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Planetary waves can activate resonant drag instabilities in 3D dusty gaseous discs

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Planetary (Rossby) waves launched by a low-mass planet can resonate with the dust–gas streaming motion and trigger a resonant drag instability that produces global filaments in a protoplanetary disc.

desk verdict Plausible but not proven: the paper isolates dust-feedback-driven filament formation with well-designed controls, but it never measures the RDI resonance condition or a growth rate, so the central mechanism remains an inference. read the letter →

arxiv 2506.13592 v1 pith:SFGQGIUF submitted 2025-06-16 astro-ph.EP

Raúl O. Chametla , Yasuhiro Hasegawa , Gennaro D'Angelo This is my paper · ORCID
classification astro-ph.EP
keywords resonantdraginstabilityplanetarywavesRossbyprotoplanetarydiscsdust-gastwo-fluiddynamicsstreamingplanet-discinteractionbuoyancyresonance
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 sets out to show that planetary (Rossby) waves, launched by a low-mass planet in a protoplanetary disc, can act as the gas wave mode that the resonant drag instability (RDI) needs. Using global 3D two-fluid simulations of an inviscid, globally isothermal disc with 0.3–3 Earth-mass planets and dust with Stokes number 0.01–0.5, the authors find filamentary dust structures that grow on dynamical timescales and spread beyond the planet's horseshoe region. They argue that because these structures appear only when dust feeds back on gas, and because they resemble streaming-instability filaments, the waves must be resonating with the dust–gas streaming motion. If true, planet-induced RDIs give a pathway to dust concentration and planetesimal formation that works at low dust-to-gas ratios and does not depend strongly on grain size or vertical settling.

What carries the argument

The load-bearing machinery is the resonant drag instability condition together with the wave source that satisfies it. The RDI occurs when a dust–gas streaming velocity $\mathbf{w}_s$ obeys $\mathbf{k}\cdot\mathbf{w}_s=\omega_{\mathrm{gas}}(\mathbf{k})$, meaning that dust drifting through gas resonantly drives an intrinsic gas wave at wavenumber $\mathbf{k}$. In this disc the intrinsic waves are planetary (Rossby) waves propagating along the downstream separatrices of the horseshoe region, excited by the vortensity structure the planet sets up. Dust feedback is what couples the streaming motion to those waves, and the inclined 'pw-stripes' seen in the vorticity and dust density are the visible signature of the resonance being driven. Vertical dust settling is present but is not the trigger; the planet's waves are.

What would settle it

Take the gas-only simulations, Fourier-transform the vorticity perturbations along the downstream separatrices to measure the wave frequency $\omega_{\mathrm{gas}}(\mathbf{k})$, and compare it with the dust–gas drift $\mathbf{w}_s$ measured in the dusty runs; if no wavenumber in the filament-forming region satisfies $\mathbf{k}\cdot\mathbf{w}_s=\omega_{\mathrm{gas}}(\mathbf{k})$, the RDI resonance is not what drives the instability.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the vortensity disturbances previously seen in the horseshoe region of a planet in a 3D isothermal disc—stripe-like vertical-oscillation features and the planetary waves propagating along downstream separatrices—become the seed of a resonant drag instability once dust aerodynamic feedback is included. The relevant waves are planetary (Rossby) waves propagating along the separatrices; the dust–gas drift provides the streaming motion; and the resonance condition $\mathbf{k}\cdot\mathbf{w}_s=\omega_{\mathrm{gas}}(\mathbf{k})$ turns the two-fluid mixture unstable. The authors report global, streaming-instability-like filamentary dust concentrations that develop within about five to twenty orbits, spread beyond the horseshoe region, and appear across the full range of Stokes numbers and planet masses tried, even when the midplane dust-to-gas ratio stays far below unity. They also report buoyancy-resonance ray patterns in the vertical velocity that emerge in a globally isothermal disc only because dust feedback is present. Their conclusion is that this is the first numerical evidence of RDI activation driven by planetary waves.

