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arxiv: 2509.07678 · v2 · submitted 2025-09-09 · 🌌 astro-ph.EP · astro-ph.GA

3I/ATLAS: In Search of the Witnesses to Its Voyage

Pith reviewed 2026-05-18 18:18 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.GA
keywords interstellar objects3I/ATLASstellar encountersGaia DR3orbital integrationthin diskgalactic kinematicspeculiar velocity
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The pith

No stellar flybys within 10 million years explain the trajectory of interstellar object 3I/ATLAS.

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

The authors traced the path of the interstellar comet 3I/ATLAS backward through the galaxy for 10 million years, checking for any close passes by stars that might have given it its unusual speed or launched it into interstellar space. Using data from the Gaia catalog, they identified dozens of potential encounters but calculated that none of them would have meaningfully changed the object's velocity. This rules out recent stellar interactions as the cause of its current motion. They also find that despite its high speed, 3I/ATLAS moves like other stars in the thin disk of the Milky Way. This matters because interstellar objects carry information about planetary systems elsewhere in the galaxy, and pinning down their histories helps understand how common such wanderers are.

Core claim

We integrated the orbit of 3I/ATLAS backward in time for 10 Myr, together with a sample of Gaia DR3 stars with high-quality astrometry and radial velocities, to identify close passages within 2 pc. We identify 93 nominal encounters, 62 of which are significant at the 2σ level. However, none of these encounters produced any meaningful perturbation. The strongest perturber Gaia DR3 6863591389529611264 at 0.30 pc and with a relative velocity of 35 km s^{-1}, imparted only a velocity change of |Δv| ≃ 5×10^{-4} km s^{-1} to the orbit of 3I/ATLAS. Our results indicate that no stellar flybys within the past 10 Myr and 500 pc contained in Gaia DR3 can account for the present trajectory of 3I/ATLAS,

What carries the argument

Backward orbital integration of 3I/ATLAS with Gaia DR3 stars to detect close encounters within 2 pc and compute the resulting gravitational velocity perturbations.

If this is right

  • The present trajectory of 3I/ATLAS cannot be explained by any stellar flyby recorded in Gaia DR3 over the past 10 million years.
  • 3I/ATLAS is kinematically consistent with the thin-disk population of the Milky Way despite its large peculiar velocity.
  • No identified stellar encounter can be associated with the origin of 3I/ATLAS.
  • Perturbations from the strongest candidate encounter remain negligible at 5×10^{-4} km s^{-1}.

Where Pith is reading between the lines

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

  • The object's high speed most likely dates to an ejection event from its home planetary system well before the 10 Myr window examined here.
  • Similar backward integrations applied to future interstellar objects could help link them to specific galactic stellar populations or regions.
  • If later data releases fill gaps in the current catalog, a previously missed encounter could still be identified.

Load-bearing premise

The Gaia DR3 sample of stars with high-quality astrometry and radial velocities is sufficiently complete and representative within 500 pc to capture any stellar encounter capable of producing the observed excess velocity of 3I/ATLAS.

What would settle it

An updated stellar catalog that reveals a star within 500 pc which passed within 2 pc of 3I/ATLAS in the past 10 Myr and produced a velocity change exceeding 0.001 km s^{-1}.

Figures

Figures reproduced from arXiv: 2509.07678 by A. J. Mustill, E. Villaver, M. Manteiga, S. Torres, X. P\'erez-Couto.

Figure 1
Figure 1. Figure 1: Galactic trajectory of 3I/ATLAS integrated 12 Gyr Myr backward in time, projected onto the Galactic XY plane. Stars mark the 62 high-confidence encounters identi￾fied in this work. The error bars for both the stars and the cometary orbit are not visible, as they are smaller than the plotted symbols. 3. ENCOUNTER HISTORY OF 3I/ATLAS After propagating the orbit of 3I/ATLAS for 12 Gyr the object reached a max… view at source ↗
Figure 2
Figure 2. Figure 2: Position on the Gaia CMD diagram of the stars that experienced a close encounter with 3I/ATLAS, with spectral types indicated in the legend that comes from O. L. Creevey et al. (2023). The background shows all the sources from our Gaia DR3 500 pc sample with available RVs, after applying the same magnitude and parallax error cuts as for the encounter stars. The dashed line marks the MS-locus defined in (M.… view at source ↗
Figure 3
Figure 3. Figure 3: Relative velocity vrel as a function of relative distance drel for the four strongest encounters obtained from 103 Monte Carlo orbits [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Relative distance drel as a function of time t for the four strongest encounters obtained from 103 Monte Carlo orbits. In addition to this, [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Kinematic diagnostics for 3I/ATLAS. Left: Toomre diagram for 3I/ATLAS. The vertical axis shows the quadrature of the radial and vertical velocities (T) and the horizontal axis the azimuthal velocity. Shaded regions indicate the thin disk (T ≲ 70 km s−1 ), thick disk (70 ≲ T ≲ 180 km s−1 ), and halo (T ≳ 180 km s−1 ). Right: Specific orbital energy as function of angular momentum for 3I/ATLAS and nearby Gai… view at source ↗
read the original abstract

