Pith. sign in

REVIEW 92 references

Capture and Escape of Planetary Mean-motion Resonances in Turbulent Discs

T0 review · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Active disc turbulence raises equilibrium eccentricities and overstability growth rates in mean-motion resonances, causing migrating planet pairs to escape toward tighter resonances.

arxiv 2505.13952 v1 pith:VOIFRGBO submitted 2025-05-20 astro-ph.EP

Yi-Xian Chen , Yinhao Wu , Ya-Ping Li , Douglas N. C. Lin , Richard Alexander , Sergei Nayakshin , Fei Dai This is my paper · ORCID
classification astro-ph.EP
keywords pairsplanetdiscmigrationmmrsresonanceturbulencecapture
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

Planets embedded in a gas disc can migrate inward, and if two planets approach each other slowly, they often get trapped in a mean-motion resonance, a configuration where their orbital periods form a tidy ratio such as 3:2. Whether the pair stays trapped depends on how strongly the disc stirs their orbits. In this paper, the authors run two-dimensional hydrodynamic simulations of a super-Earth pair migrating in a protoplanetary disc, comparing a smooth, viscous disc with a disc stirred by a stochastic turbulence model.

In the smooth disc, the pair reliably locks into the 3:2 resonance and stays there, regardless of the viscosity level. In the turbulent disc, the same pair is pushed out of the 3:2 and then the 4:3 resonance, each time resuming inward migration until it reaches a closer, tighter resonance. The reason is that turbulence sustains higher orbital eccentricities, which makes the resonant angle librate with growing amplitude until the resonance breaks. The authors quantify this with the overstability growth rate s, which is positive in the turbulent runs and negative in the laminar runs.

The libration offsets produced in the simulations are about 0.5 percent, smaller than the 1 to 3 percent spread seen in TESS data. The authors therefore conclude that turbulence alone does not explain the observed offsets and that later dynamical processes must amplify them. The main caveat is that the turbulence is a phenomenological stirring potential, not a full magnetohydrodynamic calculation, so the quantitative strength of the effect for real discs remains uncertain.

Extended reading notes

Core claim

Near-quote from the Abstract: 'realistic turbulence enhances overstability by sustaining higher equilibrium eccentricities and a positive growth rate in libration amplitude, ultimately leading to resonance escape.' Concretely, in the authors' FARGO3D runs the laminar disc captures the pair into a stable 3:2 MMR for alpha = 1e-3 to 1e-1, while with the turbulent forcing the same pair escapes the 3:2 and 4:3 MMRs and reaches the 5:4 MMR (and would, per the authors' inference, escape even the 5:4 at <alpha> = 1e-1). If the paper is correct, active turbulence broadens the overstability parameter space and yields more closely packed resonant pairs than laminar migration.

Load-bearing premise

The load-bearing premise is that the stochastic potential of Eqs 1-2, with the <alpha> ~ 35(gamma/h0)^2 calibration of Eq 3, faithfully reproduces the torque and eccentricity-damping effects of MRI/GI turbulence on a resonant planet pair. This premise enters at Section 2 and is explicitly qualified in Section 5 ('this treatment of active turbulence still differs from realistic MRI and GI generated from simulations incorporating magnetic fields and self-gravity'). If real turbulence damps eccentricities more strongly than the stirring potential, the positive growth rates and resonance escapes seen here would not occur in real discs. This is a modeling assumption, distinct from the claim that the simulated turbulent runs escape.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on two chosen turbulence amplitudes, one fiducial disc mass, and a phenomenological turbulence model. No new physical entities are introduced. The main modeling assumptions are the stochastic potential (Eq 1-2) and the alpha calibration (Eq 3), both flagged in the paper's own limitations paragraph.