Load-bearing premise

The load-bearing premise is that the wave-like disturbances travelling along the horseshoe separatrices are genuine planetary (Rossby) waves whose frequency can satisfy the RDI resonance condition $\mathbf{k}\cdot\mathbf{w}_s=\omega_{\mathrm{gas}}(\mathbf{k})$ against the local dust–gas drift; the paper infers this from morphology and from the dependence on dust feedback rather than measuring the resonance directly.

Editorial extensions

If this is right

  • Low-mass planets of 0.3–3 $M_\oplus$ can trigger dust clumping on dynamical timescales, so planetesimal formation may begin near an embryo well before classical streaming instability would act.
  • The instability operates at midplane dust-to-gas ratios $\epsilon\ll1$, so dust-rich regions are not required for it to start; a wave source is the key ingredient.
  • Because growth is fast and weakly dependent on Stokes number, it can organise a broad grain-size spectrum into coherent filaments and suppresses the planet-localised dust voids and asymmetric structures that dust-only dynamics would produce.
  • In a globally isothermal disc, dust feedback mimics buoyancy resonances normally associated with adiabatic discs, so wave patterns in isothermal dusty discs cannot be read using a purely gas adiabatic model.

Reading between the lines

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

  • The paper leaves open a direct spectral test: measuring the wave dispersion relation in the simulations and checking that some wavenumber satisfies $\mathbf{k}\cdot\mathbf{w}_s=\omega_{\mathrm{gas}}(\mathbf{k})$ in the region where filaments first appear would close the gap between morphology and mechanism.
  • The mechanism need not be limited to planets: any localised vortensity source that launches Rossby waves, such as a gap edge or an eccentric vortex, could seed the same RDI, widening the relevance to observed rings and asymmetries.
  • If real discs support these waves, the instability could erase the asymmetric dust signatures expected near low-mass planets within tens of orbits; searching for low-contrast extended filaments beyond the horseshoe region at low dust-to-gas ratios would be a concrete observational test.
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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

4 major / 4 minor

Summary. This paper reports 3D high-resolution two-fluid simulations of a dusty protoplanetary disc with an embedded low-mass planet (0.3–3 Earth masses) and dust Stokes numbers in 0.01–0.5. The central claim is that planetary waves (also called Rossby waves) propagating along the horseshoe-region separatrix resonate with the dust-gas relative streaming motion and thereby activate a resonant drag instability (RDI), producing global filamentary dust structures. The authors also claim that dust feedback enables buoyancy resonances in an otherwise isothermal disc. The evidence consists of: gas vorticity maps showing planetary-wave-like disturbances and stripes, dust-density maps showing filamentary structures when dust feedback is included, a suite of control runs (no feedback, finite-thickness dust layer, softened potential, mass tapering), and a 2D experiment with an injected Gaussian perturbation. The paper does not report a quantitative test of the RDI resonance condition, nor measurements of wave dispersion or growth rates.

Significance. If validated, the claim that low-mass planets can trigger RDIs via planetary waves would be an important new pathway for dust clumping and planetesimal formation, extending RDI theory to non-axisymmetric, global disc settings. The simulations are ambitious and carefully parameterized, and the inclusion of both-feedback and no-feedback controls, a finite-thickness dust layer, potential softening, and mass tapering is a strength. The use of the public FARGO3D code and the high resolution are additional positive features. However, the absence of any direct check of the RDI resonance condition and the lack of growth-rate measurements mean that the principal conclusion is not yet quantitatively established.

