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A potential exomoon from the predicted planet obliquity of $\beta$ Pictoris b

T0 review · 1 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The likely misalignment of β Pictoris b's spin axis points to a Neptune-mass exomoon driving a secular spin-orbit resonance.

desk verdict A clean forward-model application of spin-orbit resonance to β Pic b, with one significant untested geometry assumption. read the letter →

arxiv 2412.05988 v1 pith:VKP2QQLU submitted 2024-12-08 astro-ph.EP

Michael Poon , Hanno Rein , Dang Pham This is my paper · ORCID
classification astro-ph.EP
keywords planetobliquityexomoonsecularspin-orbitresonanceβPictorisbspin-axisprecessionnodalregressionJWSTLaplaceradius
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

The paper predicts that β Pictoris b, the outer planet in the first extrasolar multiplanet system to have its obliquity measured, will likely turn out to have a misaligned spin axis. It argues that a large obliquity is hard to produce by collision (Safronov number $\sim 65$) or by the two-planet secular spin-orbit resonance acting alone, because the spin precession timescale is about 300 times longer than the nodal regression timescale. The central claim is that an exomoon of roughly Neptune mass on a circular, equatorial orbit at $40$–$70$ planet radii can shorten the spin precession timescale enough to enter resonance and excite the obliquity to about $60^\circ$ within 1 Myr. If a nonzero obliquity is measured, that would be indirect evidence for such an exomoon, and the mechanism is argued to apply to other multiplanet systems.

What carries the argument

The load-bearing mechanism is a secular spin-orbit resonance between the planet's spin-axis precession and the nodal regression of the two-planet system. The key timescale ratio is $T_\alpha/T_g$, which must be near unity for resonance; the exomoon's role is to shorten $T_\alpha$ by acting as a lever that effectively extends the planet's equatorial bulge. The enhancement factor $f_\alpha$ for a single equatorial satellite, together with the Laplace radius that separates inner spin-coupled from outer weakly coupled satellite orbits, defines the viable moon parameter space. The analytic equations are verified with direct N-body integration.

What would settle it

A JWST obliquity measurement that constrains β Pictoris b's true obliquity to be close to zero within a few degrees would falsify the claim that a Neptune-mass equatorial exomoon at 40–70 planet radii is currently exciting a large obliquity, because the model predicts a rise to roughly $60^\circ$ in 1 Myr. A null search for the predicted $3$–$7\%$ transit over several weeks would weaken, but not fully falsify, the scenario, since the moon's orbital plane could be inclined to the line of sight.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a concrete dynamical pathway. Without a satellite, β Pictoris b's spin-axis precession timescale is $T_\alpha \simeq 9\,\mathrm{Myr}$ while the orbital nodal regression driven by β Pictoris c is $T_g \simeq 30\,000\,\mathrm{yr}$, so the ratio $T_\alpha/T_g \approx 300$ prevents secular spin-orbit resonance. A single equatorial exomoon with mass $\gtrsim 15\,M_\oplus$ on a circular orbit at semimajor axis $0.03$–$0.05\,\mathrm{au}$ ($40$–$70$ planet radii) enhances the spin precession by a factor $f_\alpha \sim 300$, bringing the system into resonance. Integration of the spin-axis equations and matching N-body simulations show the obliquity rising from $0^\circ$ to $\sim 60^\circ$ within 1 Myr. The paper therefore claims that a future nonzero obliquity measurement of β Pictoris b would be consistent with, and possibly explained by, a Neptune-mass exomoon, and that exomoon-induced obliquity excitation is a general mechanism.

Load-bearing premise

The argument assumes that β Pictoris b hosts a Neptune-mass exomoon on a circular, equatorial orbit at 40–70 planet radii, a moon that has not been observed and whose formation is uncertain.