free parameters (4)
  • turbulence amplitude gamma (weak and strong) = 1.6e-4 and 1.6e-3
    Chosen by hand to map to effective <alpha> = 1e-3 and 1e-1 through the calibration <alpha> ~ 35(gamma/h0)^2 (Eq 3, from Baruteau & Lin 2010). The central comparison between weak and strong turbulence rests on these amplitudes; the mapping is a prior calibration, not fitted to the resonance outcome.
  • initial disc surface density normalization Sigma0 = 2e-5 (M_sun/r0^2)
    Chosen so that migration is slow enough for 3:2 capture (fiducial); the heavier disc run (Sigma0=1e-4, Appendix A) deliberately bypasses capture. The escape behavior is probed only at this one disc mass, so the generality of 'turbulence broadens parameter space' depends on this choice.
  • initial outer planet radius r2 for turbulent runs = 1.35 r0 (laminar runs use 1.4 r0)
    Chosen to start just outside the 3:2 MMR. The slightly different starting separation between laminar and turbulent runs is a minor ad hoc input that could affect the capture phase, though both start outside the resonance.
  • planet-to-star mass ratios q1, q2 = 5e-6 and 1.5e-5 (1.7 and 5 M_earth)
    Chosen as representative of super-Earth pairs; the overstability criterion depends on q relative to h^3, so the conclusion may be specific to this mass range. No mass sampling is performed.
assumptions (5)
  • domain assumption The stochastic potential in Eqs 1-2 reproduces the dynamical effect of MRI/GI turbulence on planets.
    Section 2. The turbulence is a phenomenological stirring potential (Laughlin et al. 2004; Baruteau & Lin 2010), not self-consistent MHD. The paper's own Section 5 cautions that realistic MRI/GI simulations 'may not necessarily yield the same quantitative results.'
  • domain assumption Calibration <alpha> ~ 35(gamma/h0)^2 (Eq 3) is accurate for the adopted disc parameters.
    Section 2. This mapping from prior work translates gamma into effective viscosity; if the calibration is off, the quoted <alpha> values (and hence the comparison with observational alpha constraints) shift, though the weak/strong contrast remains.
  • domain assumption The locally isothermal, 2D, non-self-gravitating disc model sufficiently captures resonance capture physics.
    Section 2. Vertical stratification, cooling, and self-gravity are neglected; the model is standard for Type I migration but omits 3D effects that could modify eccentricity damping.
  • standard math Goldreich & Schlichting (2014) overstability theory (Eqs 8-9), with f_j order-unity coefficients, applies to the simulated resonant pairs.
    Section 4. The growth rate s and libration frequency omega are computed with this theory; the direct fits in Figure 11 test but do not derive it.
  • standard math Equilibrium eccentricity formula of Terquem & Papaloizou (2019), Eq 6, provides a valid benchmark for the measured e_eq.
    Section 4. The paper notes the formula overestimates e_eq for turbulent discs, indicating it may not capture all nonlinear feedback, so this axiom is partially undercut by the paper's own data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Capture and Escape of Planetary Mean-motion Resonances in Turbulent Discs." pith.science (2026). https://pith.science/paper/VOIFRGBO

@misc{pith2026250513952,
  author       = {Pith},
  title        = {Pith review of: Capture and Escape of Planetary Mean-motion Resonances in Turbulent Discs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VOIFRGBO}},
  note         = {Machine review of arXiv:2505.13952}
}
read the original abstract

Mean-motion resonances (MMRs) form through convergent disc migration of planet pairs, which may be disrupted by dynamical instabilities after protoplanetary disc (PPD) dispersal. This scenario is supported by recent analysis of TESS data showing that neighboring planet pairs in younger planetary systems are closer to resonance. To study stability of MMRs during migration, we perform hydrodynamical simulations of migrating planet pairs in PPDs, comparing the effect of laminar viscosity and realistic turbulence. We find stable 3:2 resonance capture for terrestrial planet pairs migrating in a moderately massive PPD, insensitive to a range of laminar viscosity (alpha = 0.001 to 0.1). However, realistic turbulence enhances overstability by sustaining higher equilibrium eccentricities and a positive growth rate in libration amplitude, ultimately leading to resonance escape. The equilibrium eccentricity growth rates decrease as planets migrate into tighter and more stable 4:3 and 5:4 MMRs. Our results suggest that active disc turbulence broadens the parameter space for overstability, causing planet pairs to end up in closer-in orbital separations. Libration within MMR typically lead to deviation from exact period ratio |Delta| \sim 0.5%, which alone is insufficient to produce the typical dispersion of |Delta| \sim 1 to 3% in TESS data, suggesting that post migration dynamical processes are needed to further amplify the offset.

Figures

Figures reproduced from arXiv: 2505.13952 by the authors.