major comments (4)
  1. [Section 1 and Section 3.6] The RDI resonance condition k·w_s = ω_gas(k) stated in the Introduction is never evaluated using the simulation data. The paper does not measure the frequencies or wavenumbers of the planetary waves, nor does it compute the local dust-gas relative velocity w_s. Section 3.6 merely states that the filaments arise from a 'similarity' between the gas-wave propagation velocity and the dust-gas relative velocity, without any quantitative comparison. As a result, the identification of the observed structures as an RDI is inferred from morphology and from the presence of dust feedback, which are necessary but not sufficient conditions. The disturbance could be a non-resonant forced response of the dust to the planet-induced gas flow modified by feedback. This is the central gap in the evidence for the paper's main claim.
  2. [Sections 3.3, 5 (Figs. 5, 6, 9)] No growth-rate measurement or mode-amplitude time series is presented. An instability requires exponential growth of a mode amplitude, but the paper shows only spatial spreading of finite-amplitude disturbances over 5–20 orbits. The 'rapid onset' of the structures could equally be interpreted as a fast-propagating linear response. A quantitative growth-rate analysis (e.g., tracking Fourier-mode amplitudes in time) is essential to distinguish a genuine instability from an advected or forced pattern.
  3. [Section 3.4, Eq. (17), footnote 4] The buoyancy-resonance interpretation of the colored rays is circular as presented. The overlay in Fig. 4 uses z=2H_g in Eq. (17), but footnote 4 states that the perturbations do not appear for values of z at which the dust has settled, and no independent determination of z is given. Choosing the height to match the observed pattern means Eq. (17) is not being used as a predictive test. This substantially weakens the secondary claim that dust feedback enables buoyancy resonances in a globally isothermal disc.
  4. [Appendix A, Eq. (A1)] The two-dimensional experiment in Appendix A is not a valid test of RDI activation. Injecting a localized Gaussian velocity perturbation into a Keplerian disc will inevitably shear into two inclined stripes, regardless of any resonance. This experiment demonstrates only that a finite-amplitude perturbation can produce filamentary dust density variations, not that a resonant drag instability is at work. It therefore does not close the gap left by the absence of a resonance-condition check in the main simulations.
minor comments (4)
  1. [Throughout] There are several typographical errors: 'deveolps' (Introduction), 'mow' (Section 4.3), 'Once can see' (Section 3.3), 'bouyancy' (Sections 3.4, 3.5), 'adibatic' (Section 5), and the rendering of 'sin' as 's i n' in Eq. (A1). These should be corrected.
  2. [Section 4.2] The claim that the instability 'does not depend on the dust-to-gas mass ratio' is too strong given that only two values are tested (ε=0.01 in the main simulations and ε=0.001 in the finite-layer run, which also has a different Stokes number and dust scale-height setup). A systematic variation of ε would be needed to support this conclusion.
  3. [Section 3.2 and Fig. 1] The identification of the waves as 'planetary waves (also known as Rossby waves)' is not justified in detail; the disturbances shown in Fig. 1 are localized to the horseshoe region and may be a different mode of vortensity wave. The authors should clarify the relationship to the classical Rossby-wave literature or temper the terminology.
  4. [Section 2.3] The description of the computational mesh reports (N_r, N_θ, N_φ) = (3200, 100, 12560), which gives over 4×10^9 cells. While this is stated as high resolution, the authors do not discuss how this extreme resolution is handled computationally or whether any grid-convergence tests were performed beyond the softening/taper experiments in Appendix B.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the RDI attribution is an empirical inference from self-contained two-fluid simulations, not a quantity fitted to itself.

full rationale

I walked the paper's derivation chain. The central claim is that planetary waves excite the resonant drag instability (RDI); the evidence is numerical: global 3D two-fluid simulations with and without dust feedback, with and without a planet, and a finite-thickness dust-layer control. The RDI resonance condition k·w_s = ω_gas(k) is adopted from Squire & Hopkins (2018a), an external and independently developed theory; the paper does not derive ω_gas from its own output. The identification of the disturbances as planetary waves rests on comparison with the independent simulations of Masset & Benítez-Llambay (2016), not on a self-citation chain, and the governing equations (1)-(6) are standard two-fluid hydrodynamics with no target result encoded in them. No fitted parameter is renamed as a prediction: Appendix A injects a Gaussian velocity perturbation and follows its evolution, while the main runs evolve from standard disc initial conditions, so the resulting stripe morphology is a numerical outcome rather than an imposed input. The Section 3.4 buoyancy-ray overlay uses Eq. (17) with z = 2H_g, and although this height is chosen partly for visibility (footnote 4), this is a secondary diagnostic analogy and not the load-bearing RDI claim. The paper itself states in Section 1 that the hypothesis is not yet confirmed analytically and that simulations are used to test it, which is a legitimate use of numerical experiment rather than a circular reduction. The absence of a measured dispersion relation or growth-rate time series is a real evidentiary gap in the RDI attribution, but a missing test is not circular reasoning. Self-citations such as Chametla & Masset (2021) and Chametla et al. (2025) are peripheral and non-load-bearing. Verdict: no significant circularity; score 0.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard RDI theory and on the modeling assumptions of an inviscid, globally isothermal, non-self-gravitating two-fluid disc. The tunable elements are simulation inputs and the height/adiabatic index used in the buoyancy-ray comparison; no new physical entities are introduced.