Editorial extensions

If this is right

  • If the JWST rotation-period measurement shows β Pictoris b spinning at $\gtrsim 30\%$ of break-up velocity, the paper's posterior analysis implies a large obliquity is the only physical possibility.
  • A nonzero obliquity detection would make a Neptune-mass exomoon at $40$–$70$ planet radii a plausible explanation and would motivate follow-up searches for its transit.
  • An aligned exomoon orbit with the required parameters would produce a $3$–$7\%$ transit depth with a $3$–$7$ week orbital period, potentially observable with JWST.
  • Collisional tilting is disfavoured by the high Safronov number ($\sim 65$), so resonance crossing is the more viable path considered.
  • The same exomoon-driven resonance argument applies to other multiplanet systems, making planet obliquity a potential indirect probe of massive exomoons.

Reading between the lines

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

  • If the measured obliquity comes out close to zero, the proposed moon configuration would be ruled out, but a large obliquity could still arise through other channels, such as a recent giant impact or stellar flyby, which the paper argues are less probable.
  • The mechanism suggests a follow-up strategy: time-resolved photometry of β Pictoris b should be searched specifically for a recurring $3$–$7\%$ dimming with a $3$–$7$ week period; detecting such a transit would strongly support the resonance scenario.
  • Because the viable exomoon must sit near or beyond the Laplace radius with a moon-to-planet mass ratio $\gtrsim 6\times10^{-3}$, a confirmed tilting moon would favour capture or giant-impact origins over standard in-situ accretion, a connection the paper raises but does not resolve.
  • The appendix shows that outward migration of β Pictoris c can also drive resonance capture, so an obliquity measurement alone would not uniquely prove an exomoon; combining obliquity with a transit or direct imaging detection would settle the interpretation.
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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

1 major / 3 minor

Summary. Motivated by the upcoming JWST measurement of the rotation period of β Pictoris b, the paper combines simulated rotation periods with published v sin i and orbital data to predict that the planet's obliquity is likely misaligned. It then investigates collisions and secular spin-orbit resonance as possible mechanisms. Collisions are argued to be unlikely from the large Safronov number. For the resonance channel, the paper shows that without a moon the spin precession timescale is about 300 times too long to match the nodal regression timescale, and that an equatorial exomoon of roughly Neptune mass at 40–70 planet radii provides the required enhancement f_α ≈ 300. Analytic evolution with the coupled spin–moon equations is verified with REBOUND/REBOUNDx N-body simulations, giving maximum obliquities up to ~60° within 1 Myr. The paper discusses formation pathways for such a massive moon and the prospects of detecting it via transits.

Significance. If the JWST measurement returns a nonzero obliquity, this paper provides a concrete, falsifiable scenario: a Neptune-mass exomoon at ~40–70 planet radii. The analytic framework is standard, the forward model is not circular (moon parameters are derived from the resonance condition rather than fitted), and the N-body verification strengthens the numerical claim. The prediction is new for an extrasolar multiplanet system and could motivate targeted exomoon searches. However, the exomoon is an invented entity with no direct evidence, and the robustness of the mechanism to non-ideal initial conditions is not demonstrated.

major comments (1)
  1. [§3.4, Figure 7] All analytic and N-body results initialize the exomoon on a circular orbit with its orbit normal aligned with the planet spin axis, explicitly stated in §3.4: 'The exomoon is initialized on a circular orbit having an orbit normal aligned with the planet spin axis.' No sensitivity test is provided for the initial mutual inclination between the moon orbit and the spin axis. Since Section 4 acknowledges that capture and giant-impact formation generically produce inclined and often eccentric satellite orbits (with Triton as the obvious Solar System analog), it is important to quantify how the maximum obliquity depends on this initial inclination. Please provide simulations or analytic estimates for initial moon inclinations of, e.g., 0°, 10°, 20°, and 30° (and ideally a modest initial eccentricity) to determine whether the ~60° obliquity excitation is robust or an upper bound tied to optimal alignment. Without such a test, the inferred connection between a future nonzero obliquity measurement and the presence of a large exomoon is much weaker than the abstract suggests.
minor comments (3)
  1. [§5 (Conclusions)] In item 3, 'This exomoon needs to be have at least one Neptune-mass' should read 'needs to have a mass of at least that of Neptune' or similar; this is a grammatical slip that should be corrected.
  2. [§4 (Discussion)] The phrase 'the viable range of moon semimajor axis is ∼ 40 − 70 planet radius' should use the plural 'planet radii'.
  3. [Abstract] The wording 'a nonzero obliquity detection of β Pictoris b implies that it may host a large exomoon' is stronger than the body supports, since the paper itself notes that collisions and secular spin-orbit resonance from other perturbations are also possible (though it argues they are less likely for this system). Rephrasing to 'would be consistent with' or 'could indicate' would better match the actual logical status of the claim.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the exomoon parameters are forward-modeled from the resonance condition, and the central claim rests on external dynamics and N-body verification.

