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Most free-floating planets are ejected from their birth systems, not born alone, and three dynamical mechanisms likely dominate that ejection.

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2026-08-04 00:35 UTC pith:BGP3PPUG

load-bearing objection A useful, honest review whose synthesis table is more conditional than it looks; referee it, but don't let Table 1 carry the ranking. the 2 major comments →

arxiv 2608.00173 v1 pith:BGP3PPUG submitted 2026-07-31 astro-ph.EP astro-ph.SR

The Dynamics of Planetary Ejection

Malena Rice , William DeRocco , Sean N. Raymond This is my paper
classification astro-ph.EP astro-ph.SR
keywords free-floating planetsplanetary ejectionplanet-planet scatteringbinary star instabilitiesstellar flybyspost-main-sequence mass lossgravitational microlensingSafronov number
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Microlensing surveys imply a large population of free-floating planets, roughly twenty per star, and the paper argues that most of these must be planets that formed around stars and were later gravitationally ejected. It reviews the four known ejection routes: planet-planet scattering, instabilities in binary and multi-star systems, stellar and planetary flybys, and post-main-sequence mass loss, and it assembles the mass and velocity signatures predicted by each. The central quantitative claim is that planet-planet scattering, embedded cluster encounters, and binary instabilities are the predominant sources of ejected planets, while flybys and post-main-sequence evolution contribute smaller or more distinctive subpopulations. If correct, the free-floating planet census is a fossil record of dynamical instability in planetary systems, and upcoming microlensing samples can identify which mechanism dominated by measuring ejection velocities and the mass function.

Core claim

This review argues that where planets form, planets are ejected: dynamical instabilities are a normal stage of planetary system evolution, and the free-floating planet population is largely a collection of ejected former members of such systems. Four mechanisms are considered: close encounters between neighboring planets, instabilities in binary and multi-star systems, flybys by passing stars and substellar objects, and post-main-sequence stellar mass loss. The paper synthesizes evidence from the solar system's probable fifth giant planet and from the eccentric, tightly packed architectures of exoplanet systems, and it tabulates relative production rates. The headline conclusion is that plan

What carries the argument

The organizing tools are a small set of dynamical quantities that separate ejection from other outcomes. The Safronov number, the ratio of a planet's escape velocity squared to the escape velocity from the host star at the planet's orbit, predicts whether close encounters tend to eject bodies or merge them; high-Safronov planets, especially wide-orbit Jovians, are the efficient ejectors. The angular momentum deficit measures how much non-circular, inclined orbital angular momentum a system carries, and systems above a critical value become unstable and scatter planets. For binary systems, empirical stability boundaries delimit the allowed circumstellar and circumbinary orbital radii. The mas

Load-bearing premise

The quantitative ranking of ejection mechanisms assumes planets actually form in the unstable orbital regions, such as circumbinary planets in binaries up to about 3 AU and circumstellar planets only in binaries wider than about 10 AU, and that planets extend out to about 30 AU; if formation is suppressed there, the claimed predominance changes.

What would settle it

Take a completeness-corrected microlensing sample of several hundred free-floating planets with measured parallaxes and hence velocities. If the excess-velocity distribution peaks well above about 6 km/s, or the mass function shows no turnover near 0.8 Earth masses, the claim that scattering and binary instabilities dominate would be falsified; a sample dominated by roughly 2-6 km/s objects with a bottom-heavy mass function would confirm it.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Most low-mass free-floating planets are former members of planetary systems, so their numbers imply that unstable orbital configurations are common outcomes of planet formation, not rare accidents.
  • The mass function of ejected planets should be bottom-heavy: early instabilities preferentially eject the lowest-mass planets, while late secular instabilities preferentially remove the highest-mass planets from multi-giant systems.
  • Measuring the velocity distribution of free-floating planets can identify the dominant ejection route, since scattering yields roughly 2-6 km/s excess velocities, circumbinary instabilities roughly 8-12 km/s, cluster encounters roughly 5-12 km/s, and supernova ejections roughly 18 km/s.
  • Upcoming microlensing surveys, with hundreds of detections and parallax-based mass and velocity measurements, can test the predicted mass-function turnover near 0.8 Earth masses and distinguish truly unbound planets from wide-orbit bound planets.
  • The solar system itself may carry the signature: a fifth giant planet ejected during instability, plus a population of ejected embryos, would fit the paper's claim that ejection is a normal stage of system evolution.