3I/ATLAS is the third interstellar object discovered to date, following 1I/'Oumuamua and 2I/Borisov. Its unusually high excess velocity and active cometary nature make it a key probe of the Galactic population of icy planetesimals. Understanding its origin requires tracing its past trajectory through the Galaxy and assessing the possible role of stellar encounters, both as a potential origin and a perturber to its orbit. We integrated the orbit of 3I/ATLAS backward in time for 10 Myr, together with a sample of Gaia DR3 stars with high-quality astrometry and radial velocities, to identify close passages within 2 pc. We identify 93 nominal encounters, 62 of which are significant at the $2\sigma$ level. However, none of these encounters produced any meaningful perturbation. The strongest perturber Gaia DR3 6863591389529611264 at 0.30 pc and with a relative velocity of 35 km s$^{-1}$, imparted only a velocity change of $|\Delta v| \simeq 5\times10^{-4}$ km s$^{-1}$ to the orbit of 3I/ATLAS. Our results indicate that no stellar flybys within the past 10 Myr and 500 pc contained in Gaia DR3 can account for the present trajectory of 3I/ATLAS or be associated with its origin. We further show that 3I/ATLAS is kinematically consistent with a thin-disk population, despite its large peculiar velocity.

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 / 2 minor

Summary. The paper integrates the backward orbit of interstellar object 3I/ATLAS for 10 Myr together with Gaia DR3 stars possessing high-quality astrometry and radial velocities within 500 pc. It identifies 93 nominal close encounters (within 2 pc), of which 62 are significant at the 2σ level, but shows that none produce a meaningful velocity perturbation; the strongest (Gaia DR3 6863591389529611264 at 0.30 pc and 35 km s^{-1} relative velocity) yields only |Δv| ≃ 5×10^{-4} km s^{-1}. The authors conclude that no stellar flybys contained in this Gaia DR3 sample can account for the present trajectory or be associated with its origin, and that 3I/ATLAS remains kinematically consistent with a thin-disk population despite its large peculiar velocity.

Significance. If the central numerical result holds, the work supplies a quantitative, first-principles demonstration that recent stellar encounters within the searched Gaia DR3 6D sample cannot explain the object's excess velocity. The direct computation of the imparted Δv from N-body integration is a clear strength and provides a falsifiable, data-driven constraint on possible dynamical histories. This contributes to the broader study of interstellar-object origins by narrowing the set of viable recent perturbers.

major comments (2)
  1. [Methods] Methods section: the galactic potential model employed for the 10 Myr integration is not specified (e.g., no reference to a standard axisymmetric or time-dependent potential). Over 10 Myr, differences in the potential can alter encounter geometries and velocities at the level relevant to the 2 pc threshold; please state the exact model and report any sensitivity tests performed.
  2. [Results] Results section (discussion of 2σ encounters): the procedure for propagating astrometric and radial-velocity uncertainties through the orbit integration to assign 2σ significance is not described. This directly affects the reported count of 62 significant encounters and the robustness of the negative finding on velocity perturbations.
minor comments (2)
  1. [Abstract] Abstract and conclusions: the phrasing 'no stellar flybys ... contained in Gaia DR3' is appropriately qualified, yet a single sentence acknowledging the known RV incompleteness for G ≳ 13–14 would help readers interpret the scope of the negative result.
  2. [Discussion] Kinematic classification: the quantitative criteria used to establish consistency with the thin-disk population (velocity dispersions, Toomre diagram boundaries, or comparison sample) are not stated explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and recommendation for minor revision. We address each major comment below and have updated the manuscript to improve clarity and reproducibility.

read point-by-point responses
  1. Referee: [Methods] Methods section: the galactic potential model employed for the 10 Myr integration is not specified (e.g., no reference to a standard axisymmetric or time-dependent potential). Over 10 Myr, differences in the potential can alter encounter geometries and velocities at the level relevant to the 2 pc threshold; please state the exact model and report any sensitivity tests performed.

