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REVIEW 2 major objections 5 minor 293 references

The Dynamics of Planetary Ejection

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Planetary ejection is a common, near-universal stage of planetary system evolution, and the observed census of free-floating planets is best explained by scattering, binary instabilities, and cluster flybys rather than by in-situ formation.

desk verdict A useful, honest review that consolidates ejection mechanisms and gives observers a comparative table; the central claim is conditional but explicitly flagged. read the letter →

arxiv 2608.00173 v2 pith:BGP3PPUG submitted 2026-07-31 astro-ph.EP astro-ph.SR

Malena Rice , William DeRocco , Sean N. Raymond This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords free-floatingplanetsplanetaryejectionplanet-planetscatteringbinarystarinstabilitiesstellarflybyspost-main-sequenceevolutiongravitationalmicrolensingexoplanetdynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Free-floating planets are common—roughly twenty per star in the completeness-corrected microlensing census—and this review argues that most of the low-mass ones are not born isolated but are planets ejected from their birth systems. It organizes the ejection process into four dynamical channels: planet-planet scattering, instabilities in binary and multi-star systems, flybys in dense stellar environments, and post-main-sequence stellar mass loss. Each channel leaves distinguishable signatures in the masses, velocities, and environments of the ejected planets, and the review's synthesis concludes that scattering, embedded-cluster encounters, and binary instabilities are the likely predominant producers. If that synthesis is right, the present-day planetary census records a history of violence: eccentric giant planets, tightly packed systems, and the rarity of resonant chains are all vestiges of past ejections.

What carries the argument

The carrying structure is a set of quantitative diagnostics, one per ejection channel, that convert a scenario into a testable prediction. The Safronov number $\Theta \equiv v_{\rm esc,p}^2/v_{\rm esc,*}^2$—the square of the ratio of a planet's surface escape velocity to the local escape velocity from its host star—decides whether close encounters end in collision or ejection. The angular momentum deficit (AMD) measures how far a planetary system is from circular, coplanar orbits and sets the threshold for secular chaos and orbit crossings. For binaries, empirical stability boundaries give the outermost stable orbit for a circumstellar planet and the innermost stable orbit for a circumbinary planet, while the mass-loss index $\Psi$ separates adiabatic from impulsive ejection during stellar evolution. Each channel also predicts an excess-velocity distribution, so measured FFP velocities can fingerprint the responsible mechanism.

What would settle it

Imaging the lens fields of a few dozen low-mass microlensing FFP candidates several years after the events, or searching archival precovery images, and finding host stars for a substantial fraction would show that many free-floating planets are actually bound, undercutting the census anchor. Conversely, a velocity sample from parallax measurements that clustered at 8–12 km/s rather than the 2–6 km/s predicted by planet-planet scattering would point to circumbinary or cluster mechanisms as dominant.

Watch

Extended reading notes

Core claim

This paper's central claim is that planetary ejection is not a rare accident but a standard phase of planetary system evolution: wherever planets form, some are later lost. The abstract states it directly, saying that the ubiquity of free-floating planets suggests that planetary ejection is common, and the summary sharpens it: planet-planet scattering, embedded cluster encounters, and binary instabilities are likely predominant in FFP production. The load-bearing evidence is the completeness-corrected microlensing census of roughly 20 free-floating planets per star for masses 0.33–6660 Earth masses, together with the direct-imaging limit that in-situ formation tapers off below about 3–5 Jupiter masses. The paper argues that the four reviewed mechanisms can account for all candidate FFPs, while acknowledging that some apparent FFPs may be wide-orbit bound planets rather than truly unbound ones.

Load-bearing premise

The load-bearing premise is that most microlensing free-floating planet candidates are truly unbound, so the inferred twenty per star is a real ejection count rather than a count of planets still orbiting faint host stars on very wide orbits.

Editorial extensions

If this is right

  • If the completeness-corrected census is real, the ejected mass budget of about 80 Earth masses per star implies that protoplanetary disks must be heavier than the classic minimum-mass nebula, or the observed FFPs cannot all be explained by core accretion.
  • Present-day giant-planet systems should carry vestiges of past ejection: high eccentricities, packed spacings near the stability limit, and a dearth of mean-motion resonances.
  • Upcoming microlensing surveys are projected to find hundreds of FFPs, and parallax-measured velocities could separate ejection channels by their typical speeds.
  • Directly imaged super-Jovian FFPs in star-forming regions are consistent with in-situ collapse, while low-mass microlensing FFPs are not, making the low-mass objects the crucial test bed for ejection models.
  • A fraction of apparent FFPs may be wide-orbit bound planets, so host-star follow-up of microlensing events will decide how much of the census is truly unbound.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The velocity-prediction table acts as a ready-made classification scheme: if Roman-era parallaxes yield a bimodal FFP velocity distribution, the peaks can be mapped directly onto ejection mechanisms—a test the paper describes but does not itself run.
  • The review's relative rates assume planets form in unstable regions such as circumbinary zones and wide binary orbits; if future disk surveys show that planet formation avoids these zones, the binary and tidal channels would shrink dramatically.
  • The same machinery applied to moons and planetesimals suggests that interstellar objects should share the velocity fingerprints of FFPs, so a joint census of interstellar objects and FFPs could test the universality of the ejection picture.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This review synthesizes the dynamical mechanisms by which planets can be liberated from their host stars, organized into four channels: planet-planet scattering (Section 2), instabilities in binary and multi-star systems (Section 3), stellar and substellar flybys (Section 4), and post-main-sequence stellar evolution (Section 5). The paper develops the relevant analytic tools (Safronov number, angular momentum deficit, variable-mass two-body equations, impulse approximation), surveys the solar-system and extrasolar evidence for each channel, and compiles a comparative table (Table 1) listing the percentage of stars susceptible to each mechanism, the associated ejection efficiencies, the typical ejected planet masses, and predicted excess velocities. The central claims are that planetary ejection is common, that the four mechanisms can account for the completeness-corrected microlensing census of roughly 20 free-floating planets per star (Sumi et al. 2023, Eq. 14), and that planet-planet scattering, embedded-cluster encounters, and binary instabilities are likely the predominant FFP production channels. Section 6.1 transparently lists the assumptions behind Table 1 and explicitly acknowledges that apparent microlensing FFPs may include wide-orbit bound planets; however, the Abstract and Section 7 state the conclusions without carrying that conditionality through.

Significance. If the central claim holds, this is a valuable consolidation of a dispersed literature: it unifies four research communities around common quantitative diagnostics (velocity distributions, mass-function features, environmental signatures), updates the earlier Safronov-number analysis with the current exoplanet census (Figures 3 and 4), and offers falsifiable forecasts, including velocity peaks near 2 to 3 km/s for scattering, 8 to 12 km/s for circumbinary and globular-cluster channels, a predicted mass-function trough near 0.8 Earth masses, and a roughly factor-of-ten expansion of the FFP sample with Roman. The analytic kernels (Eqs. 6 to 9, 10, 25 to 30, and 36) are standard and correctly stated; I verified that the stated integral of Eq. (14) over 0.3 to 13 Jupiter masses indeed gives about 0.09 FFPs per star and that the 14.2 AU accretion-limit example from Eq. (7) checks out. The synthesis is not circular: the cited population-level results, including several co-authored by the present authors, are independent N-body simulations with stated initial conditions rather than free parameters fitted here, and the paper does not invent new entities.

major comments (2)
  1. [Section 6.1 / Table 1] The text states that the piecewise power-law IMF of Kroupa (2001) yields 63%, 29%, and 8% of stars in the mass bins 0.075-0.225, 0.225-0.675, and >0.675 solar masses, respectively, and these fractions feed the derived '9% of stars' (p-type) and '10% of stars' (s-type) binary-instability susceptibilities listed in Table 1. Direct integration of the standard Kroupa slopes (alpha = 1.3 for 0.08-0.5 solar masses and alpha = 2.3 above 0.5 solar masses), normalized over 0.075-120 solar masses, gives approximately 50/35/16 for these same bins, and I could not reproduce the quoted 63/29/8 regardless of whether the substellar (0.01-0.075 solar masses) regime is included. Please recompute the star-count fractions from the cited IMF and state the normalization convention and mass range explicitly, or cite the source from which the 63/29/8 values were taken; the affected Table 1 entries should then be regenerated.
  2. [Section 6.1; Abstract; Section 7] Section 6.1 transparently acknowledges that 'apparent FFPs observed through microlensing are not necessarily unbound' and cites Hadden and Wu (2025) predicting that roughly half of Neptune-mass apparent FFPs may reside on wide bound orbits, yet this ambiguity is not propagated to the load-bearing inference: the Abstract and the first bullet of Section 7 assert that the low-mass FFP census 'implies a high rate of planetary ejection' without the condition, and the cross-check in Section 2.4.1 (roughly one giant planet ejected per instability) together with the 'can account for all candidate FFPs' statement in Section 6.1 treat the Sumi et al. (2023) normalization of Eq. (14) as an unbound census. Because the required ejection efficiency scales linearly with the assumed unbound fraction, I recommend adding a one-sentence sensitivity analysis (for example, noting that a 50% bound-orbit fraction halves the required efficiency while leaving the qualitative ranking intact) and inserting the conditionality into the Abstract or Section 7 where the central claim is stated.
minor comments (5)
  1. [Section 5.4] In the sentence 'for e0 = 0 and the limiting case cos f0 -> 0, more than half of the stellar mass must be lost instantaneously to eject a planet,' the qualifier 'cos f0 -> 0' is unnecessary and potentially confusing: for e0 = 0, Equation 36 reduces to beta < 1/2 for every value of f0, so the limiting-case phrase should be removed or reworded.
  2. [Table 1 / Section 6.1] The '% stars' entries for evolved open clusters (10%), globular clusters (0.5%), AGB-phase evolution (5%), and Type II supernovae (0.1-1%) are not derived anywhere in Section 6.1, which supplies stated assumptions only for the binary and cluster-encounter rows; please add a sentence or footnote tracing each of these percentages to its source or to an explicitly stated stellar-population model.
  3. [References] P. Mroz, A. Udalski, J. Skowron, et al. (2017, Nature 548, 183) appears twice as an identical entry in the reference list; please deduplicate, and verify that the in-text citations in Sections 1 and 6.2 refer to the same paper or, if not, disambiguate them with distinct years or identifiers.
  4. [Section 6.2] The sentence 'Roughly a dozen microlensing FFP candidates have been reported to date that are attributed to low-mass (super-Earth-mass or below) planets' is followed by a list of fourteen citations; please reconcile the 'roughly a dozen' count with the length of the list, or clarify which of the cited events are considered low-mass candidates.
  5. [Section 1] The phrase 'at of order ≈20 FFPs' in the first section combines 'of order' with 'approximately' and reads awkwardly; consider revising to 'of order 20 FFPs' or 'approximately 20 FFPs'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the synthesis rests on external microlensing data and independent N-body simulations, with self-citations that are not load-bearing.