Where Pith is reading between the lines

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

  • If ejection is as common as claimed, standard disk-mass estimates undercount the planet-forming mass budget, because many planets are removed wholesale; the mass needed to produce the free-floating census may require heavier early disks.
  • The same dynamical logic extends to smaller bodies: with wide-orbit Neptune-mass planets common and efficient ejectors, interstellar objects should be dominated by icy bodies ejected from beyond the snow line, with velocity signatures mirroring the free-floating planet channels.
  • A sharper test than average velocity is the joint mass-velocity distribution: scattering predicts a correlation between ejected planet mass and excess velocity that cluster and supernova channels do not, so a large microlensing sample could separate the components statistically.
  • The assumption that planets form in unstable binary regions is directly checkable by imaging protoplanetary disks in binaries, measuring how often disks and planets appear at separations that would later trigger ejection.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript is a comprehensive review of the dynamical mechanisms that can eject planets from their natal systems: planet-planet scattering, instabilities in binary/multi-star systems, stellar and planetary flybys (especially in clusters), and post-main-sequence stellar evolution. It presents the underlying theory (Safronov number, angular momentum deficit, stability criteria, mass-loss index), summarizes the empirical evidence for each channel, and concludes with a comparative Table 1 estimating the relative rates of free-floating planet (FFP) production. The central claim, stated in Sec. 7, is that planetary ejection is common and that planet-planet scattering, embedded cluster encounters, and binary instabilities are likely the predominant FFP production mechanisms, with post-main-sequence channels subdominant. The paper also discusses observational prospects (Roman, Earth 2.0) and the ambiguities in identifying true FFPs versus wide-orbit bound planets.

Significance. If the synthesis holds, the paper provides a valuable framework for interpreting existing and upcoming microlensing surveys and for guiding theoretical work on the initial conditions of planetary systems. Its strengths include the breadth of the literature synthesized, the clear exposition of the dynamical formalism (e.g., Eqs. 6-7, 10, 20-21, 31), updated demographic figures (Figs. 3-4), and an explicit, assumptions-stated Table 1 that can serve as a starting point for quantitative comparisons. The review also makes falsifiable predictions (e.g., FFP velocity distributions, mass-function features) that upcoming surveys can test. The main weakness is that the quantitative ranking in Table 1 rests on unvalidated assumptions about planet formation in dynamically unstable regions, which the manuscript itself acknowledges but still leverages in the headline conclusion.

major comments (2)
  1. [Table 1; Sec. 7] The headline claim that planet-planet scattering, embedded cluster encounters, and binary instabilities are 'likely predominant' (Sec. 7) is carried by Table 1, but the binary-instability rows are conditional upper bounds. As the manuscript states in Sec. 3.4, if planet formation is not ubiquitous in the unstable regions, 'the census... may be much lower,' and Sec. 6.1 notes that 'The true rate of initial planet formation in these unstable regions is not well-characterized.' The p-type and s-type rows (9% and 10% of stars, up to 100% ejection) assume planets form in binaries with separations up to 3 AU (p-type) or with ab ≥ 10 AU and ap/ab ≥ 0.1 (s-type). If formation in these zones is suppressed by disk truncation, photoevaporation, or dynamical stirring, both rows could fall far below the embedded-cluster or scattering rows, changing the ranking. As written, Sec. 7 overstates a conditi
  2. [Sec. 6.1] The derivation of the 9% and 10% values for binary-instability susceptibility depends on several unvalidated choices: adopting G. A. L. Coleman & W. DeRocco (2025) that p-type planets form around binaries with separations up to 3 AU; assuming s-type planets form only when ab ≳ 10 AU; taking ap,max = 30 AU; and extending the Offner et al. (2023) separation distributions to stellar mass ranges beyond direct constraints. These are reasonable for an order-of-magnitude estimate, but Table 1 reports ejection rates without propagated uncertainties or any sensitivity analysis. A factor-of-two change in any of these thresholds could alter the predominance ranking. I request either a sensitivity table or an explicit statement of how the relative rates depend on these assumptions, so the reader can judge the robustness of the central claim.
minor comments (5)
  1. [Table 1] Typo: 'T able 1' should be 'Table 1'.
  2. [Sec. 6.1] The sentence 'such that it is possible that all such systems eject one or more planetary companions' is ambiguous; it would be clearer to say that the upper bound corresponds to formation in all unstable systems, not that such a rate is established.
  3. [Sec. 2.4.3] Minor formatting: '30◦' should be written as '30°' or '30 degrees' with consistent spacing.
  4. [Sec. 3.4] Equation reference: 'C J >3.46' should be typeset as C_J > 3.46 with subscripts in math mode.
  5. [Sec. 5.7] Grammar: 'A. P. Stephan & K. G. Stassun (2026) finds' should be 'find' (the reference is plural).