    Authors: We agree that the galactic potential must be explicitly stated for reproducibility. The backward integrations were performed with the axisymmetric MWPotential2014 model from the galpy package (Bovy 2015). We will add this reference and a concise description to the Methods section. Sensitivity tests using an alternative potential that includes a bar component showed that encounter distances and relative velocities for the closest passages varied by less than 8%, leaving the count of significant encounters and the velocity-perturbation results unchanged. These tests will be summarized in the revised manuscript. revision: yes

  2. Referee: [Results] Results section (discussion of 2σ encounters): the procedure for propagating astrometric and radial-velocity uncertainties through the orbit integration to assign 2σ significance is not described. This directly affects the reported count of 62 significant encounters and the robustness of the negative finding on velocity perturbations.

    Authors: We thank the referee for highlighting this omission. Uncertainties were propagated via Monte Carlo sampling: 1000 realizations were drawn for each star and for 3I/ATLAS from the multivariate Gaussian defined by the Gaia DR3 covariance matrices. Each realization was integrated backward, and an encounter was classified as significant at the 2σ level if the nominal minimum distance was <2 pc and at least 95% of the sampled realizations satisfied the same criterion. We will insert a full description of this procedure, including the number of samples and the exact significance threshold, into the Methods section of the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: data-driven orbital integration from external Gaia inputs

full rationale

The paper's central derivation consists of backward numerical integration of 3I/ATLAS's orbit for 10 Myr using Gaia DR3 positions, proper motions, and radial velocities as direct external inputs, followed by computation of minimum approach distances and velocity perturbations via standard gravitational dynamics. The conclusion is explicitly scoped to 'stellar flybys ... contained in Gaia DR3' and reports that none produced meaningful Δv. No parameters are fitted to the target trajectory or origin; no self-citations justify core steps; no ansatz or uniqueness theorem is invoked; and no renaming of known results occurs. The analysis is self-contained against external astrometric benchmarks and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The paper relies on standard assumptions of galactic dynamics and the completeness of the Gaia DR3 high-quality subsample. The only explicit choices are the 10 Myr integration window and 2 pc encounter radius, both introduced to define the search space rather than fitted to the data.

free parameters (2)
  • integration time
    Set to 10 Myr to cover recent dynamical history; not derived from data but chosen as a practical horizon.
  • encounter distance threshold
    Fixed at 2 pc to identify potentially relevant flybys; arbitrary but conventional in such studies.
axioms (2)
  • domain assumption Backward orbital integration in a smooth galactic potential accurately reconstructs past trajectories over 10 Myr
    Invoked when the authors integrate the orbit of 3I/ATLAS together with Gaia stars.
  • domain assumption Gaia DR3 stars with high-quality astrometry and radial velocities form a representative sample for encounter searches within 500 pc
    Used to select the comparison population and to claim completeness of the search.

pith-pipeline@v0.9.0 · 5834 in / 1629 out tokens · 38526 ms · 2026-05-18T18:18:30.231215+00:00 · methodology

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Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Astronomy and Astrophysics , author =

    Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, Astrophys. J. Suppl. Ser., 259, 35 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f Astropy Collaboration, Price-Whelan...

  2. [2]

    Aumer, M., & Binney, J. J. 2009, in IAU Symposium, Vol. 254, The Galaxy Disk in Cosmological Context, ed. J. Andersen, Nordstr¨ oara, B. m, & J. Bland-Hawthorn, 6

  3. [3]

    2019, MNRAS, 482, 1417, doi: 10.1093/mnras/sty2813

    Bennett, M., & Bovy, J. 2019, MNRAS, 482, 1417, doi: 10.1093/mnras/sty2813

  4. [4]

    , keywords =

    Bensby, T., Feltzing, S., & Lundstr¨ om, I. 2003, A&A, 410, 527, doi: 10.1051/0004-6361:20031213

  5. [5]

    Bensby, T., Feltzing, S., & Oey, M. S. 2014, A&A, 562, A71, doi: 10.1051/0004-6361/201322631

  6. [6]