full rationale

The derivation chain is self-contained. Section 3.2 computes the nodal regression timescale T_g from published beta Pictoris b/c parameters and the bare spin precession timescale T_alpha, finding T_alpha/T_g ~ 300. To reach resonance the paper requires f_alpha ~ 300 (Eqs. 9-10) and then scans exomoon mass and semimajor axis as free parameters; the maximum obliquity is obtained by integrating Eq. (11) or Eqs. (15)-(16) and is verified with REBOUND N-body simulations. No quantity is fitted to the obliquity being 'predicted': the moon parameters are not derived from an obliquity measurement but from the independent resonance condition, and the resulting obliquity is a dynamical output of the chosen initial conditions. The self-citations (Poon et al. 2024 for the posterior methodology; Rein & Liu 2012, Rein & Spiegel 2015, Pham et al. 2024, Tamayo et al. 2020, Lu et al. 2023 for numerical tools) are code/tool or statistical-methodology citations and are not load-bearing for the central exomoon-obliquity claim, which rests on standard Laplace-Lagrange and spin-axis precession equations from the external literature (Ward & Hamilton 2004; Tremaine 1991; Millholland & Batygin 2019). The authors also explicitly acknowledge the formation uncertainty of a Neptune-mass moon in Section 4, which is a physical plausibility concern, not a circularity. Therefore no step in the argument reduces by construction to its own inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central mechanism depends on assumed values for k2, C, and R, and on a hypothetical exomoon with a specific initial configuration. These are clearly stated assumptions, not hidden fits.

free parameters (3)
  • Love number k2 = 0.6
    Chosen to match Jupiter's Love number (Lai 2021), used in alpha0 calculation (Eq. 7).
  • Normalized moment of inertia C = 0.2
    Assumed typical for giant planets, used in alpha0 and f_alpha.
  • Planet radius R = 1.6 RJup
    Chosen as middle of range from Kammerer et al. 2024 (1.4-1.9 RJup), affects breakup velocity and transit depth.
assumptions (5)
  • standard math The spin-axis precession equations (Ward & Hamilton 2004, Eq. 11) correctly describe the system.
    Used throughout Section 3; standard celestial mechanics.
  • standard math The Laplace-Lagrange nodal regression frequency g_LL (Eq. 4) for a two-planet system is valid at the assumed circular orbits.
    Equation 4 from Millholland & Laughlin 2019.
  • ad hoc to paper The exomoon is initially on a circular equatorial orbit around the planet.
    Stated in Section 3.4; necessary for resonance, fine-tuned.
  • domain assumption The planet and moon share the same nodal regression rate g.
    Approximation stated in Section 3.3, justified by the satellite being bound to the planet.
  • domain assumption Both beta Pictoris b and c are on circular orbits for the secular calculations.
    Stated in Section 3.2 and Appendix A; argued not significant because eccentricity evolves faster than resonance timescale.
invented entities (1)
  • Neptune-mass exomoon around beta Pictoris b
    purpose: To enhance the planet's spin precession rate and enable secular spin-orbit resonance, exciting a large obliquity
    The paper postulates this moon to explain a potential high obliquity. No direct detection; the predicted transit is contingent and low-probability. No independent evidence outside the paper.