Figure 1
Figure 1. The three panels illustrate simulation results for our fiducial case (with 𝛼 = 1 × 10−3 and Σ0 = 2 × 10−5 , as shown in the title). From top to bottom panel, we show time evolution of different orbital parameters: the radial positions of P1 (blue) and P2 (red); the period ratio between P1 and P2; the eccentricities of P1 and P2. The time axis is expressed in units of the dynamical timescale at P1’s initial position … view at source ↗
Figure 2
Figure 2. Typical surface density distribution for the fiducial case near the end of the simulation, where the planet pairs have captured into a 3:2 MMR. We use blue and red "x" symbols to indicate the positions of the inner (P1) and outer (P2) planets, respectively. 0.02 0.01 0.00 0.01 0.02 e1cos Q 0.02 0.01 0.00 0.01 0.02 e 1 sin Q = 1 × 10 3 , 3 : 2 MMR 7 8 9 10 11 12 Tim e (1 0 4 1 0 ) [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 4
Figure 4. Similar to [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: Similar to [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 7
Figure 7. Figure 7: Time evolution of the resonance angle phase space of the inner planet for our weak turbulent model 𝛾 = 1.6 × 10−4 . The three panels from left to right represent the periods when the planet pair become captured into (and escape out of, for unstable capture) the 3:2 MMR…
Figure 8
Figure 8. Figure 8: Similar to [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: Measured average eccentricity of P1 during MMRs for all our simulations, plotted against estimate from the classical laminar context (blue dotted line), as well as combining Equation 6 with 𝜏𝑒1 /𝜏𝑎 ∼ 0.01 (orange dotted line) as a rough estimate for turbulent cases. pr…
Figure 10
Figure 10. Figure 10: The dimensionless growth rate calculated from average eccentric￾ity of P1 during MMRs for all our simulations, plotted against estimate from the classical laminar context (blue dotted line) which predicts laminar case to be stable. We also plot direct measurements for…
Figure 11
Figure 11. Figure 11: Best fits to the libration during MMRs with growth rates labeled for two turbulence runs. Run 𝛼 = 10−3 𝛼 = 10−1 𝛾 = 1.6 × 10−4 → ⟨𝛼⟩ = 10−3 𝛾 = 1.6 × 10−3 → ⟨𝛼⟩ = 10−1 resonance 3:2 3:2 3:2 4:3 5:4 3:2 4:3 5:4 ⟨𝑒1 ⟩ 0.018 0.018 0.029 0.025 0.014 0.028 0.025 0.020 ⟨𝑒2 …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

92 extracted references · 18 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...

  2. [2]

    Afkanpour Z., Ataiee S., Ziampras A., Penzlin A. B. T., Sfair R., Sch \"a fer C., Kley W., Schlichting H., 2024, @doi [ ] 10.1051/0004-6361/202348826 , https://ui.adsabs.harvard.edu/abs/2024A&A...686A.277A 686, A277

    doi:10.1051/0004-6361/202348826 2024

  3. [3]

    J., Herczeg G

    Alexander R., Rosotti G., Armitage P. J., Herczeg G. J., Manara C. F., Tabone B., 2023, @doi [ ] 10.1093/mnras/stad1983 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.524.3948A 524, 3948

    doi:10.1093/mnras/stad1983 2023

  4. [4]

    Ataiee S., Kley W., 2021, @doi [ ] 10.1051/0004-6361/202038772 , https://ui.adsabs.harvard.edu/abs/2021A&A...648A..69A 648, A69

    doi:10.1051/0004-6361/202038772 2021

  5. [5]

    Baruteau C., Lin D. N. C., 2010, @doi [ ] 10.1088/0004-637X/709/2/759 , https://ui.adsabs.harvard.edu/abs/2010ApJ...709..759B 709, 759

    doi:10.1088/0004-637x/709/2/759 2010

  6. [6]

    Batygin K., Morbidelli A., 2013, @doi [ ] 10.1088/0004-6256/145/1/1 , https://ui.adsabs.harvard.edu/abs/2013AJ....145....1B 145, 1

    doi:10.1088/0004-6256/145/1/1 2013

  7. [7]

    C., 2023, @doi [ ] 10.3847/2041-8213/acc015 , https://ui.adsabs.harvard.edu/abs/2023ApJ...946L..11B 946, L11

    Batygin K., Petit A. C., 2023, @doi [ ] 10.3847/2041-8213/acc015 , https://ui.adsabs.harvard.edu/abs/2023ApJ...946L..11B 946, L11

    doi:10.3847/2041-8213/acc015 2023

  8. [8]

    J., Simon J

    Beckwith K., Armitage P. J., Simon J. B., 2011, @doi [ ] 10.1111/j.1365-2966.2011.19043.x , https://ui.adsabs.harvard.edu/abs/2011MNRAS.416..361B 416, 361

    arXiv 2011

Show all 92 references
  1. [9]

    S., 2016, @doi [ ] 10.3847/0067-0049/223/1/11 , https://ui.adsabs.harvard.edu/abs/2016ApJS..223...11B 223, 11

    Ben \' tez-Llambay P., Masset F. S., 2016, @doi [ ] 10.3847/0067-0049/223/1/11 , https://ui.adsabs.harvard.edu/abs/2016ApJS..223...11B 223, 11

    2016 doi

  2. [10]