full rationale

This paper is a review and synthesis rather than a derivation-from-principles paper. The load-bearing empirical anchor is the completeness-corrected microlensing FFP census of Sumi et al. (2023), which is external to the authors; the mechanism-by-mechanism yields cited for Table 1 are published N-body simulations with stated initial conditions (Holman & Wiegert 1999; Kaib et al. 2013; Coleman & DeRocco 2025; etc.), not parameters fitted here. The paper's own calculation in Section 2.4.1 (Eqs. 13-14) is a consistency check: it asks what ejection yield would be needed to match the observed FFP mass function, rather than 'predicting' that yield from a fitted input. The explicitly acknowledged ambiguities (Section 6.1: 'apparent FFPs observed through microlensing are not necessarily unbound' and direct collapse as an in-situ alternative) are empirical caveats, not circular reductions. Self-citations to works co-authored by Raymond and DeRocco are frequent, but they are real, independently testable simulation results and standard analytic formulas; under the review rules these do not raise the circularity score. No equation in the paper is equivalent to its own input by construction, no fitted parameter is renamed as a prediction, and no uniqueness claim is imported from the authors' prior work. Score 1 reflects the presence of self-citations while affirming that none are load-bearing.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new free parameters or invented entities. It adopts several domain assumptions from the literature, the most important being the completeness-corrected FFP census and the occurrence of planet formation in unstable regions; both are explicitly flagged as uncertain in the text.

assumptions (4)
  • domain assumption The Sumi et al. (2023) microlensing FFP mass function is correct and represents truly unbound planets.
    Load-bearing for the conclusion that ejection is common; the paper itself flags the bound-vs-unbound ambiguity in Section 6.1.
  • domain assumption Planets form and migrate into the unstable regions of parameter space at rates sufficient to populate them.
    Raised in Section 3.4 ('Do planets form or arrive in unstable regions in the first place?'); the paper treats it as an open question.
  • standard math The isotropic variable-mass two-body equations (Eqs. 26-30) are valid for the mass-loss regimes considered.
    Taken from Omarov (1962), Hadjidemetriou (1963), and Veras et al. (2011); the paper notes anisotropic corrections scale as sqrt(a) but does not include them.
  • domain assumption Cited numerical simulation results for ejection rates and velocities (e.g., Holman & Wiegert 1999; Kaib et al. 2013; Coleman & DeRocco 2025) are reliable.
    The review's synthesis inherits the correctness of its cited simulations, which are not reproduced here.

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Cite this review

Pith. "Pith review of The Dynamics of Planetary Ejection." pith.science (2026). https://pith.science/paper/BGP3PPUG

@misc{pith2026260800173,
  author       = {Pith},
  title        = {Pith review of: The Dynamics of Planetary Ejection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BGP3PPUG}},
  note         = {Machine review of arXiv:2608.00173}
}
read the original abstract

The ubiquity of free-floating planets inferred from microlensing and direct imaging surveys suggests that planetary ejection---a process in which planets initially born encircling a stellar host become gravitationally unbound---is common. Four overarching mechanisms have been proposed to induce planetary ejection: close approaches of neighboring planets, instabilities in binary or multi-star systems, stellar and planetary flybys, and post-main-sequence stellar evolution. Here we review the mechanisms underlying planetary ejection, as well as predictions derived from each. Current and upcoming microlensing surveys offer the potential to test existing models and distinguish between potential planetary ejection mechanisms, offering further insight into the demographic-level architectures of exoplanets across stellar environments.

Figures

Figures reproduced from arXiv: 2608.00173 by the authors.

Figure 1
Figure 1. Schematic overview of instability-inducing mechanisms through which planets may be ejected from a system. These mechanisms, each discussed throughout this work, include close approaches between neighboring planets (top left; Section 2), binary-induced instabilities (top center and right, and bottom left; Section 3), flyby encounters (bottom center; Section 4), and post-main-sequence orbital evolution (bottom right; … view at source ↗
Figure 2
Figure 2. Schematic depiction of the grazing-encounter sce￾nario considered in Section 2.1.1, through which the Safronov number, which is used to determine the likelihood of colli￾sions vs. ejections as the outcome of close encounters, is de￾rived. Here x is an initially large distance from which mass m, at initial velocity vi, approaches a planet with mass Mp and Rp with impact parameter b. The final velocity vf of mass m is… view at source ↗
Figure 3
Figure 3. Maximum Safronov number of known, bound planets shown as a function of semimajor axis (left) and eccentricity (right), as a scatter plot (bottom) and histogram (top). The histograms are each normalized to peak at 1 for a clearer comparison between samples. Only planets with measured, nonzero uncertainties in orbital eccentricity are included. Though these planets remain bound to their host systems, the elevated ecce… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Theoretical, piecewise mass-radius scalings across planetary mass regimes, alongside associated scalings of the Safronov number. The census of observed exoplanets with masses and radii (including uncertainties) reported in the NASA Exoplanet Archive PSCompPars table as…
Figure 5
Figure 5. Figure 5: Example thresholds for s−type and p−type bi￾nary instabilities for stellar binary mass ratio µb = 0.3, dis￾played as a function of the binary eccentricity and the ra￾tio between the planet and binary semimajor axis. Bound￾aries are drawn directly from M. J. Holman & P.…
Figure 6
Figure 6. Figure 6: Flyby rates Γ as a function of stellar density and velocity dispersion. Representative values for example stellar environments are shown alongside a reference line tracing the threshold for one flyby encounter per Gyr. Here we adopt the cross-section for flyby interact…
Figure 7
Figure 7. Figure 7: Planetary ejection regimes in the impulse approximation during a supernova explosion, shown for β = 0.8, 0.5, and 0.3 where β = µf /µi is the fractional stellar mass that remains after near-instantaneous mass loss. Here e0 and f0 are the initial orbital eccentricity an…
Figure 8
Figure 8. Figure 8: Log-normal binary separation distributions adopted from S. S. R. Offner et al. (2023) and derived from data drawn from D. Raghavan et al. (2010). The adopted limiting regimes for three categories of binary-driven instabilities are shown as the shaded background regions…

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Works this paper leans on

293 extracted references · 16 linked inside Pith

  1. [1]

    C., Hollenbach, D., Laughlin, G., & Gorti, U

    Adams, F. C., Hollenbach, D., Laughlin, G., & Gorti, U. 2004, ApJ, 611, 360, doi: 10.1086/421989

    doi:10.1086/421989 2004

  2. [2]

    C., & Laughlin, G

    Adams, F. C., & Laughlin, G. 2001, Icarus, 150, 151, doi: 10.1006/icar.2000.6567

    arXiv 2001

  3. [3]

    C., & Laughlin, G

    Adams, F. C., & Laughlin, G. 2003, Icarus, 163, 290, doi: 10.1016/S0019-1035(03)00081-2

    doi:10.1016/s0019-1035(03)00081-2 2003

  4. [4]

    C., Proszkow, E

    Adams, F. C., Proszkow, E. M., Fatuzzo, M., & Myers, P. C. 2006, ApJ, 641, 504, doi: 10.1086/500393

    doi:10.1086/500393 2006

  5. [5]

    2019, arXiv e-prints, arXiv:1902.05569, doi: 10.48550/arXiv.1902.05569

    Akeson, R., Armus, L., Bachelet, E., et al. 2019, arXiv e-prints, arXiv:1902.05569, doi: 10.48550/arXiv.1902.05569

    arXiv doi:10.48550/arxiv.1902.05569 2019

  6. [6]

    A., Zuluaga, J

    Alvarado-Montes, J. A., Zuluaga, J. I., & Sucerquia, M. 2017, MNRAS, 471, 3019, doi: 10.1093/mnras/stx1745

    doi:10.1093/mnras/stx1745 2017

  7. [7]

    2017, arXiv e-prints, arXiv:1702.00786, doi: 10.48550/arXiv.1702.00786

    Amaro-Seoane, P., Audley, H., Babak, S., et al. 2017, arXiv e-prints, arXiv:1702.00786, doi: 10.48550/arXiv.1702.00786

    arXiv doi:10.48550/arxiv.1702.00786 2017

  8. [8]

    M., Huang, J., P´ erez, L

    Andrews, S. M., Huang, J., P´ erez, L. M., et al. 2018, ApJL, 869, L41

    2018

Show all 293 references
  1. [9]

    Armitage, P. J. 2000, A&A, 362, 968, doi: 10.48550/arXiv.astro-ph/0007044

    2000 doi arXiv

  2. [10]

    A., & Thorsett, S

    Arzoumanian, Z., Joshi, K., Rasio, F. A., & Thorsett, S. E. 1996, in Astronomical Society of the Pacific Conference

    1996

  3. [11]

    105, IAU Colloquium 160: Pulsars: Problems and Progress, ed

    Series, Vol. 105, IAU Colloquium 160: Pulsars: Problems and Progress, ed. S. Johnston, M. A. Walker, & M. Bailes, 525–530, doi: 10.48550/arXiv.astro-ph/9605141 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/2013220...

    doi arXiv

  4. [12]

    Bailer-Jones, C. A. L., Farnocchia, D., Meech, K. J., et al. 2018, AJ, 156, 205, doi: 10.3847/1538-3881/aae3eb

    2018 doi

  5. [13]

    Bailer-Jones, C. A. L., Farnocchia, D., Ye, Q., Meech, K. J., & Micheli, M. 2020, A&A, 634, A14, doi: 10.1051/0004-6361/201937231

    2020 doi

  6. [14]

    2019, AJ, 158, 94, doi: 10.3847/1538-3881/ab2d2a

    Bailey, N., & Fabrycky, D. 2019, AJ, 158, 94, doi: 10.3847/1538-3881/ab2d2a

    2019 doi

  7. [15]

    2014, ApJL, 780, L4, doi: 10.1088/2041-8205/780/1/L4

    Bailey, V., Meshkat, T., Reiter, M., et al. 2014, ApJL, 780, L4, doi: 10.1088/2041-8205/780/1/L4

    2014 doi

  8. [16]