free parameters (5)
  • z = 2Hg (height used in buoyancy phase-line overlay) = 2Hg
    Chosen so the adiabatic buoyancy ray pattern (Eq. 17) aligns with the simulated v_theta rays in Fig. 4; footnote 4 states the pattern does not appear at heights where dust has settled, indicating tuning to the observed signal.
  • gamma (adiabatic index in Eq. 17) = unspecified (adiabatic value used)
    The disc is globally isothermal, so gamma is not a property of the simulation; it enters only through the comparison formula for buoyancy resonance rays, making the match partly dependent on an external parameter.
  • white noise amplitude in control runs = 1e-2 c_s
    Applied to radial and vertical velocity components of gas and dust in models RDISt0_2Mp0 and RDISt0_01HdMp1 to seed instabilities; chosen by hand and not tied to a physical turbulence model.
  • alpha_d (dust diffusion coefficient) = 1e-4
    Used in Eq. (18) to set the finite dust layer thickness in model RDISt0_01HdMp1; a modeling assumption from Youdin & Lithwick (2007), not fitted to data.
  • softening length epsilon = 0.01 Hg nominal; 0.03 Hg in Appendix B
    Numerical smoothing of the planetary potential; not physical for a point mass, but varied to show the result is robust to its choice.
assumptions (6)
  • standard math Resonant drag instability condition k·w_s = omega_gas(k)
    The RDI resonance condition is taken from Squire & Hopkins (2018a) and is the interpretive framework for the simulation results; the paper does not independently verify it for the planetary-wave modes.
  • domain assumption Two-fluid model with pressureless dust and Epstein drag
    The dust is treated as a pressureless fluid with a fixed Stokes number drag term (Eq. 6); this is standard but ignores dust size distributions, collisions, and back-reaction on the dust velocity field beyond drag.
  • domain assumption Globally isothermal equation of state
    Eq. (5) imposes p = c_s^2 rho_g, so the gas-only disc has zero Brunt-Vaisala frequency; the claim that dust feedback creates buoyancy resonances depends on this baseline being non-buoyant.
  • domain assumption Inviscid gas disc
    No viscosity is included in Eqs. (1)-(4), which affects wave propagation, the formation of vortensity stripes, and dust settling behavior.
  • domain assumption Vortensity stripes originate from vertical oscillations as in Masset & Benitez-Llambay (2016)
    The paper assumes the stripe pattern in the gas vortensity is caused by vertical excursions of gas during U-turns, citing Masset & Benitez-Llambay (2016), and uses this as the background state for the RDI.
  • domain assumption Planetary waves are Rossby-type waves on vortensity gradients
    The identification of the propagating disturbances as planetary waves (Rossby waves) follows from Lovelace et al. (1999) and Li et al. (2000, 2001, 2005); no dispersion relation is derived here for the simulated waves.

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Pith. "Pith review of Planetary waves can activate resonant drag instabilities in 3D dusty gaseous discs." pith.science (2026). https://pith.science/paper/SFGQGIUF

@misc{pith2026250613592,
  author       = {Pith},
  title        = {Pith review of: Planetary waves can activate resonant drag instabilities in 3D dusty gaseous discs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SFGQGIUF}},
  note         = {Machine review of arXiv:2506.13592}
}
abstract