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Cite this review

Pith. "Pith review of A potential exomoon from the predicted planet obliquity of $\beta$ Pictoris b." pith.science (2026). https://pith.science/paper/VKP2QQLU

@misc{pith2026241205988,
  author       = {Pith},
  title        = {Pith review of: A potential exomoon from the predicted planet obliquity of $\beta$ Pictoris b},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VKP2QQLU}},
  note         = {Machine review of arXiv:2412.05988}
}
abstract

Planet obliquity is the alignment or misalignment of a planet spin axis relative to its orbit normal. In a multiplanet system, this obliquity is a valuable signature of planet formation and evolutionary history. The young $\beta$ Pictoris system hosts two coplanar super-Jupiters and upcoming JWST observations of this system will constrain the obliquity of the outer planet, $\beta$ Pictoris b. This will be the first planet obliquity measurement in an extrasolar, multiplanet system. First, we show that this new planet obliquity is likely misaligned by using a wide range of simulated observations in combination with published measurements of the system. Motivated by current explanations for the tilted planet obliquities in the Solar System, we consider collisions and secular spin-orbit resonances. While collisions are unlikely to occur, secular spin-orbit resonance modified by the presence of an exomoon around the outer planet can excite a large obliquity. The largest induced obliquities ($\sim 60^\circ$) occur for moons with at least a Neptune-mass and a semimajor axis of $0.03-0.05~\mathrm{au}$ ($40-70$ planet radii). For certain orbital alignments, such a moon may observably transit the planet (transit depth of $3-7\%$, orbital period of $3-7$ weeks). Thus, a nonzero obliquity detection of $\beta$ Pictoris b implies that it may host a large exomoon. Although we focus on the $\beta$ Pictoris system, the idea that the presence of exomoons can excite high obliquities is very general and applicable to other exoplanetary systems.

Figures

Figures reproduced from arXiv: 2412.05988 by the authors.

Figure 1
Figure 1. Schematic diagram of planet obliquity outcomes for β Pictoris b in the limit of an exactly pole-on (Case 1, top) or edge-on (Case 2, bottom) spin axis along our line of sight. In Case 1, if β Pictoris b spins fast (i.e. v ≫ v sin ip), the resulting spin axis inclination ip ∼ 0 ◦ implies a misaligned planet obliquity. In Case 2, if β Pictoris b spins slow (i.e. v ∼ v sin ip), the spin axis and orbit normal both lie i… view at source ↗
Figure 2
Figure 2. Schematic diagram (not to scale) of four angular momentum vectors in the β Pictoris system: total angular momentum (Lˆ), orbital angular momentum of planets b and c (nˆorbit,b, nˆorbit,c), and the spin vector of planet b (nˆspin,b). The mutual inclination between nˆorbit,b and nˆorbit,c is ∼ 1 ◦. Secular spin-orbit resonance can occur when the period of orbit nodal regression (path along grey dotted circle on the le… view at source ↗
Figure 3
Figure 3. Posterior distributions of the measured projected equatorial velocity v sin ip for β Pictoris b in black and black dotted. In color are deprojected equatorial velocities v = 2πR Prot , assuming R = 1.6 ± 0.2 RJup and simulated rotation period measurements. 0 20 40 60 80 100 120 140 160 180 Planet Spin-axis Inclination ip [degrees] 0.00 0.02 0.04 0.06 0.08 Probability Density Prot = 19.8 hr (10% break-up vel.) Prot =… view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: Top panel: Normalized posterior distributions for the planet obliquity assuming various rotation period measurements, and using a randomly oriented prior (black), which is uniform in cos ψ. Bottom panel: Same as top panel, but with a different prior (dashed black). Thi…
Figure 4
Figure 4. Figure 4: Top panel: Posterior distributions of spin axis inclination ip for β Pictoris b assuming various rotation period measurements. These distributions are compared to a random inclination distribution (black), which is uniform distribution in cos ip. In contrast, the orbit…
Figure 6
Figure 6. Figure 6: Top panel: Phase portrait of planet spin-axis libration (i.e. obliquity evolution) where the planet orbit normal is centred at (0, 0). The precession angle is the angle between the projections of the planet spin axis and invariable plane normal onto the plane of the pl…
Figure 7
Figure 7. Figure 7: Maximum obliquity over 1 Myr for various exomoon parameters. Left: Following spin-axis equations of motion for an equatorial exomoon. Middle: Following more general spin-axis equations of motion for a non-equatorial exomoon. Here, the planet spin axis evolution is deco…
Figure 8
Figure 8. Figure 8: Left: As β Pictoris c migrates outwards from 2.4 au to present-day 2.7 au over a timescale of 5 Myr, the nodal regression timescale Tg increases. Middle: Simultaneously, β Pictoris b becomes captured into a secular spin-orbit resonance, and its planet obliquity is exci…