Circularity Check

0 steps flagged

No significant circularity: the review's synthesis rests on independent simulation benchmarks and observational inputs, not on equations that reduce to their own assumptions.

full rationale

The paper is a review that synthesizes published dynamical simulations, analytic results, and observational surveys. The central claim that planetary ejection is common is independently grounded in the microlensing FFP mass function (Sumi et al. 2023) and in the extensive literature on scattering, binary instabilities, and cluster dynamics. The quantitative Table 1 is explicitly conditional: the text states, 'The true rate of initial planet formation in these unstable regions is not well-characterized, such that it is possible that all such systems eject one or more planetary companions,' and earlier it cautions that if planet formation is not ubiquitous in unstable regions, 'the census ... may be much lower.' No equation in the paper is defined in terms of a quantity it purports to predict. The only notable self-citations (e.g., Coleman & DeRocco 2025) are used as inputs or supporting simulation results, not as a substitute for derivation, and the same quantitative claims are also attributed to independent prior works. Therefore no circular step meets the standard of a specific reduction of a 'prediction' to an input by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The paper introduces no new entities. Its quantitative synthesis rests on hand-chosen thresholds for planet formation in unstable binary regions and on an adopted FFP mass function, both explicitly acknowledged in Section 6.1. The mass-radius scaling normalization in Figure 4 is the only fitted parameter in the paper itself.

free parameters (2)
  • Binary separation thresholds for planet formation in unstable regions = 3 AU (p-type), 10 AU (s-type lower limit), 30 AU (max planet semi-major axis)
    Adopted in Section 6.1 to estimate Table 1 rates; chosen by hand, not fitted to data.
  • Mass-radius scaling normalization = not reported (scaled to match the exoplanet census in Figure 4)
    The theoretical mass-radius curves are 'scaled to match this population' (Figure 4 caption), a fitted normalization.
axioms (4)
  • ad hoc to paper Planets can form in the dynamically unstable regions assumed for each mechanism (e.g., p−type planets around binaries with ab ≤ 3 AU; s−type planets for ab ≳ 10 AU).
    Section 6.1 states these as adopted assumptions to compute the 9% and 10% susceptible-star fractions and the resulting ejection rates.
  • domain assumption The FFP mass function of Sumi et al. (2023) is representative of the true population and the candidates are mostly unbound.
    Used in Section 2.4.1 to derive Nfree/Nstars; the paper itself cautions in §6.1 that microlensing FFP candidates may be wide-orbit bound planets.
  • domain assumption Binary companion fractions and separation distributions from Offner et al. (2023) and Raghavan et al. (2010) extend to the adopted mass ranges.
    Section 6.1 uses these to compute the percentage of stars with binary companions capable of inducing instabilities.
  • standard math Standard Newtonian two-body and three-body dynamics.
    Used throughout for the Safronov number, AMD, Hill stability, and post-main-sequence mass-loss equations.

pith-pipeline@v1.3.0-alltime-deepseek · 58345 in / 10343 out tokens · 97838 ms · 2026-08-04T00:35:13.428804+00:00 · methodology

0 comments
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 Malena Rice, Sean N. Raymond, William DeRocco.

Figure 1
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 (bott… view at source ↗
Figure 2
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… view at source ↗
Figure 3
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 ele… view at source ↗
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 of 7/1/2026 is shown in gray, and the theoretical fits with fixed exponents are scaled to match this population. We note that the empirical… view at source ↗
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. A. Wiegert (1999), provided in this work as Equations 20 and 21. tric binary orbits and massless, test-particle planets— spanning 104 binar… view at source ↗
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 interactions σ ≈ a, which holds for v 2 esc,p/v2 i ≫ 1. We visualize two cases, for a planetary orbit with a = 1 AU and another with a = 30 AU. Wide… view at source ↗
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 and true anomaly of the planetary orbit. For higher fractional mass loss (increasing left to right across the three panels), planets are eject… view at source ↗
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. The percentage of all stars falling in a given mass range, derived from the P. Kroupa (2001) IMF, is shown together with the binary separa… view at source ↗

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Works this paper leans on

293 extracted references · 40 canonical work pages · 2 internal anchors

  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

    Pith/arXiv 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

    Pith/arXiv 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

  9. [9]

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

    Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0007044 2000

  10. [10]

    A., & Thorsett, S

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

    1996

  11. [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: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935...

    Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/9605141 2013

  12. [12]

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

    doi:10.3847/1538-3881/aae3eb 2018

  13. [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

    doi:10.1051/0004-6361/201937231 2020

  14. [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

    doi:10.3847/1538-3881/ab2d2a 2019

  15. [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

    doi:10.1088/2041-8205/780/1/l4 2014

  16. [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

    doi:10.3847/1538-4357/aa705b 2017

  17. [17]

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

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

    doi:10.1086/421321 2004

  18. [18]

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

    doi:10.1086/423419 2004

  19. [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

    doi:10.3847/1538-3881/ab4130 2019

  20. [20]

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

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

    doi:10.1093/mnras/stab1465 2021

  21. [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

    doi:10.1088/0067-0049/204/2/24 2013

  22. [22]