Resonant Drag Instabilities (RDIs) in protoplanetary discs are driven by the aerodynamic back-reaction of dust on gas and occur when the relative dust-gas motion resonate with a wave mode intrinsic to the gas fluid. Axisymmetric models indicate that the RDI generates filamentary perturbations, leading to grain clumping and planetesimal formation. Motivated by these findings, we investigate the dust-gas interaction in a non-axisymmetric inviscid protoplanetary disc with an embedded low-mass planet ($M_{\mathrm{p}}\in[0.3, 3] M_\oplus$, here $M_\oplus$ is the Earth mass). We conduct global 3D high-resolution two-fluid simulations, with the dust being parametrized by the Stokes number $\mathrm{St}\in[0.01,0.5]$. We find that planetary waves (PWs; also known as Rossby waves), which propagate along the downstream separatrices of the horseshoe region, resonate with the streaming motion and trigger the RDI. The consequent development of a global-scale filamentary dust distribution does not sensitively depend on the Stokes number, nor does it depend on the fast dust settling that takes place in an inviscid disc. The rapid onset of this instability, which is comparable to the dynamical orbital time-scale, suppresses the formation of asymmetric structures in the dust in the vicinity of the planet (such as dust voids and filaments). Additionally, we find that the dust feedback enables buoyancy resonances in an otherwise non-buoyant (globally isothermal) disc. Therefore, our results provide the first numerical evidence of RDIs generation driven by planetary waves.

Figures

Figures reproduced from arXiv: 2506.13592 by the authors.

Figure 1
Figure 1. 2D map of the vorticity in the midplane (𝜃 = 𝜋/2), resulting from model RDISt0Mp3, at 𝑡 = 20 orbits. We mark the locations of (i) the planetary waves propagating mainly along the downstream separatrices of the horseshoe region and (ii) the stripes confined within the horseshoe region. The stripes originate from the vertical oscillations of gas parcels upon executing their U-turns (see [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 2
Figure 2. 3D-view of a gas streamline in the horseshoe region for the RDISt0Mp3 model. The planet is located at (𝑟, 𝜃, 𝜙) = (1, 𝜋/2, 0). One can see vertical oscillations of fluid elements mainly during and after their encounter with the planet (as they move downstream, away from the planet), similar to the findings of Masset & Benítez-Llambay (2016). The cyan and green dashed lines in the figure represent the boundaries of t… view at source ↗
Figure 3
Figure 3. 2𝐷-maps of the vorticity at the midplane (𝜃 = 𝜋/2) for models with large Stokes numbers 𝑆𝑡 = 0.2, 0.5 and different planetary masses (see [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: 2𝐷-maps of the vertical gas velocity component 𝑣𝜃 (in code units) at the midplane (calculated at 𝑡 = 5, 10, 15 and 20 orbits, shown from left to right and top to bottom, respectively) for the RDISt0_2Mp03 model, illustrating the disturbances generated by planetary wave…
Figure 6
Figure 6. Figure 6: Dust density (code units) in the midplane for the RDISt0_2Mp1 model, at 𝑡 = 20 orbits. At this time the RDI has propagated beyond the horseshoe region. the colored-rays maintain a marginal inclination with respect to the radial axis (i.e., the direction perpendicular t…
Figure 5
Figure 5. Figure 5: Temporal evolution of the dust density (code units) at the midplane for model RDISt0_2Mp03. The cyan dotted lines show the width of the horseshoe region given by Eq (14). RDISt0_2Mp03 and RDISt0_2Mp1 models, calculated at 𝑡 = 10 orbits. In these two models, the Stokes …
Figure 7
Figure 7. Figure 7: Comparison of the disturbances generated in the dust density (code units), after 𝑡 = 10 orbits, for a case without (model RDISt0_2Mp0, left) and for a case with a planet embedded in the disc (model RDISt0_2Mp1, right). the vertical velocity map along the downstream flo…
Figure 8
Figure 8. Figure 8: Top. Dust-to-gas density ratio, 𝜖 , at the disc midplane for model RDISt0_05Mp1 at 𝑡 = 5 orbits. Bottom. Vertical dust density distribution (code units) for the RDISt0_05Mp1 model. we show in Appendix A, the formation of a single small planetary wave in the gas disc pr…
Figure 9
Figure 9. Figure 9: Top. Dust density distribution (code units) in model RDISt0_01𝐻𝑑 Mp1, calculated at the midplane, at 𝑡 = 20 orbits. Bottom. Vortensity (V ≡ 𝜁𝑧/𝜌g ) at the midplane in model RDISt0_01𝐻𝑑 Mp1, cal￾culated at the same time as in the top panel. (Bi et al. 2021) and prescrib…