    V., Raymond, S

    Barclay, T., Quintana, E. V., Raymond, S. N., & Penny, M. T. 2017, ApJ, 841, 86, doi: 10.3847/1538-4357/aa705b

    2017 doi

  9. [17]

    2004, ApJ, 611, 494, doi: 10.1086/421321

    Barnes, R., & Quinn, T. 2004, ApJ, 611, 494, doi: 10.1086/421321

    2004 doi

  10. [18]

    Barnes, R., & Raymond, S. N. 2004, ApJ, 617, 569, doi: 10.1086/423419

    2004 doi

  11. [19]

    2019, AJ, 158, 187, doi: 10.3847/1538-3881/ab4130

    Baron, F., Lafreni` ere, D., Artigau,´E., et al. 2019, AJ, 158, 187, doi: 10.3847/1538-3881/ab4130

    2019 doi

  12. [20]

    2021, MNRAS, 506, 6181, doi: 10.1093/mnras/stab1465

    Urrutxua, H. 2021, MNRAS, 506, 6181, doi: 10.1093/mnras/stab1465

    2021 doi

  13. [21]

    M., Rowe, J

    Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2013, ApJS, 204, 24, doi: 10.1088/0067-0049/204/2/24

    2013 doi

  14. [22]

    Batygin, K., & Brown, M. E. 2010, ApJ, 716, 1323, doi: 10.1088/0004-637X/716/2/1323

    2010 doi

  15. [23]

    E., & Betts, H

    Batygin, K., Brown, M. E., & Betts, H. 2012, ApJL, 744, L3, doi: 10.1088/2041-8205/744/1/L3

    2012 doi

  16. [24]

    1988a, Celestial Mechanics, 43, 47, doi: 10.1007/BF01234553

    Benest, D. 1988a, Celestial Mechanics, 43, 47, doi: 10.1007/BF01234553

    doi

  17. [25]

    1993, Celestial Mechanics and Dynamical Astronomy, 56, 45, doi: 10.1007/BF00699718

    Benest, D. 1993, Celestial Mechanics and Dynamical Astronomy, 56, 45, doi: 10.1007/BF00699718

    1993 doi

  18. [26]

    G., & Perets, H

    Bhaskar, H. G., & Perets, H. B. 2025, The Astrophysical Journal, 991, 132, doi: 10.3847/1538-4357/adf4e2

    2025 doi

  19. [27]

    Black, D. C. 1982, AJ, 87, 1333, doi: 10.1086/113220

    1982 doi

  20. [28]

    J., Kenworthy, M

    Bohn, A. J., Kenworthy, M. A., Ginski, C., et al. 2020, ApJL, 898, L16, doi: 10.3847/2041-8213/aba27e

    2020 doi

  21. [29]

    J., Ginski, C., Kenworthy, M

    Bohn, A. J., Ginski, C., Kenworthy, M. A., et al. 2021, A&A, 648, A73, doi: 10.1051/0004-6361/202140508

    2021 doi

  22. [30]

    C., Payne, M

    Boley, A. C., Payne, M. J., & Ford, E. B. 2012, ApJ, 754, 57, doi: 10.1088/0004-637X/754/1/57

    2012 doi

  23. [31]

    M., Christiansen, J

    Boley, K. M., Christiansen, J. L., Zink, J., et al. 2024, AJ, 168, 128, doi: 10.3847/1538-3881/ad6570

    2024 doi

  24. [32]

    T., Belyakov, M., Fremling, C., et al

    Bolin, B. T., Belyakov, M., Fremling, C., et al. 2025, MNRAS, 542, L139, doi: 10.1093/mnrasl/slaf078

    2025 doi

  25. [33]

    V., & Mordasini, C

    Bolmont, E., Galantay, E., Blanco-Cuaresma, S., Oza, A. V., & Mordasini, C. 2025, A&A, 704, A9, doi: 10.1051/0004-6361/202554625

    2025 doi

  26. [35]

    S., H´ ebrard, G., Raymond, S

    Bonomo, A. S., H´ ebrard, G., Raymond, S. N., et al. 2017, A&A, 603, A43, doi: 10.1051/0004-6361/201730624

    2017 doi

  27. [36]

    T., Sato, H., et al

    Borisov, G., Durig, D. T., Sato, H., et al. 2019, Comet C/2019 Q4 (Borisov),, Central Bureau Electronic

    2019

  28. [37]

    J., Koch, D., Basri, G., et al

    Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977

    2010

  29. [38]

    J., Koch, D

    Borucki, W. J., Koch, D. G., Basri, G., et al. 2011, ApJ, 736, 19, doi: 10.1088/0004-637X/736/1/19

    2011 doi

  30. [39]

    2026, A&A, 708, A218, doi: 10.1051/0004-6361/202555031

    Bouy, H., Duchˆ ene, G., Strampelli, G., et al. 2026, A&A, 708, A218, doi: 10.1051/0004-6361/202555031

    2026 doi

  31. [40]

    Bowler, B. P. 2016, PASP, 128, 102001, doi: 10.1088/1538-3873/128/968/102001

    2016 doi

  32. [41]

    Brasil, P. I. O., Roig, F., Nesvorn´ y, D., et al. 2016, Icarus, 266, 142, doi: 10.1016/j.icarus.2015.11.015

    2016 doi

  33. [42]

    P., & Strader, J

    Brodie, J. P., & Strader, J. 2006, ARA&A, 44, 193, doi: 10.1146/annurev.astro.44.051905.092441

    2006

  34. [43]

    2025, The Open Journal of Astrophysics, 8, E161, doi: 10.33232/001c.146688

    Brown, G., Malhotra, R., & Rein, H. 2025, The Open Journal of Astrophysics, 8, E161, doi: 10.33232/001c.146688

    2025 doi

  35. [44]

    2022, MNRAS, 515, 5942, doi: 10.1093/mnras/stac1763

    Brown, G., & Rein, H. 2022, MNRAS, 515, 5942, doi: 10.1093/mnras/stac1763

    2022 doi

  36. [45]

    2014, A&A, 561, L9, doi: 10.1051/0004-6361/201322584

    Brucalassi, A., Pasquini, L., Saglia, R., et al. 2014, A&A, 561, L9, doi: 10.1051/0004-6361/201322584

    2014 doi

  37. [46]

    2018, A&A, 619, A91, doi: 10.1051/0004-6361/201833097

    Busetti, F., Beust, H., & Harley, C. 2018, A&A, 619, A91, doi: 10.1051/0004-6361/201833097

    2018 doi

  38. [47]

    X., Kouwenhoven, M

    Cai, M. X., Kouwenhoven, M. B. N., Portegies Zwart, S. F., & Spurzem, R. 2017, MNRAS, 470, 4337, doi: 10.1093/mnras/stx1464

    2017 doi

  39. [48]

    X., Portegies Zwart, S., & van Elteren, A

    Cai, M. X., Portegies Zwart, S., & van Elteren, A. 2018, MNRAS, 474, 5114, doi: 10.1093/mnras/stx3064 ´Calovi´ c, A., Nayakshin, S., Casewell, S., & Miret-Roig, N. 2026, MNRAS, 545, staf2097, doi: 10.1093/mnras/staf2097

    2018 doi

  40. [49]

    N., & Davies, M

    Carrera, D., Raymond, S. N., & Davies, M. B. 2019, A&A, 629, L7, doi: 10.1051/0004-6361/201935744

    2019 doi

  41. [50]

    Chambers, J. E. 2001, Icarus, 152, 205, doi: 10.1006/icar.2001.6639

    2001

  42. [51]

    E., Wetherill, G

    Chambers, J. E., Wetherill, G. W., & Boss, A. P. 1996, Icarus, 119, 261, doi: 10.1006/icar.1996.0019

    1996

  43. [52]

    B., Geller, A

    Chatterjee, S., Ford, E. B., Geller, A. M., & Rasio, F. A. 2012, MNRAS, 427, 1587, doi: 10.1111/j.1365-2966.2012.22057.x

    2012

  44. [53]

    B., Matsumura, S., & Rasio, F

    Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A. 2008, ApJ, 686, 580

    2008

  45. [54]

    2017, ApJ, 834, 17, doi: 10.3847/1538-4357/834/1/17

    Chen, J., & Kipping, D. 2017, ApJ, 834, 17, doi: 10.3847/1538-4357/834/1/17

    2017 doi

  46. [55]

    2013, MNRAS, 431, 3444, doi: 10.1093/mnras/stt424

    Chiang, E., & Laughlin, G. 2013, MNRAS, 431, 3444, doi: 10.1093/mnras/stt424

    2013 doi

  47. [56]

    Chirikov, B. V. 1979, PhR, 52, 263, doi: 10.1016/0370-1573(79)90023-1

    1979 doi

  48. [57]

    2026, arXiv e-prints, arXiv:2604.05035, doi: 10.48550/arXiv.2604.05035

    Choksi, N., Lithwick, Y., Chiang, E., & Li, R. 2026, arXiv e-prints, arXiv:2604.05035, doi: 10.48550/arXiv.2604.05035

    2026 doi arXiv

  49. [58]

    L., McElroy, D

    Christiansen, J. L., McElroy, D. L., Harbut, M., et al. 2025, PSJ, 6, 186, doi: 10.3847/PSJ/ade3c2

    2025 doi

  50. [59]

    Clanton, C., & Gaudi, B. S. 2014, ApJ, 791, 90, doi: 10.1088/0004-637X/791/2/90

    2014 doi

  51. [60]

    Clanton, C., & Gaudi, B. S. 2016, ApJ, 819, 125, doi: 10.3847/0004-637X/819/2/125

    2016 doi

  52. [61]

    J., & Pringle, J

    Clarke, C. J., & Pringle, J. E. 1993, MNRAS, 261, 190, doi: 10.1093/mnras/261.1.190

    1993 doi

  53. [62]

    S., Deienno, R., Kaib, N

    Clement, M. S., Deienno, R., Kaib, N. A., et al. 2021a, Icarus, 367, 114556, doi: 10.1016/j.icarus.2021.114556

    2021

  54. [63]

    S., Kaib, N

    Clement, M. S., Kaib, N. A., Raymond, S. N., & Walsh, K. J. 2018, Icarus, 311, 340, doi: 10.1016/j.icarus.2018.04.008

    2018 doi

  55. [64]

    S., Raymond, S

    Clement, M. S., Raymond, S. N., Kaib, N. A., et al. 2021b, Icarus, 355, 114122, doi: 10.1016/j.icarus.2020.114122

    2020

  56. [65]