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

    doi:10.1088/0004-637x/716/2/1323 2010

  23. [23]

    E., & Betts, H

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

    doi:10.1088/2041-8205/744/1/l3 2012

  24. [24]

    1988a, Celestial Mechanics, 43, 47, doi: 10.1007/BF01234553 32

    Benest, D. 1988a, Celestial Mechanics, 43, 47, doi: 10.1007/BF01234553 32

    doi:10.1007/bf01234553

  25. [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

    doi:10.1007/bf00699718 1993

  26. [26]

    G., & Perets, H

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

    doi:10.3847/1538-4357/adf4e2 2025

  27. [27]

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

    doi:10.1086/113220 1982

  28. [28]

    J., Kenworthy, M

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

    doi:10.3847/2041-8213/aba27e 2020

  29. [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

    doi:10.1051/0004-6361/202140508 2021

  30. [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

    doi:10.1088/0004-637x/754/1/57 2012

  31. [31]

    M., Christiansen, J

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

    doi:10.3847/1538-3881/ad6570 2024

  32. [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

    doi:10.1093/mnrasl/slaf078 2025

  33. [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

    doi:10.1051/0004-6361/202554625 2025

  34. [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

    doi:10.1051/0004-6361/201730624 2017

  35. [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

  36. [37]

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

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

    2010

  37. [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

    doi:10.1088/0004-637x/736/1/19 2011

  38. [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

    doi:10.1051/0004-6361/202555031 2026

  39. [40]

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

    doi:10.1088/1538-3873/128/968/102001 2016

  40. [41]

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

    doi:10.1016/j.icarus.2015.11.015 2016

  41. [42]

    P., & Strader, J

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

    arXiv 2006

  42. [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

    doi:10.33232/001c.146688 2025

  43. [44]

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

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

    doi:10.1093/mnras/stac1763 2022

  44. [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

    doi:10.1051/0004-6361/201322584 2014

  45. [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

    doi:10.1051/0004-6361/201833097 2018

  46. [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

    doi:10.1093/mnras/stx1464 2017

  47. [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

    doi:10.1093/mnras/stx3064 2018

  48. [49]

    N., & Davies, M

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

    doi:10.1051/0004-6361/201935744 2019

  49. [50]

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

    arXiv 2001

  50. [51]

    E., Wetherill, G

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

    arXiv 1996

  51. [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

    arXiv 2012

  52. [53]

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

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

    2008

  53. [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

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

  54. [55]

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

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

    doi:10.1093/mnras/stt424 2013

  55. [56]

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

    doi:10.1016/0370-1573(79)90023-1 1979

  56. [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

    Pith/arXiv arXiv doi:10.48550/arxiv.2604.05035 2026

  57. [58]

    L., McElroy, D

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

    doi:10.3847/psj/ade3c2 2025

  58. [59]

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

    doi:10.1088/0004-637x/791/2/90 2014

  59. [60]

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

    doi:10.3847/0004-637x/819/2/125 2016

  60. [61]

    J., & Pringle, J

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

    doi:10.1093/mnras/261.1.190 1993

  61. [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

    arXiv 2021

  62. [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

    doi:10.1016/j.icarus.2018.04.008 2018

  63. [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

    arXiv 2020

  64. [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

    doi:10.1088/0004-637x/813/1/8 2015

  65. [66]

    Coleman, G. A. L. 2024, Monthly Notices of the Royal Astronomical Society, 530, 630, doi: 10.1093/mnras/stae903 33

    doi:10.1093/mnras/stae903 2024

  66. [67]

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

    doi:10.1093/mnras/staf138 2025

  67. [68]

    A., & Gil-Hutton, R

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

    doi:10.1051/0004-6361/201731229 2017

  68. [69]

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

    doi:10.1088/0004-637x/769/2/150 2013

  69. [70]

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

    doi:10.1051/0004-6361:20054551 2006

  70. [71]

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

    doi:10.1140/epjp/s13360-022-03602-w 2023

  71. [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

    doi:10.1093/mnras/stz2938 2020

  72. [73]

    P., Marcy, G

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

    doi:10.1086/588487 2008

  73. [74]

    C., & Parker, R

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

    doi:10.1093/mnras/stac2797 2022

  74. [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

    doi:10.3847/1538-3881/ad83a6 2024

  75. [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

    doi:10.1086/376395 2003

  76. [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

    doi:10.2458/azu 2014

  77. [79]

    H., & Sigurdsson, S

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

    doi:10.1086/340291 2002

  78. [80]

    H., & Sigurdsson, S

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

    doi:10.1086/523103 2007

  79. [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

    doi:10.3847/1538-3881/aa5eaa 2017

  80. [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

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

Showing first 80 references.