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Works this paper leans on

39 extracted references · 4 canonical work pages

  1. [1]

    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

    doi:10.3847/0067-0049/223/1/11 2016

  2. [2]

    E., 2018, @doi [ ] 10.3847/2041-8213/aab2ae , https://ui.adsabs.harvard.edu/abs/2018ApJ...855L..28B 855, L28

    Ben \' tez-Llambay P., Pessah M. E., 2018, @doi [ ] 10.3847/2041-8213/aab2ae , https://ui.adsabs.harvard.edu/abs/2018ApJ...855L..28B 855, L28

    doi:10.3847/2041-8213/aab2ae 2018

  3. [3]

    E., 2019, @doi [ ] 10.3847/1538-4365/ab0a0e , https://ui.adsabs.harvard.edu/abs/2019ApJS..241...25B 241, 25

    Ben \' tez-Llambay P., Krapp L., Pessah M. E., 2019, @doi [ ] 10.3847/1538-4365/ab0a0e , https://ui.adsabs.harvard.edu/abs/2019ApJS..241...25B 241, 25

    doi:10.3847/1538-4365/ab0a0e 2019

  4. [4]

    Bi J., Lin M.-K., Dong R., 2021, @doi [ ] 10.3847/1538-4357/abef6b , https://ui.adsabs.harvard.edu/abs/2021ApJ...912..107B 912, 107

    doi:10.3847/1538-4357/abef6b 2021

  5. [5]

    O., Masset F

    Chametla R. O., Masset F. S., 2021, @doi [ ] 10.1093/mnras/staa3681 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.501...24C 501, 24

    work page doi:10.1093/mnras/staa3681 2021

  6. [6]

    O., Chrenko O., Masset F

    Chametla R. O., Chrenko O., Masset F. S., D'Angelo G., Nesvorny D., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2503.21922 , https://ui.adsabs.harvard.edu/abs/2025arXiv250321922C p. arXiv:2503.21922

    arXiv doi:10.48550/arxiv.2503.21922 2025

  7. [7]

    Chen K., Lin M.-K., 2020, @doi [ ] 10.3847/1538-4357/ab76ca , https://ui.adsabs.harvard.edu/abs/2020ApJ...891..132C 891, 132

    doi:10.3847/1538-4357/ab76ca 2020

  8. [8]

    O., Masset F

    Chrenko O., Chametla R. O., Masset F. S., Baruteau C., Bro z M., 2024, @doi [ ] 10.1051/0004-6361/202450922 , https://ui.adsabs.harvard.edu/abs/2024A&A...690A..41C 690, A41

    doi:10.1051/0004-6361/202450922 2024

Show all 39 references
  1. [9]

    D'Angelo G., Podolak M., 2015, @doi [ ] 10.1088/0004-637X/806/2/203 , https://ui.adsabs.harvard.edu/abs/2015ApJ...806..203D 806, 203

    2015 doi

  2. [10]

    Dong R., Li S., Chiang E., Li H., 2017, @doi [ ] 10.3847/1538-4357/aa72f2 , https://ui.adsabs.harvard.edu/abs/2017ApJ...843..127D 843, 127

    2017 doi

  3. [11]

    Fu W., Li H., Lubow S., Li S., Liang E., 2014, @doi [ ] 10.1088/2041-8205/795/2/L39 , https://ui.adsabs.harvard.edu/abs/2014ApJ...795L..39F 795, L39

    2014 doi

  4. [12]

    Huang P., Li H., Isella A., Miranda R., Li S., Ji J., 2020, @doi [ ] 10.3847/1538-4357/ab8199 , https://ui.adsabs.harvard.edu/abs/2020ApJ...893...89H 893, 89

