70]

    2005, ApJ, 618, 502, doi: 10.1086/425976

    Granata, V. 2005, ApJ, 618, 502, doi: 10.1086/425976

    work page doi:10.1086/425976 2005

  70. [71]

    2021, A&A, 650, A116, doi: 10.1051/0004-6361/202039210

    Matsumura, S., Brasser, R., & Ida, S. 2021, A&A, 650, A116, doi: 10.1051/0004-6361/202039210

    work page doi:10.1051/0004-6361/202039210 2021

  71. [72]

    J., & Rasio, F

    Matsumura, S., Peale, S. J., & Rasio, F. A. 2010, ApJ, 725, 1995, doi: 10.1088/0004-637X/725/2/1995

    work page doi:10.1088/0004-637x/725/2/1995 2010

  72. [73]

    Moe, M., & Kratter, K. M. 2021, MNRAS, 507, 3593, doi: 10.1093/mnras/stab2328

    work page doi:10.1093/mnras/stab2328 2021

  73. [74]

    2014, MNRAS, 439, 1063, doi: 10.1093/mnras/stu044

    Mugrauer, M., Ginski, C., & Seeliger, M. 2014, MNRAS, 439, 1063, doi: 10.1093/mnras/stu044

    work page doi:10.1093/mnras/stu044 2014

  74. [75]

    J., Davies, M

    Mustill, A. J., Davies, M. B., & Johansen, A. 2017, MNRAS, 468, 3000, doi: 10.1093/mnras/stx693 18

    work page doi:10.1093/mnras/stx693 2017

  75. [76]

    W., Mayor, M., et al

    Naef, D., Latham, D. W., Mayor, M., et al. 2001, A&A, 375, L27, doi: 10.1051/0004-6361:20010853

    work page doi:10.1051/0004-6361:20010853 2001

  76. [77]

    2011, Nature, 473, 187

    Teyssandier, J. 2011, Nature, 473, 187

    2011

  77. [78]

    M., & Rasio, F

    Naoz, S., Farr, W. M., & Rasio, F. A. 2012, ApJL, 754, L36

    2012

  78. [79]

    X., Standish, E

    Newhall, X. X., Standish, E. M., & Williams, J. G. 1983, A&A, 125, 150

    1983

  79. [80]

    A., Hinkley, S., et al

    Ngo, H., Knutson, H. A., Hinkley, S., et al. 2015, ApJ, 800, 138, doi: 10.1088/0004-637X/800/2/138

    work page doi:10.1088/0004-637x/800/2/138 2015

  80. [81]

    G., Collins , K

    Paegert, M., Stassun, K. G., Collins, K. A., et al. 2021, arXiv e-prints, arXiv:2108.04778, doi: 10.48550/arXiv.2108.04778

    work page doi:10.48550/arxiv.2108.04778 2021

Showing first 80 references.