    S., Dullemond C

    Benz W., Ida S., Alibert Y., Lin D., Mordasini C., 2014, in Beuther H., Klessen R. S., Dullemond C. P., Henning T., eds, Protostars and Planets VI. pp 691--713 ( @eprint arXiv 1402.7086 ), @doi 10.2458/azu_uapress_9780816531240-ch030

    2014 arXiv

  3. [11]

    S., Tokunaga A

    Carr J. S., Tokunaga A. T., Najita J., 2004, @doi [ ] 10.1086/381356 , https://ui.adsabs.harvard.edu/abs/2004ApJ...603..213C 603, 213

    2004 doi

  4. [12]

    Chen Y.-X., Lin D. N. C., 2023, @doi [ ] 10.1093/mnras/stad992 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.522..319C 522, 319

    2023 doi

  5. [13]

    Chen Y.-X., Li Y.-P., Li H., Lin D. N. C., 2020, @doi [ ] 10.3847/1538-4357/ab9604 , https://ui.adsabs.harvard.edu/abs/2020ApJ...896..135C 896, 135

    2020 doi

  6. [14]

    Chiang E., Laughlin G., 2013, @doi [ ] 10.1093/mnras/stt424 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.431.3444C 431, 3444

    2013 doi

  7. [15]

    N., 2010, @doi [Annual Review of Earth and Planetary Sciences] 10.1146/annurev-earth-040809-152513 , https://ui.adsabs.harvard.edu/abs/2010AREPS..38..493C 38, 493

    Chiang E., Youdin A. N., 2010, @doi [Annual Review of Earth and Planetary Sciences] 10.1146/annurev-earth-040809-152513 , https://ui.adsabs.harvard.edu/abs/2010AREPS..38..493C 38, 493

    2010 doi

  8. [16]

    Choksi N., Chiang E., 2020, @doi [ ] 10.1093/mnras/staa1421 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.495.4192C 495, 4192

    2020 doi

  9. [17]

    Cleaver J., Hartmann L., Bae J., 2023, @doi [ ] 10.1093/mnras/stad1784 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.523.5522C 523, 5522

    2023 doi

  10. [18]

    Dai F., et al., 2023, @doi [ ] 10.3847/1538-3881/aca327 , https://ui.adsabs.harvard.edu/abs/2023AJ....165...33D 165, 33

    2023 doi

  11. [19]

    Dai F., et al., 2024, @doi [ ] 10.3847/1538-3881/ad83a6 , https://ui.adsabs.harvard.edu/abs/2024AJ....168..239D 168, 239

    2024 doi

  12. [20]

    M., Payne M., Holman M

    Deck K. M., Payne M., Holman M. J., 2013, @doi [ ] 10.1088/0004-637X/774/2/129 , https://ui.adsabs.harvard.edu/abs/2013ApJ...774..129D 774, 129

    2013 doi

  13. [21]

    B., Laskar J., 2014, @doi [ ] 10.1051/0004-6361/201424227 , https://ui.adsabs.harvard.edu/abs/2014A&A...570L...7D 570, L7

    Delisle J. B., Laskar J., 2014, @doi [ ] 10.1051/0004-6361/201424227 , https://ui.adsabs.harvard.edu/abs/2014A&A...570L...7D 570, L7

    2014 doi

  14. [22]

    Deng H., Mayer L., Meru F., 2017, @doi [ ] 10.3847/1538-4357/aa872b , https://ui.adsabs.harvard.edu/abs/2017ApJ...847...43D 847, 43

    2017 doi

  15. [23]

    Deng H., Mayer L., Latter H., 2020, @doi [ ] 10.3847/1538-4357/ab77b2 , https://ui.adsabs.harvard.edu/abs/2020ApJ...891..154D 891, 154

    2020 doi

  16. [24]

    J., Turner N

    Desch S. J., Turner N. J., 2015, @doi [ ] 10.1088/0004-637X/811/2/156 , https://ui.adsabs.harvard.edu/abs/2015ApJ...811..156D 811, 156

    2015 doi

  17. [25]

    C., et al., 2014, @doi [ ] 10.1088/0004-637X/790/2/146 , https://ui.adsabs.harvard.edu/abs/2014ApJ...790..146F 790, 146

    Fabrycky D. C., et al., 2014, @doi [ ] 10.1088/0004-637X/790/2/146 , https://ui.adsabs.harvard.edu/abs/2014ApJ...790..146F 790, 146

    2014 doi

  18. [26]

    Flaherty K., et al., 2020, @doi [ ] 10.3847/1538-4357/ab8cc5 , https://ui.adsabs.harvard.edu/abs/2020ApJ...895..109F 895, 109

    2020 doi

  19. [27]

    F., 1996, @doi [ ] 10.1086/176735 , https://ui.adsabs.harvard.edu/abs/1996ApJ...457..355G 457, 355