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Works this paper leans on

51 extracted references · 11 canonical work pages

  1. [1]

    2020, AJ, 159, 217, doi: 10.3847/1538-3881/ab83f0

    Bailey, N., & Fabrycky, D. 2020, AJ, 159, 217, doi: 10.3847/1538-3881/ab83f0

    doi:10.3847/1538-3881/ab83f0 2020

  2. [2]

    G., & Giles, P

    Beck, J. G., & Giles, P. 2005, ApJL, 621, L153, doi: 10.1086/429224

    doi:10.1086/429224 2005

  3. [3]

    M., Brandt, T

    Brandt, G. M., Brandt, T. D., Dupuy, T. J., Li, Y., & Michalik, D. 2021, AJ, 161, 179, doi:10.3847/1538-3881/abdc2e

    doi:10.3847/1538-3881/abdc2e 2021

  4. [4]

    Bowler, B. P. 2018, Nature Astronomy, 2, 138, doi: 10.1038/s41550-017-0325-8

    doi:10.1038/s41550-017-0325-8 2018

  5. [5]

    L., Chiang, E., Morley, C

    Bryan, M. L., Chiang, E., Morley, C. V., Mace, G. N., & Bowler, B. P. 2021, AJ, 162, 217, doi:10.3847/1538-3881/ac1bb1

    doi:10.3847/1538-3881/ac1bb1 2021

  6. [6]

    L., Ginzburg, S., Chiang, E., et al

    Bryan, M. L., Ginzburg, S., Chiang, E., et al. 2020a, ApJ, 905, 37, doi: 10.3847/1538-4357/abc0ef

    doi:10.3847/1538-4357/abc0ef

  7. [7]

    L., Chiang, E., Bowler, B

    Bryan, M. L., Chiang, E., Bowler, B. P., et al. 2020b, AJ, 159, 181, doi: 10.3847/1538-3881/ab76c6

    doi:10.3847/1538-3881/ab76c6

  8. [8]

    M., & Ward, W

    Canup, R. M., & Ward, W. R. 2006, Nature, 441, 834, doi: 10.1038/nature04860

    doi:10.1038/nature04860 2006

Show all 51 references
  1. [9]

    2022, MNRAS, 516, 3701, doi: 10.1093/mnras/stac2090

    Cassese, B., & Kipping, D. 2022, MNRAS, 516, 3701, doi: 10.1093/mnras/stac2090

    2022 doi

  2. [10]

    J., et al

    Chilcote, J., Pueyo, L., De Rosa, R. J., et al. 2017, AJ, 153, 182, doi: 10.3847/1538-3881/aa63e9

    2017 doi

  3. [11]

    2018, MNRAS, 480, 4355, doi: 10.1093/mnras/sty2163

    Cilibrasi, M., Szulágyi, J., Mayer, L., et al. 2018, MNRAS, 480, 4355, doi: 10.1093/mnras/sty2163

    2018 doi

  4. [12]

    1993, Science, 259, 350, doi: 10.1126/science.259.5093.350

    Dones, L., & Tremaine, S. 1993, Science, 259, 350, doi: 10.1126/science.259.5093.350

    1993 doi

  5. [13]

    C., Johnson, E

    Fabrycky, D. C., Johnson, E. T., & Goodman, J. 2007, ApJ, 665, 754, doi: 10.1086/519075

    2007 doi

  6. [14]

    P., & Ward, W

    Hamilton, D. P., & Ward, W. R. 2004, AJ, 128, 2510, doi: 10.1086/424534

    2004 doi

  7. [15]

    2010, MNRAS, 404, 475, doi: 10.1111/j.1365-2966.2010.16309.x

    Johansen, A., & Lacerda, P. 2010, MNRAS, 404, 475, doi: 10.1111/j.1365-2966.2010.16309.x

    2010

  8. [16]

    D., et al

    Kammerer, J., Lawson, K., Perrin, M. D., et al. 2024, AJ, 168, 51, doi: 10.3847/1538-3881/ad4ffe

