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Dust dynamics in radially convective regions of protoplanetary disks

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper argues that the convective overstability's zonal flows trap dust only weakly, and that dust feedback suppresses those flows even at dust-to-gas ratios near 0.1.

desk verdict Well-benchmarked simulation study that limits COS zonal flows as dust traps, but a questionable control run muddies the late-time feedback story. read the letter →

arxiv 2501.09792 v1 pith:AA56ENO5 submitted 2025-01-16 astro-ph.EP

Min-Kai Lin (ASIAA , NCTS Physics Division) , Marius Lehmann (ASIAA) This is my paper · ORCID
classification astro-ph.EP
keywords convectiveoverstabilitydustdynamicsprotoplanetarydiskszonalflowsfeedbackangularmomentumfluxplanetesimalformationshearingbox
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

This paper asks whether the convective overstability (COS), a hydrodynamic instability that operates in protoplanetary disks where the entropy decreases outward, can concentrate dust enough to seed planet formation. Using high-resolution axisymmetric Boussinesq shearing-box simulations with dust modeled as a second fluid, it finds that the zonal flows (pressure bumps) produced by the COS do trap dust, but only to about ten times the background density. The central discovery is that dust feedback suppresses the formation of these zonal flows even at dust-to-gas ratios as low as epsilon ~ 0.1, because dust drifting toward pressure maxima carries a positive angular momentum flux that offsets the negative flux that builds the zonal flow. The paper concludes that COS-driven zonal flows cannot by themselves trigger planetesimal formation, since the attainable dust-to-gas ratio stays below epsilon ~ 1.

What carries the argument

The load-bearing object is the dusty Boussinesq shearing box in axisymmetry, with dust treated as a pressureless fluid coupled by drag (Stokes number St = tau_s $\Omega$) and evolved through a positive-definite formulation of the dust-to-gas ratio. The argument's central identity is the angular momentum flux budget: the gas flux F_g = delta v_gx delta v_gy is negative in COS turbulence, while the dust flux F_d is more positive than F_g because dust drifts toward pressure maxima; to first order in the terminal-velocity approximation, F_d = F_g + 2 St (delta v_gy)^2. Since the total flux F = F_g + epsilon0 F_d must be negative for zonal flows to form, dust loading can suppress them once epsilon is large enough. The paper estimates the threshold epsilon greater than about $h_g^{2}$/St for dust feedback to inhibit zonal flows in a global disk.

What would settle it

Run a stratified, full-3D equivalent of the fiducial setup at the same resolution: if persistent zonal flows form at epsilon0 = 0.1 and concentrate dust to epsilon > 1, the paper's central limit is false. Alternatively, find an observed disk ring in a COS-susceptible region whose dust-to-gas ratio exceeds unity with a weak pressure perturbation.

Watch

Extended reading notes

Core claim

In the unstratified, axisymmetric Boussinesq shearing box, the nonlinear saturated state of the convective overstability is a set of quasi-steady zonal flows that act as pressure traps for dust. The paper's central result is that this dust-trapping is self-limiting: dust accumulates only until its back-reaction on the gas becomes significant, at which point the zonal flows weaken or never form. In the fiducial run with initial dust-to-gas ratio epsilon0 = 0.01, dust-to-gas ratios reach roughly 0.6 transiently and 0.2-0.3 on average before the zonal flows decay; at epsilon0 = 0.1, zonal flows do not form at all and the gas settles into wave turbulence. The mechanism identified is a competition between the negative gas angular momentum flux that creates zonal flows and the positive dust angular momentum flux produced by dust drifting toward pressure maxima. A global radial pressure gradient, which drives a background dust drift, further weakens trapping. The paper concludes that COS-driven zonal flows are not directly conducive to triggering planetesimal formation.

Load-bearing premise

The result assumes that an unstratified, axisymmetric Boussinesq shearing box with a constant heat sink captures the relevant dust-concentration physics of real disks; if vertical dust settling or 3D vortex formation strengthens trapping, the conclusion that COS cannot trigger planetesimal formation would not hold.