    Gammie C. F., 1996, @doi [ ] 10.1086/176735 , https://ui.adsabs.harvard.edu/abs/1996ApJ...457..355G 457, 355

    1996 doi

  20. [28]

    Garaud P., Lin D. N. C., 2007, @doi [ ] 10.1086/509041 , https://ui.adsabs.harvard.edu/abs/2007ApJ...654..606G 654, 606

    2007 doi

  21. [29]

    E., 2014, @doi [ ] 10.1088/0004-6256/147/2/32 , https://ui.adsabs.harvard.edu/abs/2014AJ....147...32G 147, 32

    Goldreich P., Schlichting H. E., 2014, @doi [ ] 10.1088/0004-6256/147/2/32 , https://ui.adsabs.harvard.edu/abs/2014AJ....147...32G 147, 32

    2014 doi

  22. [30]

    Goldreich P., Tremaine S., 1980, @doi [ ] 10.1086/158356 , https://ui.adsabs.harvard.edu/abs/1980ApJ...241..425G 241, 425

    1980 doi

  23. [31]

    M., Benitez-Llambay P., Miller Bertolami M

    Guilera O. M., Benitez-Llambay P., Miller Bertolami M. M., Pessah M. E., 2023, @doi [ ] 10.3847/1538-4357/acd2cb , https://ui.adsabs.harvard.edu/abs/2023ApJ...953...97G 953, 97

    2023 doi

  24. [32]

    O., Alexander R

    Hands T. O., Alexander R. D., 2018, @doi [ ] 10.1093/mnras/stx2711 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.474.3998H 474, 3998

    2018 doi

  25. [33]

    O., Alexander R

    Hands T. O., Alexander R. D., Dehnen W., 2014, @doi [ ] 10.1093/mnras/stu1751 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.445..749H 445, 749

    2014 doi

  26. [34]

    Hartmann L., Calvet N., Gullbring E., D'Alessio P., 1998, @doi [ ] 10.1086/305277 , https://ui.adsabs.harvard.edu/abs/1998ApJ...495..385H 495, 385

    1998 doi

  27. [35]

    Hou Q., Yu C., 2024, @doi [ ] 10.3847/1538-4357/ad6a5c , https://ui.adsabs.harvard.edu/abs/2024ApJ...972..152H 972, 152

    2024 doi

  28. [36]

    Hou Q., Yu C., 2025, @doi [ ] 10.3847/1538-4357/ada15a , https://ui.adsabs.harvard.edu/abs/2025ApJ...979..185H 979, 185

    2025 doi

  29. [37]

    W., 2023, @doi [ ] 10.1093/mnras/stad1032 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.522..828H 522, 828

    Huang S., Ormel C. W., 2023, @doi [ ] 10.1093/mnras/stad1032 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.522..828H 522, 828

    2023 doi

  30. [38]

    Ida S., Lin D. N. C., 2008, @doi [ ] 10.1086/523754 , https://ui.adsabs.harvard.edu/abs/2008ApJ...673..487I 673, 487

    2008 doi

  31. [39]

    Ida S., Muto T., Matsumura S., Brasser R., 2020, @doi [ ] 10.1093/mnras/staa1073 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.5666I 494, 5666

    2020 doi

  32. [40]

    N., Morbidelli A., Pierens A., Bitsch B., Cossou C., Hersant F., 2017, @doi [ ] 10.1093/mnras/stx1232 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.470.1750I 470, 1750

    Izidoro A., Ogihara M., Raymond S. N., Morbidelli A., Pierens A., Bitsch B., Cossou C., Hersant F., 2017, @doi [ ] 10.1093/mnras/stx1232 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.470.1750I 470, 1750

    2017 doi

  33. [41]

    D., Tanaka H., Muto T., Tanigawa T., Takeuchi T., 2015, @doi [ ] 10.1093/mnras/stv025 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.448..994K 448, 994

    Kanagawa K. D., Tanaka H., Muto T., Tanigawa T., Takeuchi T., 2015, @doi [ ] 10.1093/mnras/stv025 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.448..994K 448, 994

    2015 doi

  34. [42]

    arXiv:2504.12596

    Keller F., Dai F., Xu W., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2504.12596 , https://ui.adsabs.harvard.edu/abs/2025arXiv250412596K p. arXiv:2504.12596

    2025 doi

  35. [43]

    P., 2012, @doi [ ] 10.1146/annurev-astro-081811-125523 , https://ui.adsabs.harvard.edu/abs/2012ARA&A..50..211K 50, 211