    2024 doi

  9. [17]

    A., Teodoro, L

    Kegerreis, J. A., Teodoro, L. F. A., Eke, V. R., et al. 2018, ApJ, 861, 52, doi:10.3847/1538-4357/aac725

    2018 doi

  10. [18]

    A., Mellon, S

    Kenworthy, M. A., Mellon, S. N., Bailey, J. I., et al. 2021, A&A, 648, A15, doi:10.1051/0004-6361/202040060

    2021 doi

  11. [19]

    2022, Nature Astronomy, 6, 367, doi:10.1038/s41550-021-01539-1

    Kipping, D., Bryson, S., Burke, C., et al. 2022, Nature Astronomy, 6, 367, doi:10.1038/s41550-021-01539-1

    2022 doi

  12. [20]

    2020, ApJL, 897, L8, doi: 10.3847/2041-8213/ab9d27

    Kraus, S., Le Bouquin, J.-B., Kreplin, A., et al. 2020, ApJL, 897, L8, doi: 10.3847/2041-8213/ab9d27

    2020 doi

  13. [21]

    2021, The Planetary Science Journal, 2, 122, doi: 10.3847/PSJ/ac013b

    Lai, D. 2021, The Planetary Science Journal, 2, 122, doi: 10.3847/PSJ/ac013b

    2021 doi

  14. [22]

    Landman, R., Stolker, T., Snellen, I. A. G., et al. 2024, A&A, 682, A48, doi:10.1051/0004-6361/202347846

    2024 doi

  15. [23]

    2024, arXiv e-prints, arXiv:2406.11644, doi: 10.48550/arXiv.2406.11644

    Liu, Q., Zhu, W., Zhou, Y., et al. 2024, arXiv e-prints, arXiv:2406.11644, doi: 10.48550/arXiv.2406.11644

    2024 doi arXiv

  16. [24]

    2022, The Planetary Science Journal, 3, 221, doi: 10.3847/PSJ/ac83c1

    Lu, T., & Laughlin, G. 2022, The Planetary Science Journal, 3, 221, doi: 10.3847/PSJ/ac83c1

    2022 doi

  17. [25]

    2024, arXiv e-prints, arXiv:2410.00641, doi: 10.48550/arXiv.2410.00641

    Lu, T., Li, G., Cassese, B., & Lin, D. 2024, arXiv e-prints, arXiv:2410.00641, doi: 10.48550/arXiv.2410.00641

    2024 doi arXiv

  18. [26]

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

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

    2023 doi

  19. [27]

    E., & Bell, C

    Mamajek, E. E., & Bell, C. P. M. 2014, MNRAS, 445, 2169, doi: 10.1093/mnras/stu1894

    2014 doi

  20. [28]

    Masuda, K., & Winn, J. N. 2020, AJ, 159, 81, doi: 10.3847/1538-3881/ab65be

    2020 doi

  21. [29]

    A., Heinze, A., Apai, D., et al

    Metchev, S. A., Heinze, A., Apai, D., et al. 2015, ApJ, 799, 154, doi: 10.1088/0004-637X/799/2/154

    2015 doi

  22. [30]

    2019, ApJ, 876, 119, doi: 10.3847/1538-4357/ab19be

    Millholland, S., & Batygin, K. 2019, ApJ, 876, 119, doi: 10.3847/1538-4357/ab19be

    2019 doi

  23. [31]

    2019, Nature Astronomy, 3, 424, doi: 10.1038/s41550-019-0701-7

    Millholland, S., & Laughlin, G. 2019, Nature Astronomy, 3, 424, doi: 10.1038/s41550-019-0701-7

    2019 doi

  24. [32]

    A., & Vieira Neto, E

    Moraes, R. A., & Vieira Neto, E. 2020, MNRAS, 495, 3763, doi: 10.1093/mnras/staa1441

    2020 doi

  25. [33]

    M., Males, J

    Morzinski, K. M., Males, J. R., Skemer, A. J., et al. 2015, ApJ, 815, 108, doi:10.1088/0004-637X/815/2/108