    2015, ApJ, 813, 8, doi: 10.1088/0004-637X/813/1/8

    Cloutier, R., Tamayo, D., & Valencia, D. 2015, ApJ, 813, 8, doi: 10.1088/0004-637X/813/1/8

    2015 doi

  57. [66]

    Coleman, G. A. L. 2024, Monthly Notices of the Royal Astronomical Society, 530, 630, doi: 10.1093/mnras/stae903

    2024 doi

  58. [67]

    Coleman, G. A. L., & DeRocco, W. 2025, Monthly Notices of the Royal Astronomical Society, 537, 2303, doi: 10.1093/mnras/staf138

    2025 doi

  59. [68]

    A., & Gil-Hutton, R

    Correa-Otto, J. A., & Gil-Hutton, R. A. 2017, A&A, 608, A116, doi: 10.1051/0004-6361/201731229 33

    2017 doi

  60. [69]

    Craig, J., & Krumholz, M. R. 2013, ApJ, 769, 150, doi: 10.1088/0004-637X/769/2/150

    2013 doi

  61. [70]

    Cresswell, P., & Nelson, R. P. 2006, A&A, 450, 833, doi: 10.1051/0004-6361:20054551

    2006 doi

  62. [71]

    Cuello, N., M´ enard, F., & Price, D. J. 2023, European Physical Journal Plus, 138, 11, doi: 10.1140/epjp/s13360-022-03602-w

    2023 doi

  63. [72]

    2020, MNRAS, 491, 504, doi: 10.1093/mnras/stz2938 ´Cuk, M

    Cuello, N., Louvet, F., Mentiplay, D., et al. 2020, MNRAS, 491, 504, doi: 10.1093/mnras/stz2938 ´Cuk, M. 2018, ApJ, 852, L15, doi: 10.3847/2041-8213/aaa3db

    2020 doi

  64. [73]

    P., Marcy, G

    Cumming, A., Butler, R. P., Marcy, G. W., et al. 2008, PASP, 120, 531, doi: 10.1086/588487

    2008 doi

  65. [74]

    C., & Parker, R

    Daffern-Powell, E. C., & Parker, R. J. 2022, MNRAS, 517, 2103, doi: 10.1093/mnras/stac2797

    2022 doi

  66. [75]

    2024, AJ, 168, 239, doi: 10.3847/1538-3881/ad83a6

    Dai, F., Goldberg, M., Batygin, K., et al. 2024, AJ, 168, 239, doi: 10.3847/1538-3881/ad83a6

    2024 doi

  67. [76]

    V., Fatuzzo, M., & Adams, F

    David, E.-M., Quintana, E. V., Fatuzzo, M., & Adams, F. C. 2003, PASP, 115, 825, doi: 10.1086/376395

    2003 doi

  68. [77]

    B., Adams, F

    Davies, M. B., Adams, F. C., Armitage, P., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning, 787–808, doi: 10.2458/azu uapress 9780816531240-ch034

    2014 doi

  69. [79]

    H., & Sigurdsson, S

    Debes, J. H., & Sigurdsson, S. 2002, The Astrophysical Journal, 572, 556, doi: 10.1086/340291

    2002 doi

  70. [80]

    H., & Sigurdsson, S

    Debes, J. H., & Sigurdsson, S. 2007, ApJL, 668, L167, doi: 10.1086/523103

    2007 doi

  71. [81]

    S., & Nesvorn´ y, D

    Deienno, R., Morbidelli, A., Gomes, R. S., & Nesvorn´ y, D. 2017, AJ, 153, 153, doi: 10.3847/1538-3881/aa5eaa

    2017 doi

  72. [82]

    2014, AJ, 148, 25, doi: 10.1088/0004-6256/148/2/25

    Deienno, R., Nesvorn´ y, D., Vokrouhlick´ y, D., & Yokoyama, T. 2014, AJ, 148, 25, doi: 10.1088/0004-6256/148/2/25

    2014 doi

  73. [83]

    2025, Minor Planet Electronic Circulars, 2025-N12, doi: 10.48377/MPEC/2025-N12

    Denneau, L., Siverd, R., Tonry, J., et al. 2025, Minor Planet Electronic Circulars, 2025-N12, doi: 10.48377/MPEC/2025-N12

    2025 doi

  74. [84]

    1983, Celestial Mechanics, 31, 1, doi: 10.1007/BF01272557

    Deprit, A. 1983, Celestial Mechanics, 31, 1, doi: 10.1007/BF01272557

    1983 doi

  75. [85]

    2026, AJ, 172, 7, doi: 10.3847/1538-3881/ae6e36

    McGill, P. 2026, AJ, 172, 7, doi: 10.3847/1538-3881/ae6e36

    2026 doi

  76. [86]

    L., & Parker, R

    Diamond, J. L., & Parker, R. J. 2024, ApJ, 975, 204, doi: 10.3847/1538-4357/ad8644

    2024 doi

  77. [87]

    A., & Tonry, J

    Do, A., Tucker, M. A., & Tonry, J. 2018, ApJL, 855, L10

    2018

  78. [88]

    Dobos, V., Charnoz, S., P´ al, A., Roque-Bernard, A., & Szab´ o, G. M. 2021, PASP, 133, 094401, doi: 10.1088/1538-3873/abfe04

    2021 doi

  79. [89]

    2026, arXiv e-prints, arXiv:2603.22426, doi: 10.48550/arXiv.2603.22426

    Gupta, A. 2026, arXiv e-prints, arXiv:2603.22426, doi: 10.48550/arXiv.2603.22426

    2026 doi

  80. [91]

    2026b, Science, 391, 96, doi: 10.1126/science.adv9266

    Dong, S., Wu, Z., Ryu, Y.-H., et al. 2026b, Science, 391, 96, doi: 10.1126/science.adv9266

    doi

  81. [93]

    R., Carter, J

    Doyle, L. R., Carter, J. A., Fabrycky, D. C., et al. 2011, Science, 333, 1602, doi: 10.1126/science.1210923

    2011 doi

  82. [94]

    2018, Nature Astronomy, 2, 407, doi: 10.1038/s41550-018-0440-1 Duchˆ ene, G., & Kraus, A

    Drahus, M., Guzik, P., Waniak, W., et al. 2018, Nature Astronomy, 2, 407, doi: 10.1038/s41550-018-0440-1 Duchˆ ene, G., & Kraus, A. 2013, ARA&A, 51, 269, doi: 10.1146/annurev-astro-081710-102602

    2018 doi

  83. [95]

    J., & Lissauer, J

    Duncan, M. J., & Lissauer, J. J. 1998, Icarus, 134, 303, doi: 10.1006/icar.1998.5962

    1998

  84. [96]

    1991, A&A, 248, 485

    Duquennoy, A., & Mayor, M. 1991, A&A, 248, 485

    1991

  85. [97]

    1984, Celestial Mechanics, 34, 369, doi: 10.1007/BF01235815

    Dvorak, R. 1984, Celestial Mechanics, 34, 369, doi: 10.1007/BF01235815

    1984 doi

  86. [98]

    1986, A&A, 167, 379

    Dvorak, R. 1986, A&A, 167, 379

    1986

  87. [99]

    1989, A&A, 226, 335 Dybczy´ nski, P

    Dvorak, R., Froeschle, C., & Froeschle, C. 1989, A&A, 226, 335 Dybczy´ nski, P. A., & Kr´ olikowska, M. 2018, A&A, 610, L11, doi: 10.1051/0004-6361/201732309

    1989 doi

  88. [100]

    2018, MNRAS, 480, 4884, doi: 10.1093/mnras/sty2186

    El-Badry, K., & Rix, H.-W. 2018, MNRAS, 480, 4884, doi: 10.1093/mnras/sty2186

    2018 doi

  89. [101]

    2019, MNRAS, 489, 5822, doi: 10.1093/mnras/stz2480

    El-Badry, K., Rix, H.-W., Tian, H., Duchˆ ene, G., & Moe, M. 2019, MNRAS, 489, 5822, doi: 10.1093/mnras/stz2480

    2019 doi

  90. [102]

    A., & Kaib, N

    Ellithorpe, E. A., & Kaib, N. A. 2022, MNRAS, 515, 2914, doi: 10.1093/mnras/stac1973

    2022 doi

  91. [103]

    2026, arXiv e-prints, arXiv:2603.22409, doi: 10.48550/arXiv.2603.22409

    Esposito, J., Li, G., & Wang, S. 2026, arXiv e-prints, arXiv:2603.22409, doi: 10.48550/arXiv.2603.22409

    2026 doi

  92. [104]

    Faber, P., & Quillen, A. C. 2007, MNRAS, 382, 1823, doi: 10.1111/j.1365-2966.2007.12490.x

    2007

  93. [105]

    C., Lissauer, J

    Fabrycky, D. C., Lissauer, J. J., Ragozzine, D., et al. 2014, ApJ, 790, 146

    2014

  94. [106]

    2013, ApJ, 767, 115, doi: 10.1088/0004-637X/767/2/115

    Fang, J., & Margot, J.-L. 2013, ApJ, 767, 115, doi: 10.1088/0004-637X/767/2/115

    2013 doi

  95. [108]

    Williams, K. A. 2003, ApJL, 595, L53, doi: 10.1086/379005

    2003 doi

  96. [109]

    Feng, F., & Jones, H. R. A. 2018, ApJL, 852, L27, doi: 10.3847/2041-8213/aaa404 34

    2018 doi

  97. [110]

    B., Mulders, G

    Fernandes, R. B., Mulders, G. D., Pascucci, I., Mordasini, C., & Emsenhuber, A. 2019, ApJ, 874, 81, doi: 10.3847/1538-4357/ab0300

    2019 doi

  98. [111]

    A., & Ip, W.-H

    Fernandez, J. A., & Ip, W.-H. 1984, Icarus, 58, 109, doi: 10.1016/0019-1035(84)90101-5

    1984 doi

  99. [112]

    A., & Valenti, J

    Fischer, D. A., & Valenti, J. 2005, ApJ, 622, 1102 Flammini Dotti, F., Kouwenhoven, M. B. N., Berczik, P.,

    2005

  100. [113]

    2025, A&A, 693, A166, doi: 10.1051/0004-6361/202452441 Flammini Dotti, F., Kouwenhoven, M

    Shu, Q., & Spurzem, R. 2025, A&A, 693, A166, doi: 10.1051/0004-6361/202452441 Flammini Dotti, F., Kouwenhoven, M. B. N., Wu, K., et al. 2026, A&A, 706, A219, doi: 10.1051/0004-6361/202557334

    2025 doi

  101. [114]