    Kley W., Nelson R. P., 2012, @doi [ ] 10.1146/annurev-astro-081811-125523 , https://ui.adsabs.harvard.edu/abs/2012ARA&A..50..211K 50, 211

    2012 doi

  36. [44]

    Kubli N., Mayer L., Deng H., Lin D. N. C., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2503.01973 , https://ui.adsabs.harvard.edu/abs/2025arXiv250301973K p. arXiv:2503.01973

    2025 doi

  37. [45]

    Lammers C., Hadden S., Murray N., 2024, @doi [ ] 10.3847/1538-4357/ad5be6 , https://ui.adsabs.harvard.edu/abs/2024ApJ...972...53L 972, 53

    2024 doi

  38. [46]

    C., 2004, @doi [ ] 10.1086/386316 , https://ui.adsabs.harvard.edu/abs/2004ApJ...608..489L 608, 489

    Laughlin G., Steinacker A., Adams F. C., 2004, @doi [ ] 10.1086/386316 , https://ui.adsabs.harvard.edu/abs/2004ApJ...608..489L 608, 489

    2004 doi

  39. [47]

    H., Peale S

    Lee M. H., Peale S. J., 2002, @doi [ ] 10.1086/338504 , https://ui.adsabs.harvard.edu/abs/2002ApJ...567..596L 567, 596

    2002 doi

  40. [48]

    H., Fabrycky D., Lin D

    Lee M. H., Fabrycky D., Lin D. N. C., 2013, @doi [ ] 10.1088/0004-637X/774/1/52 , https://ui.adsabs.harvard.edu/abs/2013ApJ...774...52L 774, 52

    2013 doi

  41. [49]

    534, Protostars and Planets VII

    Lesur G., et al., 2023, in Inutsuka S., Aikawa Y., Muto T., Tomida K., Tamura M., eds, Astronomical Society of the Pacific Conference Series Vol. 534, Protostars and Planets VII. p. 465 ( @eprint arXiv 2203.09821 ), @doi 10.48550/arXiv.2203.09821

    2023 doi arXiv

  42. [50]

    Li Y.-P., Li H., Li S., Lin D. N. C., 2019, @doi [ ] 10.3847/1538-4357/ab4bc8 , https://ui.adsabs.harvard.edu/abs/2019ApJ...886...62L 886, 62

    2019 doi

  43. [51]

    arXiv:2408.10206

    Li R., Chiang E., Choksi N., Dai F., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2408.10206 , https://ui.adsabs.harvard.edu/abs/2024arXiv240810206L p. arXiv:2408.10206

    2024 doi arXiv

  44. [52]

    Lin D. N. C., Papaloizou J., 1979, @doi [ ] 10.1093/mnras/188.2.191 , https://ui.adsabs.harvard.edu/abs/1979MNRAS.188..191L 188, 191

    1979 doi

  45. [53]

    Lin D. N. C., Papaloizou J., 1986, @doi [ ] 10.1086/164653 , https://ui.adsabs.harvard.edu/abs/1986ApJ...309..846L 309, 846

    1986 doi

  46. [54]

    arXiv:2501.12650

    Lin L., Liu B., Zheng Z., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2501.12650 , https://ui.adsabs.harvard.edu/abs/2025arXiv250112650L p. arXiv:2501.12650

    2025 doi

  47. [55]

    Lithwick Y., Wu Y., 2012, @doi [ ] 10.1088/2041-8205/756/1/L11 , https://ui.adsabs.harvard.edu/abs/2012ApJ...756L..11L 756, L11

    2012 doi

  48. [56]

    Liu B., Zhang X., Lin D. N. C., Aarseth S. J., 2015, @doi [ ] 10.1088/0004-637X/798/1/62 , https://ui.adsabs.harvard.edu/abs/2015ApJ...798...62L 798, 62

    2015 doi

  49. [57]

    Masset F., 2000, @doi [ ] 10.1051/aas:2000116 , https://ui.adsabs.harvard.edu/abs/2000A&AS..141..165M 141, 165

    2000 doi

  50. [58]

    P., Nelson R

    McNally C. P., Nelson R. P., Paardekooper S.-J., Gressel O., Lyra W., 2017, @doi [ ] 10.1093/mnras/stx2136 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.472.1565M 472, 1565

    2017 doi

  51. [59]

    P., Nelson R

    McNally C. P., Nelson R. P., Paardekooper S.-J., 2018, @doi [ ] 10.1093/mnras/sty905 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.4596M 477, 4596

    2018 doi

  52. [60]

    Meyer J., Wisdom J., 2008, @doi [ ] 10.1016/j.icarus.2007.09.008 , https://ui.adsabs.harvard.edu/abs/2008Icar..193..213M 193, 213

    2008 doi

  53. [61]