Editorial extensions

If this is right

  • COS zonal flows concentrate dust by at most a factor of order ten, with maximum dust-to-gas ratios near epsilon ~ 0.6 transiently and roughly 0.2-0.3 on average.
  • Dust feedback suppresses zonal flow formation for initial dust-to-gas ratios epsilon0 ~ 0.1, leaving the gas in wave turbulence with negligible dust concentration.
  • A background radial pressure gradient corresponding to Pi greater than about 0.02 reduces dust trapping to factors of about two, because the local pressure bump is weak compared with the global drift.
  • The critical dust-to-gas ratio for dust feedback to inhibit zonal flows is estimated as epsilon greater than about h_g^2/St, which can be below unity for plausible disk parameters.
  • COS-assisted planetesimal formation, if it occurs through vortices, is likely restricted to dust-poor disk regions, since dusty zonal flows either fail to form or are too weak to act as precursors.

Reading between the lines

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

  • Inference: In a stratified disk, dust settles toward the midplane, so local dust-to-gas ratios there would exceed the box-averaged values used here; whether this raises epsilon above unity before feedback shuts off zonal flows is an open question the paper leaves implicit.
  • Inference: If 3D vortex formation proceeds through the breakup of zonal flows, the axisymmetric result implies a dust-abundance ceiling for COS-assisted planetesimal formation; vortices forming in dust-poor gas may later accrete dust faster than feedback can suppress them.
  • Inference: The identity F_d = F_g + 2 St (delta v_gy)^2 could be tested directly in full 3D simulations or particle-loaded local models where dust back-reaction is resolved, providing a quantitative check of the proposed feedback mechanism.
  • Inference: An observational consequence would be that dust rings in COS-active disk regions should show internal dust-to-gas ratios below unity and weak pressure perturbations, distinguishing them from rings produced by planets or dead-zone edges.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper studies dust dynamics in the convective overstability (COS) of protoplanetary disks using high-resolution axisymmetric, unstratified Boussinesq shearing-box simulations with a pressureless dust fluid. The authors find that COS-driven zonal flows can concentrate dust to typical factors of O(10) (with transient maxima reaching ε ~ 0.6 for a background ε0 = 0.01), that dust feedback can suppress zonal-flow formation at dust-to-gas ratios ε ~ 0.1, and that a background radial pressure gradient substantially weakens dust trapping. They interpret the feedback effect as a competition between negative gas angular momentum flux and positive dust angular momentum flux, and derive a critical dust-to-gas ratio ε ≳ N/(4St) for feedback to inhibit zonal flows. The paper concludes that COS-driven zonal flows are not directly conducive to planetesimal formation, while acknowledging that stratified and 3D simulations are needed to assess the broader picture.

Significance. If the results are correct, this paper provides a significant counterpoint to earlier suggestions that COS-driven structures can directly trigger planetesimal formation. The work is carefully benchmarked: the code reproduces linear COS and SI growth rates to relative errors of O(10^-4) (Appendix B, Table 1), and the resolution study in Appendix C supports convergence at Nx×Nz = 1024×512. The no-feedback control run isolates the effect of dust drag, and the analytical model for the dust angular momentum flux (Eq. 48 and Appendix D) gives a plausible mechanistic explanation. The main conclusions, however, depend on specific model restrictions—axisymmetry, no vertical gravity, and a constant heat sink—which the authors explicitly identify as limitations. These restrictions mean the astrophysical implications are provisional, but the paper's core results stand as a well-executed study of an idealized but relevant configuration.