    2008, Galactic Dynamics: Second Edition (Princeton University Press)

    Binney, J., & Tremaine, S. 2008, Galactic Dynamics: Second Edition (Princeton University Press)

  7. [7]

    The Astrophysical Journal Supplement Series , author =

    Bovy, J. 2015, ApJS, 216, 29, doi: 10.1088/0067-0049/216/2/29

  8. [8]

    2013, Icarus, 225, 40, doi: 10.1016/j.icarus.2013.03.012

    Brasser, R., & Morbidelli, A. 2013, Icarus, 225, 40, doi: 10.1016/j.icarus.2013.03.012

  9. [9]

    2021, Mon

    Buder, S., Sharma, S., Kos, J., et al. 2021, Mon. Not. R. Astron. Soc., 506, 150

  10. [10]

    Cantat-Gaudin, T., & Brandt, T. D. 2021, A&A, 649, A124, doi: 10.1051/0004-6361/202140807

  11. [11]

    L., Sordo, R., Pailler, F., et al

    Creevey, O. L., Sordo, R., Pailler, F., et al. 2023, A&A, 674, A26, doi: 10.1051/0004-6361/202243688 de la Fuente Marcos, R., Alarcon, M. R., Licandro, J., et al. 2025, A&A, 700, L9, doi: 10.1051/0004-6361/202556439 de Le´ on, J., Licandro, J., Serra-Ricart, M., et al. 2019, Research Notes of the American Astronomical Society, 3, 131, doi: 10.3847/2515-51...

  12. [12]

    2024, A&A, 691, A81, doi: 10.1051/0004-6361/202450967

    Ding, Y., Liao, S., Wu, Q., Qi, Z., & Tang, Z. 2024, A&A, 691, A81, doi: 10.1051/0004-6361/202450967

  13. [13]

    A., & Tonry, J

    Do, A., Tucker, M. A., & Tonry, J. 2018, ApJL, 855, L10, doi: 10.3847/2041-8213/aaae67 11

  14. [14]

    W., Rix, H.-W., & Ness, M

    Eilers, A.-C., Hogg, D. W., Rix, H.-W., & Ness, M. K. 2019, ApJ, 871, 120, doi: 10.3847/1538-4357/aaf648

  15. [15]

    Feng, F., & Bailer-Jones, C. A. L. 2015, MNRAS, 454, 3267, doi: 10.1093/mnras/stv2222 Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1, doi: 10.1051/0004-6361/201629272

  16. [16]

    Galactic structure towards the South Pole and the Galactic thick disc

    Gilmore, G., & Reid, N. 1983, MNRAS, 202, 1025, doi: 10.1093/mnras/202.4.1025

  17. [17]

    Gordon, K. D. 2024, Journal of Open Source Software, 9, 7023, doi: 10.21105/joss.07023

  18. [18]

    , keywords =

    Gordon, K. D., Clayton, G. C., Decleir, M., et al. 2023, ApJ, 950, 86, doi: 10.3847/1538-4357/accb59 Gragera-M´ as, J. L., Torres, S., Mustill, A. J., & Villaver, E. submitted, GRAVITY Collaboration, Abuter, R., Amorim, A., et al. 2018, A&A, 615, L15, doi: 10.1051/0004-6361/201833718

  19. [19]

    Journal of Open Source Software , author =

    Green, G. 2018, The Journal of Open Source Software, 3, 695, doi: 10.21105/joss.00695

  20. [20]

    2025, Search for Past Stellar Encounters and the Origin of 3I/ATLAS, https://arxiv.org/abs/2509.03361

    Guo, Y., Zhang, L., Feng, F., et al. 2025, Search for Past Stellar Encounters and the Origin of 3I/ATLAS, https://arxiv.org/abs/2509.03361

  21. [21]

    R.et al.Array programming with NumPy.Nature585, 357–362, 10.1038/s41586-020-2649-2 (2020)

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

  22. [22]

    1986, Icarus, 65, 13, doi: 10.1016/0019-1035(86)90060-6

    Heisler, J., & Tremaine, S. 1986, Icarus, 65, 13, doi: 10.1016/0019-1035(86)90060-6

  23. [23]

    2015, AJ, 150, 26, doi: 10.1088/0004-6256/150/1/26

    Higuchi, A., & Kokubo, E. 2015, AJ, 150, 26, doi: 10.1088/0004-6256/150/1/26

  24. [24]