    2020 doi

  5. [13]

    Jacquet E., Balbus S., Latter H., 2011, @doi [ ] 10.1111/j.1365-2966.2011.18971.x , https://ui.adsabs.harvard.edu/abs/2011MNRAS.415.3591J 415, 3591

    2011

  6. [14]

    A., Masset F

    Jim \'e nez M. A., Masset F. S., 2017, @doi [ ] 10.1093/mnras/stx1946 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.471.4917J 471, 4917

    2017 doi

  7. [15]

    Koller J., Li H., Lin D. N. C., 2003, @doi [ ] 10.1086/379032 , https://ui.adsabs.harvard.edu/abs/2003ApJ...596L..91K 596, L91

    2003 doi

  8. [16]

    N., Kratter K

    Krapp L., Youdin A. N., Kratter K. M., Ben \' tez-Llambay P., 2020, @doi [ ] 10.1093/mnras/staa1854 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.497.2715K 497, 2715

    2020 doi

  9. [17]

    M., Lovelace R

    Li H., Finn J. M., Lovelace R. V. E., Colgate S. A., 2000, @doi [ ] 10.1086/308693 , https://ui.adsabs.harvard.edu/abs/2000ApJ...533.1023L 533, 1023

    2000 doi

  10. [18]

    A., Wendroff B., Liska R., 2001, @doi [ ] 10.1086/320241 , https://ui.adsabs.harvard.edu/abs/2001ApJ...551..874L 551, 874

    Li H., Colgate S. A., Wendroff B., Liska R., 2001, @doi [ ] 10.1086/320241 , https://ui.adsabs.harvard.edu/abs/2001ApJ...551..874L 551, 874

    2001 doi

  11. [19]

    B., Liska R., Orban C

    Li H., Li S., Koller J., Wendroff B. B., Liska R., Orban C. M., Liang E. P. T., Lin D. N. C., 2005, @doi [ ] 10.1086/429367 , https://ui.adsabs.harvard.edu/abs/2005ApJ...624.1003L 624, 1003

    2005 doi

  12. [20]

    Lin M.-K., 2019, @doi [ ] 10.1093/mnras/stz701 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.485.5221L 485, 5221

    2019 doi

  13. [21]

    N., 2017, @doi [ ] 10.3847/1538-4357/aa92cd , https://ui.adsabs.harvard.edu/abs/2017ApJ...849..129L 849, 129

    Lin M.-K., Youdin A. N., 2017, @doi [ ] 10.3847/1538-4357/aa92cd , https://ui.adsabs.harvard.edu/abs/2017ApJ...849..129L 849, 129

    2017 doi

  14. [22]

    Lovelace R. V. E., Li H., Colgate S. A., Nelson A. F., 1999, @doi [ ] 10.1086/306900 , https://ui.adsabs.harvard.edu/abs/1999ApJ...513..805L 513, 805

    1999 doi

  15. [23]

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

    2000 doi

  16. [24]

    S., Ben \' tez-Llambay P., 2016, @doi [ ] 10.3847/0004-637X/817/1/19 , https://ui.adsabs.harvard.edu/abs/2016ApJ...817...19M 817, 19

    Masset F. S., Ben \' tez-Llambay P., 2016, @doi [ ] 10.3847/0004-637X/817/1/19 , https://ui.adsabs.harvard.edu/abs/2016ApJ...817...19M 817, 19

    2016 doi

  17. [25]

    P., Nelson R

    McNally C. P., Nelson R. P., Paardekooper S.-J., Ben \' tez-Llambay P., Gressel O., 2020, @doi [ ] 10.1093/mnras/staa576 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.493.4382M 493, 4382

    2020 doi

  18. [26]

    M., Muscianisi G., 2012, @doi [ ] 10.1051/0004-6361/201219557 , https://ui.adsabs.harvard.edu/abs/2012A&A...545A.152M 545, A152

    Mignone A., Flock M., Stute M., Kolb S. M., Muscianisi G., 2012, @doi [ ] 10.1051/0004-6361/201219557 , https://ui.adsabs.harvard.edu/abs/2012A&A...545A.152M 545, A152