major comments (2)
  1. [§5.2, Fig. 3] The no-feedback control run is not a valid control for the claimed dust-feedback effect. In this run the drag term in the gas momentum equation (Eq. 14) is set to zero, so the gas should be dynamically independent of dust. Yet the text states that this run 'behaves similarly to the fiducial case until 900P, whence ε reaches O(0.1), and activity drops towards the ε0=0.1 run.' If feedback is truly disabled, the gas cannot respond to ε, so the late-time drop in the orange curve must either be an intrinsic property of the pure-gas COS in this box (long-term modulation or decay of zonal flows) or indicate an unintended residual dust-gas coupling in the implementation. In the former case, the drop in the fiducial run at ~800P, attributed in §5.1 to 'dust feedback onto the zonal flows,' is partly or wholly an intrinsic gas-phase process, and the causal role of dust feedback is not established. In the latter case, the control is invalid. The authors should compare with a genuine dust-free gas run (evolving only Eqs. 13–15) or otherwise demonstrate that the pure-gas COS does not exhibit a similar decline over the 1000-orbit timescale. This issue is load-bearing for the attribution of the late-time weakening to dust feedback, although the ε0 = 0.1 run provides independent evidence that strong dust loading can suppress zonal-flow formation.
  2. [Abstract, §5.1, Fig. 7] The abstract states that dust densities 'increase at most by a factor of O(10)', but the fiducial run's maximum dust-to-gas ratio reaches ε ≈ 0.6 on a background of ε0 = 0.01, i.e., a factor of 60, at 800P and 850P (Fig. 7 and §5.1). The text also says 'concentration factors are typically O(10)' but then says they 'appear limited by ε = 0.6', which is a factor of 60. This is an internal inconsistency in a quantitative claim that appears in the abstract. The authors should rephrase to distinguish typical concentration factors (O(10)) from transient maxima (up to a factor of ~60), or restrict the 'at most' statement to time-averaged values.
minor comments (4)
  1. [§2.6] The description of disabling dust feedback is clear, but the sentence 'Neglecting feedback is usually justified for ε≪1, but we shall find that it affects the COS even in this regime' could be made more precise: the subsequent results show that feedback affects zonal-flow formation at ε ~ 0.1, not necessarily at ε ≪ 0.01.
  2. [§5.3] The notation δvgx, δvgy for deviations from equilibrium is introduced in Eq. 40, but in earlier sections δ denotes Eulerian linear perturbations. To avoid confusion, the authors could use a different symbol (e.g., Δ or prime) for nonlinear deviations from the equilibrium state.
  3. [§5.1] The sentence 'The two epochs of rapid dust growth at 800P and 850P in the fiducial run show that feedback may temporarily boost concentrations, probably via streaming-type instabilities' is speculative: the fiducial setup has Π = 0, and the paper earlier states that the streaming instability is suppressed in that case. The local radial pressure gradients from zonal flows can indeed drive relative drift, but the connection to streaming-type instabilities should be explained or softened.
  4. [§7.2.2] The empirical fit max(ε) ≃ 1.25St + 0.01 in §6.2 is presented without error bars or a discussion of the scatter shown in Fig. 17. Reporting the goodness of fit and the range of St over which the linear relation holds would strengthen this result.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: central results are direct simulations benchmarked against independent linear theory; self-citations are verified and not load-bearing.

full rationale

The paper's central claims are produced by direct numerical simulations (Dedalus) of the full dusty-gas equations, and the derivation chain is not circular. The simulation code is benchmarked in Appendix B against independently computed linear growth rates for both the COS and SI, reproducing theory to O(10^-4) relative error, so the linear-theory input from Lehmann & Lin (2023) is independently verified rather than merely self-cited. The critical dust-to-gas ratio estimate in Sec. 7.2.1 and Appendix D is a linear-theory prediction using the external inviscid COS growth rate s = N/4 from Latter (2016), combined with the authors' own AMF expressions; the agreement with the saturation level max(eps) ~ 0.25 seen in Fig. 14 is a genuine comparison, not a fitted parameter. The AMF decomposition leading to Eq. (48) is derived from the governing equations using the terminal velocity approximation and geostrophic balance, then checked against measured fluxes in Fig. 19; it is an interpretive diagnostic, not an input to the simulations. The only empirical fit, max(eps) ~ 1.25 St + 0.01 (Sec. 6.2), is explicitly presented as a fit and used to infer alpha_d ~ St^-1, with a call for future Lagrangian-particle tests; it is not renamed as a prediction. Self-citations to Lehmann & Lin (2023, 2024) supply the linear dusty-gas framework and related context, but they are either externally anchored (Latter 2016; TL21) or verified by the paper's own code tests, so they are not load-bearing circular citations. One non-circular caveat should be weighed: the no-feedback control run (Sec. 5.2, orange curve) is described as behaving like the fiducial run until ~900 P, 'whence eps reaches O(0.1), and activity drops towards the eps0=0.1 run,' even though the gas momentum equation has its dust-drag term set to zero; this suggests either an intrinsic late-time decay of the pure-gas COS or an unintended residual coupling, which weakens the attribution of the fiducial run's zonal-flow weakening to dust feedback. This is a correctness/control-validity concern, not a circular reduction, and it does not raise the circularity score. Overall: low circularity burden, score 2 for minor non-load-bearing self-citations.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The model parameters are disk-like input values (N = 0.1, Pe = 160 pi^2, Re = 10^5, St = 0.1, epsilon0 = 0.01, Pi = 0) rather than fitted quantities; the only fit to data is an empirical linear relation in §6.2. The load-bearing assumptions are geometric (axisymmetric, unstratified), thermal (constant heat sink), and the choice of dust diffusion equal to viscosity. All are stated in the text.