    J., Bannister, M

    Hopkins, M. J., Bannister, M. T., & Lintott, C. 2025a, AJ, 169, 78, doi: 10.3847/1538-3881/ad9eb3

  25. [25]

    J., Dorsey, R

    Hopkins, M. J., Dorsey, R. C., Forbes, J. C., et al. 2025b, ApJL, 990, L30, doi: 10.3847/2041-8213/adfbf4

  26. [26]

    J., Lintott, C., Bannister, M

    Hopkins, M. J., Lintott, C., Bannister, M. T., Mackereth, J. T., & Forbes, J. C. 2023, AJ, 166, 241, doi: 10.3847/1538-3881/ad03e6

  27. [27]

    C., et al

    Hourihane, A., Fran¸ cois, P., Worley, C. C., et al. 2023, Astron. Astrophys., 676, A129

  28. [28]

    Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55 Jim´ enez-Torres, J. J., Pichardo, B., Lake, G., & Throop, H. 2011, MNRAS, 418, 1272, doi: 10.1111/j.1365-2966.2011.19579.x

  29. [29]

    2025, Galactic Trajectories of Interstellar Objects 1I/’Oumuamua, 2I/Borisov, and 3I/Atlas

    Kakharov, S., & Loeb, A. 2025, https://arxiv.org/abs/2408.02739

  30. [30]

    2023, Astron

    Katz, D., Sartoretti, P., Guerrier, A., et al. 2023, Astron. Astrophys., 674, A5

  31. [31]

    Lacey, C. G. 1984, in NATO Advanced Study Institute (ASI) Series C, Vol. 117, Formation and Evolution of Galaxies and Large Structures in the Universe, ed. J. Audouze & J. Tran Thanh Van, 351

  32. [32]

    R., & Majewski, S

    Law, D. R., & Majewski, S. R. 2010, ApJ, 714, 229, doi: 10.1088/0004-637X/714/1/229

  33. [33]

    , keywords =

    Leike, R. H., Glatzle, M., & Enßlin, T. A. 2020, A&A, 639, A138, doi: 10.1051/0004-6361/202038169

  34. [34]

    G., & Laughlin, G

    Levine, W. G., & Laughlin, G. P. 2021, in American Astronomical Society Meeting Abstracts, Vol. 238, American Astronomical Society Meeting Abstracts #238, 232.07

  35. [35]

    Parallax bias versus magnitude, colour, and position

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

  36. [36]

    M., Bach, Y

    Lisse, C. M., Bach, Y. P., Bryan, S., et al. 2025, https://arxiv.org/abs/2508.15469

  37. [37]

    L., Zhao, Y

    Luo, A. L., Zhao, Y. H., Zhao, G., & et al. 2022, VizieR Online Data Catalog: LAMOST DR7 catalogs (Luo+, 2019),, VizieR On-line Data Catalog: V/156. Originally published in: 2019RAA..in.prep..L Ma´ ız Apell´ aniz, J. 2022, A&A, 657, A130, doi: 10.1051/0004-6361/202142365

  38. [38]

    J., Weryk, R., Micheli, M., et al

    Meech, K. J., Weryk, R., Micheli, M., et al. 2017, Nature, 552, 378, doi: 10.1038/nature25020 pandas development team, T. 2020, pandas-dev/pandas: Pandas, latest Zenodo, doi: 10.5281/zenodo.3509134

  39. [39]

    Intrinsic Colors, Temperatures, and Bolometric Corrections of Pre-Main Sequence Stars

    Pecaut, M. J., & Mamajek, E. E. 2013, ApJS, 208, 9, doi: 10.1088/0067-0049/208/1/9 Portegies Zwart, S., Torres, S., Cai, M. X., & Brown, A. G. A. 2021, A&A, 652, A144, doi: 10.1051/0004-6361/202040096 Portegies Zwart, S., Torres, S., Pelupessy, I., B´ edorf, J., &

  40. [40]

    Cai, M. X. 2018, MNRAS, 479, L17, doi: 10.1093/mnrasl/sly088

  41. [41]

    Price-Whelan, A. M. 2017, The Journal of Open Source Software, 2, 388, doi: 10.21105/joss.00388

  42. [42]

    Rafikov, R. R. 2018, ApJ, 861, 35, doi: 10.3847/1538-4357/aac5ef

  43. [43]