    D., Dermott S

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

    1999 doi

  54. [62]

    Nayakshin S., Cruz S \'a enz de Miera F., K \'o sp \'a l \'A ., \'C alovi \'c A., Eisl \"o ffel J., Lin D. N. C., 2024, @doi [ ] 10.1093/mnras/stae877 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.530.1749N 530, 1749

    2024 doi

  55. [63]

    P., 2005, @doi [ ] 10.1051/0004-6361:20042605 , https://ui.adsabs.harvard.edu/abs/2005A&A...443.1067N 443, 1067

    Nelson R. P., 2005, @doi [ ] 10.1051/0004-6361:20042605 , https://ui.adsabs.harvard.edu/abs/2005A&A...443.1067N 443, 1067

    2005 doi

  56. [64]

    Ogihara M., Ida S., Morbidelli A., 2007, @doi [ ] 10.1016/j.icarus.2006.12.006 , https://ui.adsabs.harvard.edu/abs/2007Icar..188..522O 188, 522

    2007 doi

  57. [65]

    J., Baruteau C., Crida A., Kley W., 2010, @doi [ ] 10.1111/j.1365-2966.2009.15782.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.401.1950P 401, 1950

    Paardekooper S. J., Baruteau C., Crida A., Kley W., 2010, @doi [ ] 10.1111/j.1365-2966.2009.15782.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.401.1950P 401, 1950

    2010

  58. [66]

    Paardekooper S.-J., Rein H., Kley W., 2013, @doi [ ] 10.1093/mnras/stt1224 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.434.3018P 434, 3018

    2013 doi

  59. [67]

    S., Ogilvie G., Tanaka H., 2023, in Inutsuka S., Aikawa Y., Muto T., Tomida K., Tamura M., eds, Astronomical Society of the Pacific Conference Series Vol

    Paardekooper S., Dong R., Duffell P., Fung J., Masset F. S., Ogilvie G., Tanaka H., 2023, in Inutsuka S., Aikawa Y., Muto T., Tomida K., Tamura M., eds, Astronomical Society of the Pacific Conference Series Vol. 534, Protostars and Planets VII. p. 685 ( @eprint arXiv 2203.0959...

    2023 doi arXiv

  60. [68]

    Papaloizou J. C. B., Larwood J. D., 2000, @doi [ ] 10.1046/j.1365-8711.2000.03466.x , https://ui.adsabs.harvard.edu/abs/2000MNRAS.315..823P 315, 823

    2000

  61. [69]

    Papaloizou J. C. B., Terquem C., 2010, @doi [ ] 10.1111/j.1365-2966.2010.16477.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.405..573P 405, 573

    2010

  62. [70]

    J., Cassen P., Reynolds R

    Peale S. J., Cassen P., Reynolds R. T., 1979, @doi [Science] 10.1126/science.203.4383.892 , https://ui.adsabs.harvard.edu/abs/1979Sci...203..892P 203, 892

    1979 doi

  63. [71]

    G., Simon J

    Rea D. G., Simon J. B., Carrera D., Lesur G., Lyra W., Sengupta D., Yang C.-C., Youdin A. N., 2024, @doi [ ] 10.3847/1538-4357/ad57c5 , https://ui.adsabs.harvard.edu/abs/2024ApJ...972..128R 972, 128

    2024 doi

  64. [72]

    Rein H., Papaloizou J. C. B., 2009, @doi [ ] 10.1051/0004-6361/200811330 , https://ui.adsabs.harvard.edu/abs/2009A&A...497..595R 497, 595

    2009 doi

  65. [73]

    Ricci L., Liu S.-F., Isella A., Li H., 2018, @doi [ ] 10.3847/1538-4357/aaa546 , https://ui.adsabs.harvard.edu/abs/2018ApJ...853..110R 853, 110

    2018 doi

  66. [74]

    Rice W. K. M., Armitage P. J., Bate M. R., Bonnell I. A., 2003, @doi [ ] 10.1046/j.1365-8711.2003.06253.x , https://ui.adsabs.harvard.edu/abs/2003MNRAS.339.1025R 339, 1025

    2003

  67. [75]

    E., et al., 2024, @doi [ ] 10.3847/1538-4357/ad20e9 , https://ui.adsabs.harvard.edu/abs/2024ApJ...964...36R 964, 36

    Romero-Mirza C. E., et al., 2024, @doi [ ] 10.3847/1538-4357/ad20e9 , https://ui.adsabs.harvard.edu/abs/2024ApJ...964...36R 964, 36

    2024 doi

  68. [76]

    P., 2023, @doi [ ] 10.1016/j.newar.2023.101674 , https://ui.adsabs.harvard.edu/abs/2023NewAR..9601674R 96, 101674