    2012 doi

  19. [27]

    W., Kuiper R., Shi J.-M., 2015, @doi [ ] 10.1093/mnras/stu2101 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.446.1026O 446, 1026

    Ormel C. W., Kuiper R., Shi J.-M., 2015, @doi [ ] 10.1093/mnras/stu2101 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.446.1026O 446, 1026

    2015 doi

  20. [28]

    Paardekooper S.-J., Lesur G., Papaloizou J. C. B., 2010, @doi [ ] 10.1088/0004-637X/725/1/146 , https://ui.adsabs.harvard.edu/abs/2010ApJ...725..146P 725, 146

    2010 doi

  21. [29]

    Reg \'a ly Z., 2020, @doi [ ] 10.1093/mnras/staa2181 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.497.5540R 497, 5540

    2020 doi

  22. [30]

    Schubert W., Ruprecht E., Hertenstein R., Ferreira R. N., Taft R., Rozoff C., Ciesielski P., Kuo H.-C., 2004, @doi [Meteorologische Zeitschrift] 10.1127/0941-2948/2004/0013-0527 , https://ui.adsabs.harvard.edu/abs/2004MetZe..13..527S 13, 527

    2004 doi

  23. [31]

    F., 2018a, @doi [ ] 10.1093/mnras/sty854 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.5011S 477, 5011

    Squire J., Hopkins P. F., 2018a, @doi [ ] 10.1093/mnras/sty854 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.5011S 477, 5011

    doi

  24. [32]

    F., 2018b, @doi [ ] 10.3847/2041-8213/aab54d , https://ui.adsabs.harvard.edu/abs/2018ApJ...856L..15S 856, L15

    Squire J., Hopkins P. F., 2018b, @doi [ ] 10.3847/2041-8213/aab54d , https://ui.adsabs.harvard.edu/abs/2018ApJ...856L..15S 856, L15

    doi

  25. [33]

    F., 2020, @doi [ ] 10.1093/mnras/staa2311 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.498.1239S 498, 1239

    Squire J., Hopkins P. F., 2020, @doi [ ] 10.1093/mnras/staa2311 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.498.1239S 498, 1239

    2020 doi

  26. [34]

    N., Goodman J., 2005, @doi [ ] 10.1086/426895 , https://ui.adsabs.harvard.edu/abs/2005ApJ...620..459Y 620, 459

    Youdin A. N., Goodman J., 2005, @doi [ ] 10.1086/426895 , https://ui.adsabs.harvard.edu/abs/2005ApJ...620..459Y 620, 459

    2005 doi

  27. [35]

    N., Lithwick Y., 2007, @doi [ ] 10.1016/j.icarus.2007.07.012 , https://ui.adsabs.harvard.edu/abs/2007Icar..192..588Y 192, 588

    Youdin A. N., Lithwick Y., 2007, @doi [ ] 10.1016/j.icarus.2007.07.012 , https://ui.adsabs.harvard.edu/abs/2007Icar..192..588Y 192, 588

    2007 doi

  28. [36]

    Yun H.-G., Kim W.-T., Bae J., Han C., 2022, @doi [ ] 10.3847/1538-4357/ac9185 , https://ui.adsabs.harvard.edu/abs/2022ApJ...938..102Y 938, 102

    2022 doi

  29. [37]

    M., Rafikov R

    Zhu Z., Dong R., Stone J. M., Rafikov R. R., 2015, @doi [ ] 10.1088/0004-637X/813/2/88 , https://ui.adsabs.harvard.edu/abs/2015ApJ...813...88Z 813, 88

    2015 doi

  30. [38]

    P., 2023, @doi [ ] 10.1093/mnras/stad2692 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.525.5893Z 525, 5893

    Ziampras A., Paardekooper S.-J., Nelson R. P., 2023, @doi [ ] 10.1093/mnras/stad2692 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.525.5893Z 525, 5893

    2023 doi

  31. [39]

    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 15, 2026 · model on record in the stance chip above.