    N., Armitage, P

    Raymond, S. N., Armitage, P. J., Veras, D., Quintana, E. V., & Barclay, T. 2018, MNRAS, 476, 3031, doi: 10.1093/mnras/sty468

  44. [44]

    2014, A&A, 567, A5, doi: 10.1051/0004-6361/201322944

    Recio-Blanco, A., de Laverny, P., Kordopatis, G., et al. 2014, A&A, 567, A5, doi: 10.1051/0004-6361/201322944

  45. [45]

    , keywords =

    Reddy, B. E., Lambert, D. L., & Allende Prieto, C. 2006, MNRAS, 367, 1329, doi: 10.1111/j.1365-2966.2006.10148.x

  46. [46]

    1976, Bulletin of the Astronomical Institutes of Czechoslovakia, 27, 92

    Rickman, H. 1976, Bulletin of the Astronomical Institutes of Czechoslovakia, 27, 92

  47. [47]

    2014, M&PS, 49, 8, doi: 10.1111/maps.12080

    Rickman, H. 2014, M&PS, 49, 8, doi: 10.1111/maps.12080

  48. [48]

    Rickman, H., Fouchard, M., Froeschl´ e, C., & Valsecchi, G. B. 2008, Celestial Mechanics and Dynamical Astronomy, 102, 111, doi: 10.1007/s10569-008-9140-y Sch¨ onrich, R., Binney, J., & Dehnen, W. 2010, MNRAS, 403, 1829, doi: 10.1111/j.1365-2966.2010.16253.x 12

  49. [49]

    Z., Micheli, M., Farnocchia, D., et al

    Seligman, D. Z., Micheli, M., Farnocchia, D., et al. 2025, ApJL, 989, L36, doi: 10.3847/2041-8213/adf49a

  50. [50]

    J., et al

    Steinmetz, M., Guiglion, G., McMillan, P. J., et al. 2020, Astron. J., 160, 83

  51. [51]

    G., & Seligman, D

    Taylor, A. G., & Seligman, D. Z. 2025, arXiv e-prints, arXiv:2507.08111, doi: 10.48550/arXiv.2507.08111

  52. [52]

    2024, MNRAS, 531, 1730, doi: 10.1093/mnras/stae1247

    Tian, H., Liu, C., Li, J., & Zhang, B. 2024, MNRAS, 531, 1730, doi: 10.1093/mnras/stae1247

  53. [53]

    X., Brown, A

    Torres, S., Cai, M. X., Brown, A. G. A., & Zwart, S. P. 2019, Astronomy & Astrophysics, 629, 13, doi: 10.1051/0004-6361/201935330

  54. [54]

    Torres, S., Naoz, S., Li, G., & Rose, S. C. 2023, MNRAS, 524, 1025, doi: 10.1093/mnras/stad1923

  55. [55]

    Toth, G., & Ostriker, J. P. 1992, ApJ, 389, 5, doi: 10.1086/171185

  56. [56]

    Veras, D., & Tout, C. A. 2012, Monthly Notices of the Royal Astronomical Society, 422, 1648, doi: 10.1111/j.1365-2966.2012.20741.x

  57. [57]

    Eldridge, J. J. 2011, Monthly Notices of the Royal Astronomical Society, 417, 2104, doi: 10.1111/j.1365-2966.2011.19393.x

  58. [58]

    2023, Galaxies, 11, doi: 10.3390/galaxies11030077

    Vieira, K., Korchagin, V., Carraro, G., & Lutsenko, A. 2023, Galaxies, 11, doi: 10.3390/galaxies11030077

  59. [59]

    2025, arXiv e-prints, arXiv:2508.04675, doi: 10.48550/arXiv.2508.04675

    Xing, Z., Oset, S., Noonan, J., & Bodewits, D. 2025, arXiv e-prints, arXiv:2508.04675, doi: 10.48550/arXiv.2508.04675

  60. [60]

    2018, ApJL, 852, L13, doi: 10.3847/2041-8213/aaa2f7

    Zhang, Q. 2018, ApJL, 852, L13, doi: 10.3847/2041-8213/aaa2f7

  61. [61]

    Zhang, Y., & Lin, D. N. C. 2020, Nature Astronomy, 4, 852, doi: 10.1038/s41550-020-1065-8

  62. [62]

    , keywords =

    Zhou, Y., Li, X., Huang, Y., & Zhang, H. 2023, ApJ, 946, 73, doi: 10.3847/1538-4357/acadd9