    Rosotti G. P., 2023, @doi [ ] 10.1016/j.newar.2023.101674 , https://ui.adsabs.harvard.edu/abs/2023NewAR..9601674R 96, 101674

    2023

  69. [77]

    M., Blake G

    Salyk C., Pontoppidan K. M., Blake G. A., Lahuis F., van Dishoeck E. F., Evans II N. J., 2008, @doi [ ] 10.1086/586894 , https://ui.adsabs.harvard.edu/abs/2008ApJ...676L..49S 676, L49

    2008 doi

  70. [78]

    Secunda A., Bellovary J., Mac Low M.-M., Ford K. E. S., McKernan B., Leigh N. W. C., Lyra W., S \'a ndor Z., 2019, @doi [ ] 10.3847/1538-4357/ab20ca , https://ui.adsabs.harvard.edu/abs/2019ApJ...878...85S 878, 85

    2019 doi

  71. [79]

    I., Sunyaev R

    Shakura N. I., Sunyaev R. A., 1973, , https://ui.adsabs.harvard.edu/abs/1973A&A....24..337S 24, 337

    1973

  72. [80]

    B., Beckwith K., Armitage P

    Simon J. B., Beckwith K., Armitage P. J., 2012, @doi [ ] 10.1111/j.1365-2966.2012.20835.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.422.2685S 422, 2685

    2012

  73. [81]

    R., 2002, @doi [ ] 10.1086/324713 , https://ui.adsabs.harvard.edu/abs/2002ApJ...565.1257T 565, 1257

    Tanaka H., Takeuchi T., Ward W. R., 2002, @doi [ ] 10.1086/324713 , https://ui.adsabs.harvard.edu/abs/2002ApJ...565.1257T 565, 1257

    2002 doi

  74. [82]

    Terquem C., Papaloizou J. C. B., 2019, @doi [ ] 10.1093/mnras/sty2693 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.482..530T 482, 530

    2019 doi

  75. [83]

    R., 1997, @doi [ ] 10.1006/icar.1996.5647 , https://ui.adsabs.harvard.edu/abs/1997Icar..126..261W 126, 261

    Ward W. R., 1997, @doi [ ] 10.1006/icar.1996.5647 , https://ui.adsabs.harvard.edu/abs/1997Icar..126..261W 126, 261

    1997

  76. [84]

    H., Lee M

    Wong K. H., Lee M. H., 2024, @doi [ ] 10.3847/1538-3881/ad1f60 , https://ui.adsabs.harvard.edu/abs/2024AJ....167..112W 167, 112

    2024 doi

  77. [85]

    Wu Y., Chen Y.-X., 2025, @doi [ ] 10.1093/mnrasl/slae102 , https://ui.adsabs.harvard.edu/abs/2025MNRAS.536L..13W 536, L13

    2025 doi

  78. [86]

    Wu Y., Baruteau C., Nayakshin S., 2023, @doi [ ] 10.1093/mnras/stad1791 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.523.4869W 523, 4869

    2023 doi

  79. [87]

    Wu Y., Chen Y.-X., Lin D. N. C., 2024a, @doi [ ] 10.1093/mnrasl/slad183 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528L.127W 528, L127

    doi

  80. [88]

    N., 2024b, @doi [ ] 10.3847/1538-4357/ad15fe , https://ui.adsabs.harvard.edu/abs/2024ApJ...962..173W 962, 173

    Wu Y., Lin M.-K., Cui C., Krapp L., Lee Y.-N., Youdin A. N., 2024b, @doi [ ] 10.3847/1538-4357/ad15fe , https://ui.adsabs.harvard.edu/abs/2024ApJ...962..173W 962, 173

    doi

  81. [89]

    Wu Y., Liu S.-F., Jiang H., Nayakshin S., 2024c, @doi [ ] 10.3847/1538-4357/ad323b , https://ui.adsabs.harvard.edu/abs/2024ApJ...965..110W 965, 110

    doi

  82. [90]

    Xu Y., Dai F., 2025, @doi [ ] 10.3847/1538-4357/adb281 , https://ui.adsabs.harvard.edu/abs/2025ApJ...981..142X 981, 142

    2025 doi

  83. [91]

    Yang H., Li Y.-P., 2024, @doi [ ] 10.1093/mnras/stae2097 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.534..485Y 534, 485

    2024 doi

  84. [92]

    de Val-Borro M., et al., 2006, @doi [ ] 10.1111/j.1365-2966.2006.10488.x , https://ui.adsabs.harvard.edu/abs/2006MNRAS.370..529D 370, 529

    2006

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.