    2015 doi

  26. [34]

    D., & Dermott, S

    Murray, C. D., & Dermott, S. F. 1999, Solar System Dynamics, doi: 10.1017/CBO9781139174817

    1999 doi

  27. [35]

    W., Liu, B., & Schoonenberg, D

    Ormel, C. W., Liu, B., & Schoonenberg, D. 2017, A&A, 604, A1, doi: 10.1051/0004-6361/201730826

    2017 doi

  28. [36]

    2023, A&A, 670, A90, doi:10.1051/0004-6361/202244294

    Palma-Bifani, P., Chauvin, G., Bonnefoy, M., et al. 2023, A&A, 670, A90, doi:10.1051/0004-6361/202244294

    2023 doi

  29. [37]

    T., Birkby, J

    Parker, L. T., Birkby, J. L., Landman, R., et al. 2024, MNRAS, 531, 2356, doi:10.1093/mnras/stae1277

    2024 doi

  30. [38]

    Pham, D., Rein, H., & Spiegel, D. S. 2024, The Open Journal of Astrophysics, 7, 1, doi:10.21105/astro.2401.02849

    2024 arXiv

  31. [39]

    L., Rein, H., et al

    Poon, M., Bryan, M. L., Rein, H., et al. 2024, arXiv e-prints, arXiv:2410.02672, doi: 10.3847/1538-3881/ad84e5

    2024 arXiv

  32. [40]

    Rein, H., & Liu, S. F. 2012, A&A, 537, A128, doi: 10.1051/0004-6361/201118085

    2012 doi

  33. [41]

    Rein, H., & Spiegel, D. S. 2015, MNRAS, 446, 1424, doi: 10.1093/mnras/stu2164

    2015 doi

  34. [42]

    Safronov, V. S. 1966, Soviet Ast., 9, 987

    1966

  35. [43]

    2021a, Nature Astronomy, 5, 345, doi: 10.1038/s41550-020-01284-x

    Saillenfest, M., Lari, G., & Boué, G. 2021a, Nature Astronomy, 5, 345, doi: 10.1038/s41550-020-01284-x

    doi

  36. [44]

    2021b, A&A, 647, A92, doi:10.1051/0004-6361/202039891

    Saillenfest, M., Lari, G., Boué, G., & Courtot, A. 2021b, A&A, 647, A92, doi:10.1051/0004-6361/202039891

    doi

  37. [45]

    Tamayo, D., Rein, H., Shi, P., & Hernandez, D. M. 2020, MNRAS, 491, 2885, doi:10.1093/mnras/stz2870

    2020 doi

  38. [46]

    Teachey, A., & Kipping, D. M. 2018, Science Advances, 4, eaav1784, doi: 10.1126/sciadv.aav1784

    2018 doi

  39. [47]

    2020, A&A, 635, A59, doi:10.1051/0004-6361/201937325

    Timmermann, A., Heller, R., Reiners, A., & Zechmeister, M. 2020, A&A, 635, A59, doi:10.1051/0004-6361/201937325

    2020 doi

  40. [48]

    Tokadjian, A., & Piro, A. L. 2022, ApJL, 929, L2, doi: 10.3847/2041-8213/ac61e8

    2022 doi

  41. [49]

    1991, Icarus, 89, 85, doi: 10.1016/0019-1035(91)90089-C —

    Tremaine, S. 1991, Icarus, 89, 85, doi: 10.1016/0019-1035(91)90089-C —. 2023, Dynamics of Planetary Systems

    1991 doi

  42. [50]

    R., & Hamilton, D

    Ward, W. R., & Hamilton, D. P. 2004, AJ, 128, 2501, doi: 10.1086/424533

    2004 doi

  43. [51]

    2022, Science, 377, 1285, doi: 10.1126/science.abn1234 This paper was built using the Open Journal of Astrophysics LATEX template

    Wisdom, J., Dbouk, R., Militzer, B., et al. 2022, Science, 377, 1285, doi: 10.1126/science.abn1234 This paper was built using the Open Journal of Astrophysics LATEX template. The OJA is a journal which provides fast and easy peer review for new papers in the astro-ph section o...

    2022 doi

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