    Ford, E. B. 2014, Proceedings of the National Academy of Science, 111, 12616, doi: 10.1073/pnas.1304219111

    2014 doi

  102. [115]

    B., & Chiang, E

    Ford, E. B., & Chiang, E. I. 2007, The Astrophysical Journal, 661, 602, doi: 10.1086/513598

    2007 doi

  103. [116]

    B., Lystad, V., & Rasio, F

    Ford, E. B., Lystad, V., & Rasio, F. A. 2005, Nature, 434, 873, doi: 10.1038/nature03427

    2005 doi

  104. [117]

    B., & Rasio, F

    Ford, E. B., & Rasio, F. A. 2008, ApJ, 686, 621, doi: 10.1086/590926

    2008 doi

  105. [118]

    J., & Rice, K

    Forgan, D., Parker, R. J., & Rice, K. 2015, MNRAS, 447, 836, doi: 10.1093/mnras/stu2504

    2015 doi

  106. [120]

    H., Hall, C., Meru, F., & Rice, W

    Forgan, D. H., Hall, C., Meru, F., & Rice, W. K. M. 2018, MNRAS, 474, 5036, doi: 10.1093/mnras/stx2870

    2018 doi

  107. [121]

    M., & Nelson, R

    Fragner, M. M., & Nelson, R. P. 2009, A&A, 505, 873, doi: 10.1051/0004-6361/200912292 Froeschl´ e, C., Gonczi, R., & Lega, E. 1997, Planet. Space Sci., 45, 881, doi: 10.1016/S0032-0633(97)00058-5

    2009 doi

  108. [122]

    S., & Hori, Y

    Fujii, M. S., & Hori, Y. 2019, Astronomy & Astrophysics, 624, A110, doi: 10.1051/0004-6361/201834677

    2019 doi

  109. [123]

    J., Rosenthal, L

    Fulton, B. J., Rosenthal, L. J., Hirsch, L. A., et al. 2021, ApJS, 255, 14

    2021

  110. [124]

    2010, A&A, 516, A82, doi: 10.1051/0004-6361/200912698 Gagn´ e, J., Faherty, J

    Eggl, S. 2010, A&A, 516, A82, doi: 10.1051/0004-6361/200912698 Gagn´ e, J., Faherty, J. K., Mamajek, E. E., et al. 2017, ApJS, 228, 18, doi: 10.3847/1538-4365/228/2/18

    2010 doi

  111. [125]

    Gavino, S., & Lissauer, J. J. 2026, A&A, 710, A119, doi: 10.1051/0004-6361/202557642

    2026 doi

  112. [126]

    2022, arXiv e-prints, arXiv:2206.06693, doi: 10.48550/arXiv.2206.06693

    Ge, J., Zhang, H., Zang, W., et al. 2022, arXiv e-prints, arXiv:2206.06693, doi: 10.48550/arXiv.2206.06693

    2022 doi

  113. [127]

    2020, ApJ, 896, 80, doi: 10.3847/1538-4357/ab911a

    Gennaro, M., & Robberto, M. 2020, ApJ, 896, 80, doi: 10.3847/1538-4357/ab911a

    2020 doi

  114. [128]

    2024, AJ, 168, 224, doi: 10.3847/1538-3881/ad7a78

    Georgakarakos, N., Eggl, S., Ali-Dib, M., & Dobbs-Dixon, I. 2024, AJ, 168, 224, doi: 10.3847/1538-3881/ad7a78

    2024 doi

  115. [129]

    L., Brown, T

    Gilliland, R. L., Brown, T. M., Guhathakurta, P., et al. 2000, ApJL, 545, L47, doi: 10.1086/317334

    2000 doi

  116. [130]

    M., Brasseur, C., et al

    Ginsburg, A., Sip˝ ocz, B. M., Brasseur, C., et al. 2019, AJ, 157, 98

    2019

  117. [131]

    1993, Icarus, 106, 247, doi: 10.1006/icar.1993.1169

    Gladman, B. 1993, Icarus, 106, 247, doi: 10.1006/icar.1993.1169

    1993

  118. [132]

    2002, Icarus, 157, 269, doi: 10.1006/icar.2002.6860

    Gladman, B., Holman, M., Grav, T., et al. 2002, Icarus, 157, 269, doi: 10.1006/icar.2002.6860

    2002

  119. [133]

    2004a, ARA&A, 42, 549, doi: 10.1146/annurev.astro.42.053102.134004

    Goldreich, P., Lithwick, Y., & Sari, R. 2004a, ARA&A, 42, 549, doi: 10.1146/annurev.astro.42.053102.134004

  120. [134]

    2004b, ApJ, 614, 497, doi: 10.1086/423612

    Goldreich, P., Lithwick, Y., & Sari, R. 2004b, ApJ, 614, 497, doi: 10.1086/423612

    doi

  121. [135]

    F., Tsiganis, K., & Morbidelli, A

    Gomes, R., Levison, H. F., Tsiganis, K., & Morbidelli, A. 2005, Nature, 435, 466, doi: 10.1038/nature03676

    2005 doi

  122. [136]

    2013, ApJL, 769, L14, doi: 10.1088/2041-8205/769/1/L14

    Gong, Y.-X., Zhou, J.-L., Xie, J.-W., & Wu, X.-M. 2013, ApJL, 769, L14, doi: 10.1088/2041-8205/769/1/L14

    2013 doi

  123. [137]

    K., Hwang, K.-H., et al

    Gould, A., Jung, Y. K., Hwang, K.-H., et al. 2022, Journal of Korean Astronomical Society, 55, 173, doi: 10.5303/JKAS.2022.55.5.173

    2022 doi

  124. [138]

    Grishin, E., Winter, J., & Alvarado-Montes, J. A. 2025, arXiv e-prints, arXiv:2512.13773, doi: 10.48550/arXiv.2512.13773

    2025 doi

  125. [139]

    2024, A&A, 688, A202, doi: 10.1051/0004-6361/202450340

    Morbidelli, A. 2024, A&A, 688, A202, doi: 10.1051/0004-6361/202450340

    2024 doi

  126. [140]

    K., Saunders, N., Sun, M., et al

    Grunblatt, S. K., Saunders, N., Sun, M., et al. 2022, AJ, 163, 120, doi: 10.3847/1538-3881/ac4972

    2022 doi

  127. [141]

    2025, Formation of Free-Floating Planets via Ejection: Population Synthesis with a Realistic IMF and Comparison to Microlensing Observations, arXiv, doi: 10.48550/arXiv.2511.03246

    Guo, K., Ida, S., & Ogihara, M. 2025, Formation of Free-Floating Planets via Ejection: Population Synthesis with a Realistic IMF and Comparison to Microlensing Observations, arXiv, doi: 10.48550/arXiv.2511.03246

    2025 doi

  128. [142]

    2025, AJ, 170, 362, doi: 10.3847/1538-3881/ae1833

    Guo, Y., Zhang, L., Feng, F., et al. 2025, AJ, 170, 362, doi: 10.3847/1538-3881/ae1833

    2025 doi

  129. [143]

    2020, Nature Astronomy, 4, 53

    Guzik, P., Drahus, M., Rusek, K., et al. 2020, Nature Astronomy, 4, 53

    2020

  130. [144]

    2025, Free Floating or Merely Detached? arXiv, doi: 10.48550/arXiv.2507.08968

    Hadden, S., & Wu, Y. 2025, Free Floating or Merely Detached? arXiv, doi: 10.48550/arXiv.2507.08968

    2025 doi arXiv

  131. [145]

    Hadjidemetriou, J. D. 1963, Icarus, 2, 440, doi: 10.1016/0019-1035(63)90072-1

    1963 doi

  132. [146]

    S., & Tremaine, S

    Hamers, A. S., & Tremaine, S. 2017, AJ, 154, 272, doi: 10.3847/1538-3881/aa9926

    2017 doi

  133. [147]

    2019, MNRAS, 490, 21, doi: 10.1093/mnras/stz1069

    Moore, B. 2019, MNRAS, 490, 21, doi: 10.1093/mnras/stz1069

    2019 doi

  134. [148]

    Hao, W., Kouwenhoven, M. B. N., & Spurzem, R. 2013, MNRAS, 433, 867, doi: 10.1093/mnras/stt771

    2013 doi

  135. [149]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357 35

    2020

  136. [150]

    B., Abe, F., Bond, I

    Hearnshaw, J. B., Abe, F., Bond, I. A., et al. 2006, in The 9th Asian-Pacific Regional IAU Meeting, ed. W. Sutantyo, P. W. Premadi, P. Mahasena, T. Hidayat, & S. Mineshige, 272, doi: 10.48550/arXiv.astro-ph/0509420

    2006 doi arXiv

  137. [151]

    Heggie, D. C. 1975, MNRAS, 173, 729, doi: 10.1093/mnras/173.3.729

    1975 doi

  138. [152]

    Heggie, D. C. 2006, in Few-Body Problem: Theory and Computer Simulations, 20, doi: 10.48550/arXiv.astro-ph/0512504

    2006 doi arXiv

  139. [153]

    C., & Rasio, F

    Heggie, D. C., & Rasio, F. A. 1996, MNRAS, 282, 1064, doi: 10.1093/mnras/282.3.1064

    1996 doi

  140. [154]

    B., Gaudi, B

    Henderson, C. B., Gaudi, B. S., Han, C., et al. 2014, ApJ, 794, 52, doi: 10.1088/0004-637X/794/1/52 H´ enon, M., & Guyot, M. 1970, in Periodic Orbits Stability and Resonances, ed. G. E. O. Giacaglia, 349

    2014 doi

  141. [155]

    Hills, J. G. 1983, ApJ, 267, 322, doi: 10.1086/160871

    1983 doi

  142. [156]

    Hills, J. G. 1984, AJ, 89, 1559, doi: 10.1086/113659

    1984 doi

  143. [157]

    G., & Dissly, R

    Hills, J. G., & Dissly, R. W. 1989, AJ, 98, 1069, doi: 10.1086/115197

    1989 doi

  144. [158]

    J., & Wiegert, P

    Holman, M. J., & Wiegert, P. A. 1999, AJ, 117, 621, doi: 10.1086/300695

    1999 doi

  145. [159]

    N., Nicholson, P

    Hong, Y.-C., Raymond, S. N., Nicholson, P. D., & Lunine, J. I. 2018, The Astrophysical Journal, 852, 85, doi: 10.3847/1538-4357/aaa0db

    2018 doi

  146. [160]

    2026, ApJ, 998, 245, doi: 10.3847/1538-4357/ae394f

    Huang, X., & Lai, D. 2026, ApJ, 998, 245, doi: 10.3847/1538-4357/ae394f

    2026 doi

  147. [161]

    Hunter, J. D. 2007, Computing in science & engineering, 9, 90

    2007

  148. [162]

    R., & Shara, M

    Hurley, J. R., & Shara, M. M. 2002, ApJ, 565, 1251, doi: 10.1086/337921

    2002 doi

  149. [163]

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

    2022 doi

  150. [164]

    Hwang, H.-C., & Zakamska, N. L. 2025, ApJ, 991, 226, doi: 10.3847/1538-4357/adfa1c

    2025 doi

  151. [165]

    2018, ApJ, 864, 77, doi: 10.3847/1538-4357/aad69c

    Tanigawa, T. 2018, ApJ, 864, 77, doi: 10.3847/1538-4357/aad69c

    2018 doi

  152. [166]

    K., Yang, H., et al

    Inyanya, T., Jung, Y. K., Yang, H., et al. 2026, KMT-2024-BLG-3237: Another Free-Floating Planet Candidate with Angular Einstein Radius Measurement, https://arxiv.org/abs/2602.22709

    2026

  153. [167]

    N., et al

    Izidoro, A., Bitsch, B., Raymond, S. N., et al. 2021, A&A, 650, A152, doi: 10.1051/0004-6361/201935336

    2021 doi

  154. [168]

    2015, A&A, 582, A99, doi: 10.1051/0004-6361/201425525

    Pierens, A. 2015, A&A, 582, A99, doi: 10.1051/0004-6361/201425525

    2015 doi

  155. [169]

    N., et al

    Izidoro, A., Ogihara, M., Raymond, S. N., et al. 2017, Monthly Notices of the Royal Astronomical Society, 470, 1750

    2017

  156. [170]

    2025, Nature Astronomy, 9, 982, doi: 10.1038/s41550-025-02556-0

    Isella, A. 2025, Nature Astronomy, 9, 982, doi: 10.1038/s41550-025-02556-0

    2025 doi

  157. [171]

    2018, MNRAS: Letters, 478, L49 Jakub ´ ık, M., Morbidelli, A., Nesluˇ san, L., & Brasser, R

    Rein, H. 2018, MNRAS: Letters, 478, L49 Jakub ´ ık, M., Morbidelli, A., Nesluˇ san, L., & Brasser, R. 2012, A&A, 540, A71, doi: 10.1051/0004-6361/201117687

    2018 doi

  158. [172]

    2021, Nature, 600, 231, doi: 10.1038/s41586-021-04124-8

    Janson, M., Gratton, R., Rodet, L., et al. 2021, Nature, 600, 231, doi: 10.1038/s41586-021-04124-8

    2021 doi

  159. [173]

    2020, ApJL, 888, L23, doi: 10.3847/2041-8213/ab621b

    Jewitt, D., Hui, M.-T., Kim, Y., et al. 2020, ApJL, 888, L23, doi: 10.3847/2041-8213/ab621b

    2020 doi

  160. [174]

    2025, ApJL, 990, L2, doi: 10.3847/2041-8213/adf8d8

    Jewitt, D., Hui, M.-T., Mutchler, M., Kim, Y., & Agarwal, J. 2025, ApJL, 990, L2, doi: 10.3847/2041-8213/adf8d8

    2025 doi

  161. [175]

    2019, ApJL, 886, L29, doi: 10.3847/2041-8213/ab530b

    Jewitt, D., & Luu, J. 2019, ApJL, 886, L29, doi: 10.3847/2041-8213/ab530b

    2019 doi

  162. [176]

    2017, arXiv preprint arXiv:1711.05687

    Jewitt, D., Luu, J., Rajagopal, J., et al. 2017, arXiv preprint arXiv:1711.05687

    2017 arXiv

  163. [177]

    Jewitt, D., & Seligman, D. Z. 2023, ARA&A, 61, 197, doi: 10.1146/annurev-astro-071221-054221

    2023 doi

  164. [178]

    2010, MNRAS, 401, 977, doi: 10.1111/j.1365-2966.2009.15744.x

    Jiang, Y.-F., & Tremaine, S. 2010, MNRAS, 401, 977, doi: 10.1111/j.1365-2966.2009.15744.x

    2010

  165. [179]

    A., Penny, M., Gaudi, B

    Johnson, S. A., Penny, M., Gaudi, B. S., et al. 2020, AJ, 160, 123, doi: 10.3847/1538-3881/aba75b

    2020 doi

  166. [180]

    K., Hwang, K.-H., Yang, H., et al

    Jung, Y. K., Hwang, K.-H., Yang, H., et al. 2024, AJ, 168, 152, doi: 10.3847/1538-3881/ad6b12 Juri´ c, M., & Tremaine, S. 2008, ApJ, 686, 603, doi: 10.1086/590047

    2024 doi

  167. [181]

    Clement, M. S. 2024, Icarus, 415, 116057, doi: 10.1016/j.icarus.2024.116057

    2024

  168. [182]

    A., & Raymond, S

    Kaib, N. A., & Raymond, S. N. 2025, Icarus, 439, 116632, doi: 10.1016/j.icarus.2025.116632

    2025

  169. [183]

    A., Raymond, S

    Kaib, N. A., Raymond, S. N., & Duncan, M. 2013, Nature, 493, 381, doi: 10.1038/nature11780

    2013 doi

  170. [184]

    2026, A&A, 706, A110, doi: 10.1051/0004-6361/202555863

    Kapusta, M., Mr´ oz, P., Ryu, Y.-H., et al. 2026, A&A, 706, A110, doi: 10.1051/0004-6361/202555863

    2026 doi

  171. [185]

    2018, AJ, 155, 76, doi: 10.3847/1538-3881/aaa47b

    Kim, D.-J., Kim, H.-W., Hwang, K.-H., et al. 2018, AJ, 155, 76, doi: 10.3847/1538-3881/aaa47b

    2018 doi

  172. [186]

    2021, The Astronomical Journal, 162, 15, doi: 10.3847/1538-3881/abfc4a

    Kim, H.-W., Hwang, K.-H., Gould, A., et al. 2021, The Astronomical Journal, 162, 15, doi: 10.3847/1538-3881/abfc4a

    2021 doi

  173. [187]

    M., Protopapa, S., Kelley, M

    Knight, M. M., Protopapa, S., Kelley, M. S., et al. 2017, ApJL, 851, L31

    2017

  174. [188]

    1998, Icarus, 131, 171, doi: 10.1006/icar.1997.5840

    Kokubo, E., & Ida, S. 1998, Icarus, 131, 171, doi: 10.1006/icar.1997.5840

    1998

  175. [189]

    P., et al

    Koshimoto, N., Sumi, T., Bennett, D. P., et al. 2023, AJ, 166, 107, doi: 10.3847/1538-3881/ace689 36

    2023 doi

  176. [190]

    M., & Perets, H

    Kratter, K. M., & Perets, H. B. 2012, The Astrophysical Journal, 753, 91, doi: 10.1088/0004-637X/753/1/91

    2012 doi

  177. [191]

    Rasio, F. A. 2019, The Astrophysical Journal, 885, 2, doi: 10.3847/1538-4357/ab44d1

    2019 doi

  178. [192]

    2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

    Kroupa, P. 2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

    2001

  179. [193]

    A., & Gilmore, G

    Kroupa, P., Tout, C. A., & Gilmore, G. 1993, MNRAS, 262, 545, doi: 10.1093/mnras/262.3.545

    1993 doi

  180. [194]

    J., & Lada, E

    Lada, C. J., & Lada, E. A. 2003, ARA&A, 41, 57, doi: 10.1146/annurev.astro.41.011802.094844

    2003 arXiv

  181. [195]

    2018, MNRAS, 476, 5692, doi: 10.1093/mnras/sty022

    Lam, C., & Kipping, D. 2018, MNRAS, 476, 5692, doi: 10.1093/mnras/sty022

    2018 doi

  182. [196]

    B., Scholz, A., Muˇ zi´ c, K., et al

    Langeveld, A. B., Scholz, A., Muˇ zi´ c, K., et al. 2024, AJ, 168, 179, doi: 10.3847/1538-3881/ad6f0c

    2024 doi

  183. [197]

    1997, A&A, 317, L75

    Laskar, J. 1997, A&A, 317, L75

    1997

  184. [198]

    2000, PhRvL, 84, 3240, doi: 10.1103/PhysRevLett.84.3240

    Laskar, J. 2000, PhRvL, 84, 3240, doi: 10.1103/PhysRevLett.84.3240

    2000 doi

  185. [199]

    Laskar, J., & Petit, A. C. 2017, A&A, 605, A72, doi: 10.1051/0004-6361/201630022

    2017 doi

  186. [200]

    S., Johnson, S

    Lastovka, M., Gaudi, B. S., Johnson, S. A., et al. 2025, AJ, 170, 258, doi: 10.3847/1538-3881/ae0196

    2025 doi

  187. [201]

    Laughlin, G., & Adams, F. C. 1998, The Astrophysical Journal, 508, L171, doi: 10.1086/311736

    1998 doi

  188. [202]

    Laughlin, G., & Adams, F. C. 2000, Icarus, 145, 614, doi: 10.1006/icar.2000.6355

    2000

  189. [203]

    2017, Research Notes of the AAS, 1, 43

    Laughlin, G., & Batygin, K. 2017, Research Notes of the AAS, 1, 43

    2017

  190. [204]

    J., DeRocco, W., Hadden, S., & Gaudi, B

    Lee, E. J., DeRocco, W., Hadden, S., & Gaudi, B. S. 2026, The Astrophysical Journal Letters, 1005, L18, doi: 10.3847/2041-8213/ae796f

    2026 doi

  191. [205]

    H., & Peale, S

    Lee, M. H., & Peale, S. J. 2002, ApJ, 567, 596

    2002

  192. [206]

    F., Dones, L., Chapman, C

    Levison, H. F., Dones, L., Chapman, C. R., et al. 2001, Icarus, 151, 286, doi: 10.1006/icar.2001.6608

    2001

  193. [207]

    F., Morbidelli, A., Tsiganis, K., Nesvorn´ y, D., & Gomes, R

    Levison, H. F., Morbidelli, A., Tsiganis, K., Nesvorn´ y, D., & Gomes, R. 2011, AJ, 142, 152, doi: 10.1088/0004-6256/142/5/152

    2011 doi

  194. [208]

    J., & Davies, M

    Li, D., Mustill, A. J., & Davies, M. B. 2019, MNRAS, 488, 1366, doi: 10.1093/mnras/stz1794

    2019 doi

  195. [209]

    Li, G., & Adams, F. C. 2015, MNRAS, 448, 344, doi: 10.1093/mnras/stv012

    2015 doi

  196. [210]

    J., & Tao, M

    Li, G., Holman, M. J., & Tao, M. 2016, ApJ, 831, 96, doi: 10.3847/0004-637X/831/1/96

    2016 doi

  197. [211]

    2022, ApJ, 934, 154, doi: 10.3847/1538-4357/ac7c0d

    Li, J., Lai, D., & Rodet, L. 2022, ApJ, 934, 154, doi: 10.3847/1538-4357/ac7c0d

    2022 doi

  198. [212]

    2008, Astronomy Reports, 52, 806, doi: 10.1134/S106377290810003X

    Li, L.-S. 2008, Astronomy Reports, 52, 806, doi: 10.1134/S106377290810003X

    2008 doi

  199. [213]

    Lin, D. N. C., & Ida, S. 1997, ApJ, 477, 781, doi: 10.1086/303738

    1997 doi

  200. [214]

    J., & Gavino, S

    Lissauer, J. J., & Gavino, S. 2021, Icarus, 364, 114470, doi: 10.1016/j.icarus.2021.114470

    2021

  201. [215]

    J., Ragozzine, D., Fabrycky, D

    Lissauer, J. J., Ragozzine, D., Fabrycky, D. C., et al. 2011, ApJS, 197, 8

    2011

  202. [216]

    2011, ApJ, 739, 31

    Lithwick, Y., & Wu, Y. 2011, ApJ, 739, 31

    2011

  203. [217]

    2014, Proceedings of the National Academy of Science, 111, 12610, doi: 10.1073/pnas.1308261110

    Lithwick, Y., & Wu, Y. 2014, Proceedings of the National Academy of Science, 111, 12610, doi: 10.1073/pnas.1308261110

    2014 doi

  204. [218]

    N., & Jacobson, S

    Liu, B., Raymond, S. N., & Jacobson, S. A. 2022, Nature, 604, 643, doi: 10.1038/s41586-022-04535-1

    2022 doi

  205. [219]

    2026, arXiv e-prints, arXiv:2604.08383, doi: 10.48550/arXiv.2604.08383

    LoRusso, R., Petrovich, C., & Gautham Bhaskar, H. 2026, arXiv e-prints, arXiv:2604.08383, doi: 10.48550/arXiv.2604.08383

    2026 doi arXiv

  206. [220]

    2011, A&A, 528, A112, doi: 10.1051/0004-6361/201015577

    Lovis, C., S´ egransan, D., Mayor, M., et al. 2011, A&A, 528, A112, doi: 10.1051/0004-6361/201015577

    2011 doi

  207. [221]

    C., Rice, M., et al

    Lu, T., Millholland, S. C., Rice, M., et al. 2026, arXiv preprint arXiv:2605.30177. https://arxiv.org/abs/2605.30177

    2026 arXiv

  208. [222]

    W., & Roche, P

    Lucas, P. W., & Roche, P. F. 2000, MNRAS, 314, 858, doi: 10.1046/j.1365-8711.2000.03515.x

    2000

  209. [223]

    Luhman, K. L. 2004, ApJ, 617, 1216, doi: 10.1086/425647

    2004 doi

  210. [224]

    Luhman, K. L. 2012, ARA&A, 50, 65, doi: 10.1146/annurev-astro-081811-125528

    2012 doi

  211. [225]

    L., Alves de Oliveira, C., Baraffe, I., et al

    Luhman, K. L., Alves de Oliveira, C., Baraffe, I., et al. 2024, AJ, 167, 19, doi: 10.3847/1538-3881/ad00b7

    2024 doi

  212. [226]

    L., Burgasser, A

    Luhman, K. L., Burgasser, A. J., & Bochanski, J. J. 2011, ApJL, 730, L9, doi: 10.1088/2041-8205/730/1/L9

    2011 doi

  213. [227]

    L., Esplin, T

    Luhman, K. L., Esplin, T. L., & Loutrel, N. P. 2016, ApJ, 827, 52, doi: 10.3847/0004-637X/827/1/52

    2016 doi

  214. [228]

    Ma, S., Mao, S., Ida, S., Zhu, W., & Lin, D. N. C. 2016, MNRAS, 461, L107, doi: 10.1093/mnrasl/slw110

    2016 doi

  215. [229]

    2016, A&A, 588, A118, doi: 10.1051/0004-6361/201527933

    Malavolta, L., Nascimbeni, V., Piotto, G., et al. 2016, A&A, 588, A118, doi: 10.1051/0004-6361/201527933

    2016 doi

  216. [230]

    F., Villaver, E., Mustill, A

    Maldonado, R. F., Villaver, E., Mustill, A. J., & Ch´ avez, M. 2022, MNRAS, 512, 104, doi: 10.1093/mnras/stac481

    2022 doi

  217. [231]

    1993, Nature, 365, 819, doi: 10.1038/365819a0

    Malhotra, R. 1993, Nature, 365, 819, doi: 10.1038/365819a0

    1993 doi

  218. [232]

    1995, AJ, 110, 420, doi: 10.1086/117532

    Malhotra, R. 1995, AJ, 110, 420, doi: 10.1086/117532

    1995 doi

  219. [233]

    1998, in Astronomical Society of the Pacific Conference Series, Vol

    Malhotra, R. 1998, in Astronomical Society of the Pacific Conference Series, Vol. 149, Solar System Formation and Evolution, ed. D. Lazzaro, R. Vieira Martins, S. Ferraz-Mello, & J. Fernandez, 37

    1998

  220. [234]

    B., & Chambers, J

    Malmberg, D., Davies, M. B., & Chambers, J. E. 2007, MNRAS, 377, L1, doi: 10.1111/j.1745-3933.2007.00291.x

    2007

  221. [235]

    B., & Heggie, D

    Malmberg, D., Davies, M. B., & Heggie, D. C. 2011, MNRAS, 411, 859, doi: 10.1111/j.1365-2966.2010.17730.x

    2011

  222. [236]

    W., Gaidos, E., Mace, G

    Mann, A. W., Gaidos, E., Mace, G. N., et al. 2016, ApJ, 818, 46, doi: 10.3847/0004-637X/818/1/46 37

    2016 doi

  223. [237]

    V., Triaud, A

    Martin, D. V., Triaud, A. H. M. J., Udry, S., et al. 2019, A&A, 624, A68, doi: 10.1051/0004-6361/201833669

    2019 doi

  224. [238]

    G., Lubow, S

    Martin, R. G., Lubow, S. H., Vallet, D., Anugu, N., & Gies, D. R. 2023, ApJL, 957, L28, doi: 10.3847/2041-8213/ad0730

    2023 doi

  225. [239]

    2014, MNRAS, 444, 1419, doi: 10.1093/mnras/stu1544

    Marzari, F. 2014, MNRAS, 444, 1419, doi: 10.1093/mnras/stu1544

    2014 doi

  226. [240]

    2025, MNRAS, 536, 422, doi: 10.1093/mnras/stae2602

    Marzari, F. 2025, MNRAS, 536, 422, doi: 10.1093/mnras/stae2602

    2025 doi

  227. [241]

    2013, A&A, 550, A64, doi: 10.1051/0004-6361/201220436

    Marzari, F., & Picogna, G. 2013, A&A, 550, A64, doi: 10.1051/0004-6361/201220436

    2013 doi

  228. [242]

    Marzari, F., & Weidenschilling, S. J. 2002, Icarus, 156, 570, doi: 10.1006/icar.2001.6786

    2002

  229. [243]

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

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

    2005 doi

  230. [244]

    Masuda, K., & Winn, J. N. 2017, AJ, 153, 187, doi: 10.3847/1538-3881/aa647c

    2017 doi

  231. [245]

    2011, arXiv e-prints, arXiv:1109.2497, doi: 10.48550/arXiv.1109.2497

    Mayor, M., Marmier, M., Lovis, C., et al. 2011, arXiv e-prints, arXiv:1109.2497, doi: 10.48550/arXiv.1109.2497

    2011 doi arXiv

  232. [246]

    2010, in Proceedings of the 9th Python in Science Conference, Vol

    McKinney, W. 2010, in Proceedings of the 9th Python in Science Conference, Vol. 445, Austin, TX, 51–56

    2010

  233. [247]

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

    Meech, K. J., Weryk, R., Micheli, M., et al. 2017, Nature, 552, 378

    2017

  234. [248]

    2013, Nature, 499, 55, doi: 10.1038/nature12279

    Meibom, S., Torres, G., Fressin, F., et al. 2013, Nature, 499, 55, doi: 10.1038/nature12279

    2013 doi

  235. [249]

    N., et al

    Miret-Roig, N., Bouy, H., Raymond, S. N., et al. 2022, Nature Astronomy, 6, 89, doi: 10.1038/s41550-021-01513-x

    2022 doi

  236. [250]

    2017, ApJS, 230, 15, doi: 10.3847/1538-4365/aa6fb6

    Moe, M., & Di Stefano, R. 2017, ApJS, 230, 15, doi: 10.3847/1538-4365/aa6fb6

    2017 doi

  237. [251]

    2018, in Handbook of Exoplanets, ed

    Morbidelli, A. 2018, in Handbook of Exoplanets, ed. H. J. Deeg & J. A. Belmonte, 145, doi: 10.1007/978-3-319-55333-7 145

    2018 doi

  238. [252]

    Morbidelli, A., Batygin, K., Brasser, R., & Raymond, S. N. 2020, MNRAS, 497, L46, doi: 10.1093/mnrasl/slaa111

    2020 doi

  239. [253]

    F., Tsiganis, K., & Gomes, R

    Morbidelli, A., Levison, H. F., Tsiganis, K., & Gomes, R. 2005, Nature, 435, 462

    2005

  240. [254]

    J., & Kratter, K

    Morrison, S. J., & Kratter, K. M. 2016, ApJ, 823, 118, doi: 10.3847/0004-637X/823/2/118 Mr´ oz, P., Ban, M., Marty, P., & Poleski, R. 2024, AJ, 167, 40, doi: 10.3847/1538-3881/ad1106 Mr´ oz, P., Udalski, A., Skowron, J., et al. 2017, Nature, 548, 183, doi: 10.1038/nature23276 ...

    2016 doi

  241. [255]

    R., & Wu, Y

    Mudryk, L. R., & Wu, Y. 2006, The Astrophysical Journal, 639, 423, doi: 10.1086/499347

    2006 doi

  242. [256]

    J., Veras, D., & Villaver, E

    Mustill, A. J., Veras, D., & Villaver, E. 2014, MNRAS, 437, 1404, doi: 10.1093/mnras/stt1973 Muˇ zi´ c, K., Scholz, A., Geers, V., Jayawardhana, R., &

    2014 doi

  243. [257]

    2012, ApJ, 744, 134, doi: 10.1088/0004-637X/744/2/134

    Tamura, M. 2012, ApJ, 744, 134, doi: 10.1088/0004-637X/744/2/134

    2012 doi

  244. [258]

    2008, ApJ, 678, 498, doi: 10.1086/529369

    Nagasawa, M., Ida, S., & Bessho, T. 2008, ApJ, 678, 498, doi: 10.1086/529369

    2008 doi

  245. [259]

    Rich, R. M. 2012, A&A, 541, A144, doi: 10.1051/0004-6361/201118655

    2012 doi

  246. [260]

    2026, MNRAS, 546, stag043, doi: 10.1093/mnras/stag043 Nesvorn´ y, D

    Nayakshin, S., Zhang, L., ´Calovi´ c, A., et al. 2026, MNRAS, 546, stag043, doi: 10.1093/mnras/stag043 Nesvorn´ y, D. 2015a, AJ, 150, 73, doi: 10.1088/0004-6256/150/3/73 Nesvorn´ y, D. 2015b, AJ, 150, 68, doi: 10.1088/0004-6256/150/3/68 Nesvorn´ y, D., Vokrouhlick´ y, D., & De...

    2026 doi

  247. [261]

    L., De Rosa, R

    Nielsen, E. L., De Rosa, R. J., Macintosh, B., et al. 2019, AJ, 158, 13

    2019

  248. [262]

    Chambers, J. E. 2026, A&A, 706, A96, doi: 10.1051/0004-6361/202452890 Nordstr¨ om, B., Mayor, M., Andersen, J., et al. 2004, A&A, 418, 989, doi: 10.1051/0004-6361:20035959

    2026 doi

  249. [263]

    1999, ApJ, 526, 336, doi: 10.1086/307964

    Oasa, Y., Tamura, M., & Sugitani, K. 1999, ApJ, 526, 336, doi: 10.1086/307964

    1999 doi

  250. [264]

    2017, Icarus, 293, 52, doi: 10.1016/j.icarus.2017.04.010 O’Brien, M

    Obertas, A., Van Laerhoven, C., & Tamayo, D. 2017, Icarus, 293, 52, doi: 10.1016/j.icarus.2017.04.010 O’Brien, M. W., Tremblay, P.-E., Klein, B. L., et al. 2024, MNRAS, 527, 8687, doi: 10.1093/mnras/stad3773 O’Connor, C. E. 2026, ApJ, 998, 280, doi: 10.3847/1538-4357/ae3b26 38

    2017 doi

  251. [265]

    Offner, S. S. R., Moe, M., Kratter, K. M., et al. 2023, in Astronomical Society of the Pacific Conference Series, Vol. 534, Protostars and Planets VII, ed. S. Inutsuka, Y. Aikawa, T. Muto, K. Tomida, & M. Tamura, 275, doi: 10.48550/arXiv.2203.10066

    2023 doi arXiv

  252. [266]

    2009, ApJ, 699, 824, doi: 10.1088/0004-637X/699/1/824

    Ogihara, M., & Ida, S. 2009, ApJ, 699, 824, doi: 10.1088/0004-637X/699/1/824

    2009 doi

  253. [267]

    Oliphant, T. E. 2006, A guide to NumPy, Vol. 1 (Trelgol Publishing USA)

    2006

  254. [268]

    Omarov, T. B. 1962, Akademiia Nauk Kazakhskoi SSR,

    1962

  255. [269]

    T., Bhandare, A., et al

    Izvestiia, Seriia Fiziko-Matematicheskaia, 14, 66 ’Oumuamua ISSI Team, Bannister, M. T., Bhandare, A., et al. 2019, Nature Astronomy, 3, 594, doi: 10.1038/s41550-019-0816-x

    2019 doi

  256. [270]

    W., & Lissauer, J

    Outland, B., Noble, G., Smith, A. W., & Lissauer, J. J. 2026, Icarus, 452, 117025, doi: 10.1016/j.icarus.2026.117025

    2026

  257. [271]

    C., Nelson, R

    Papaloizou, J. C., Nelson, R. P., & Masset, F. 2001, A&A, 366, 263

    2001

  258. [272]

    Papaloizou, J. C. B., & Terquem, C. 2006, Reports on Progress in Physics, 69, 119, doi: 10.1088/0034-4885/69/1/R03

    2006 doi

  259. [273]

    Goodwin, S. P. 2021, ApJ, 913, 95, doi: 10.3847/1538-4357/abf4cc

    2021 doi

  260. [275]

    J., & Veras, D

    Parker, R. J., & Veras, D. 2026, arXiv e-prints, arXiv:2607.00080. https://arxiv.org/abs/2607.00080

    2026 arXiv

  261. [276]

    Peale, S. J. 1976, ARA&A, 14, 215, doi: 10.1146/annurev.aa.14.090176.001243

    1976

  262. [277]

    G., & McCaughrean, M

    Pearson, S. G., & McCaughrean, M. J. 2023, arXiv e-prints, arXiv:2310.01231, doi: 10.48550/arXiv.2310.01231

    2023 doi arXiv

  263. [278]

    J., & Black, D

    Pendleton, Y. J., & Black, D. C. 1983, AJ, 88, 1415, doi: 10.1086/113430

    1983 doi

  264. [279]

    T., Gaudi, B

    Penny, M. T., Gaudi, B. S., Kerins, E., et al. 2019, ApJS, 241, 3, doi: 10.3847/1538-4365/aafb69

    2019 doi

  265. [280]

    C., Pichierri, G., Davies, M

    Petit, A. C., Pichierri, G., Davies, M. B., & Johansen, A. 2020, A&A, 641, A176, doi: 10.1051/0004-6361/202038764

    2020 doi

  266. [281]

    L., Bhandare, A., & Veras, D

    Pfalzner, S., Aizpuru Vargas, L. L., Bhandare, A., & Veras, D. 2021, A&A, 651, A38, doi: 10.1051/0004-6361/202140587

    2021 doi

  267. [282]

    2014, A&A, 564, A28, doi: 10.1051/0004-6361/201322816

    Picogna, G., & Marzari, F. 2014, A&A, 564, A28, doi: 10.1051/0004-6361/201322816

    2014 doi

  268. [283]

    2003, A&A, 400, 1085, doi: 10.1051/0004-6361:20021811

    Pilat-Lohinger, E., Funk, B., & Dvorak, R. 2003, A&A, 400, 1085, doi: 10.1051/0004-6361:20021811

    2003 doi

  269. [284]

    2002, in ESA Special Publication, Vol

    Pilat-Lohinger, E., Funk, B., Freistetter, F., & Dvorak, R. 2002, in ESA Special Publication, Vol. 518, Exo-Astrobiology, ed. H. Lacoste, 547–548

    2002

  270. [285]

    2021, AcA, 71, 1, doi: 10.32023/0001-5237/71.1.1

    Poleski, R., Skowron, J., Mr´ oz, P., et al. 2021, AcA, 71, 1, doi: 10.32023/0001-5237/71.1.1

    2021 doi

  271. [286]

    2025, AcA, 75, 279, doi: 10.32023/0001-5237/75.4.1 Portegies Zwart, S

    Poleski, R., Ryu, Y.-H., Udalski, A., et al. 2025, AcA, 75, 279, doi: 10.32023/0001-5237/75.4.1 Portegies Zwart, S. 2021, A&A, 647, A136, doi: 10.1051/0004-6361/202038888 Portegies Zwart, S., Torres, S., Pelupessy, I., B´ edorf, J., &

    2025 doi

  272. [287]

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

    2018 doi

  273. [288]

    M., Sip˝ ocz, B

    Price-Whelan, A. M., Sip˝ ocz, B. M., G¨ unther, H. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f

    2018 doi

  274. [289]

    Proszkow, E.-M., & Adams, F. C. 2009, ApJS, 185, 486, doi: 10.1088/0067-0049/185/2/486

    2009 doi

  275. [290]

    2021, MNRAS, 508, 597, doi: 10.1093/mnras/stab2504

    Pu, B., & Lai, D. 2021, MNRAS, 508, 597, doi: 10.1093/mnras/stab2504

    2021 doi

  276. [291]

    2015, ApJ, 807, 44, doi: 10.1088/0004-637X/807/1/44

    Pu, B., & Wu, Y. 2015, ApJ, 807, 44, doi: 10.1088/0004-637X/807/1/44

    2015 doi

  277. [292]

    2020, AJ, 159, 80, doi: 10.3847/1538-3881/ab64fa

    Quarles, B., Li, G., Kostov, V., & Haghighipour, N. 2020, AJ, 159, 80, doi: 10.3847/1538-3881/ab64fa

    2020 doi

  278. [293]

    Quarles, B., & Lissauer, J. J. 2016, AJ, 151, 111, doi: 10.3847/0004-6256/151/5/111

    2016 doi

  279. [294]

    2018, ApJ, 856, 150, doi: 10.3847/1538-4357/aab264

    Haghighipour, N. 2018, ApJ, 856, 150, doi: 10.3847/1538-4357/aab264

    2018 doi

  280. [295]

    Quillen, A. C. 2011, MNRAS, 418, 1043, doi: 10.1111/j.1365-2966.2011.19555.x

    2011

  281. [296]

    Rabago, I., & Steffen, J. H. 2019, MNRAS, 489, 2323, doi: 10.1093/mnras/sty2552

    2019 doi

  282. [297]

    1988, A&A, 191, 385

    Rabl, G., & Dvorak, R. 1988, A&A, 191, 385

    1988

  283. [298]

    A., Henry, T

    Raghavan, D., McAlister, H. A., Henry, T. J., et al. 2010, ApJS, 190, 1, doi: 10.1088/0067-0049/190/1/1

    2010 doi

  284. [299]

    A., & Ford, E

    Rasio, F. A., & Ford, E. B. 1996, Science, 274, 954

    1996

  285. [300]

    N., Armitage, P

    Raymond, S. N., Armitage, P. J., & Gorelick, N. 2009, ApJL, 699, L88, doi: 10.1088/0004-637X/699/2/L88

    2009 doi

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