free parameters (1)
  • slope of max(epsilon) vs St empirical fit = 1.25
    Empirical linear fit max(epsilon) ~ 1.25 St + 0.01 reported in §6.2; describes simulation trend but is not used in the main conclusions.
assumptions (5)
  • domain assumption Unstratified, axisymmetric Boussinesq approximation captures the essential dust-COS interaction
    Used throughout; §2.1-2.2. Excludes vertical settling, vortices, and compressible effects; authors flag in §7.4.
  • domain assumption Constant heat sink offsets dust-induced background entropy transport
    §2.4: a dusty non-isothermal disk cannot stay in thermodynamic equilibrium because dust-induced radial gas flow transports entropy; model assumes a compensating heat sink.
  • domain assumption Dust is a pressureless fluid with constant stopping time and dust diffusion equal to gas viscosity (D = nu_d = nu)
    §2.1, Eqs. 8-10; valid for tightly coupled grains; D is 'primarily for numerical stability'.
  • domain assumption Terminal velocity approximation and geostrophic balance hold for interpreting dust angular momentum flux
    §7.1 and Appendix A; used to derive Fd = Fg + 2St(delta vgy)^2, verified in Fig. 19.
  • standard math Latter (2016) linear COS growth rate s = N/4 applies
    Used in §7.2.1 to estimate the critical dust-to-gas ratio epsilon ~ N/(4St); external result.

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Pith. "Pith review of Dust dynamics in radially convective regions of protoplanetary disks." pith.science (2026). https://pith.science/paper/AA56ENO5

@misc{pith2026250109792,
  author       = {Pith},
  title        = {Pith review of: Dust dynamics in radially convective regions of protoplanetary disks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AA56ENO5}},
  note         = {Machine review of arXiv:2501.09792}
}
abstract

Hydrodynamic instabilities likely operate in protoplanetary disks. One candidate, Convective Overstability (COS), can be triggered in regions with a negative radial entropy gradient. The ensuing turbulence and flow structures are expected to affect dust dynamics directly. We revisit the interaction between dust and the COS with high-resolution spectral simulations in the unstratified, axisymmetric Boussinesq shearing box framework. We find zonal flows, or pressure bumps, formed by the COS trap dust, as expected, but dust densities increase at most by a factor of $O(10)$ over its background value due to the zonal flows' unsteady nature. Furthermore, dust feedback can impede the formation of zonal flows, even at small dust-to-gas ratios $\epsilon \sim O(0.1)$. We interpret this phenomenon as a competition between the negative gas angular momentum flux associated with zonal flow formation and the positive dust angular momentum flux associated with its drift towards pressure maxima. Dust concentration significantly weakens when a large-scale radial pressure gradient induces a background dust drift. Ultimately, we find that dust concentration by COS-induced zonal flows is limited to $\epsilon \lesssim 1$. Whether this can be improved under more realistic geometries must be addressed with stratified and full 3D simulations at equivalent resolutions.

Figures

Figures reproduced from arXiv: 2501.09792 by the authors.

Figure 1
Figure 1. COS with ϵ0 = 0.01 (left) and ϵ0 = 1 (right). Other parameters are: N = 0.1, Pe = 160π 2 , Re = 105 , and St = 0.1. No background global radial pressure gradient is applied [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 3
Figure 3. Evolution of the gas velocity perturbations for the COS in the fiducial run (blue), that without feedback (orange), a larger dust-to-gas ratio (green), and with a non￾zero pressure gradient (red) [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Space-time plot of the vertically-averaged pres￾sure distribution in the fiducial run. We examine the role of dust feedback with one run strictly without feedback and one run with stronger feed- [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (15 more)
Figure 5
Figure 5. Figure 5: Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Selected snapshots of the dust-to-gas ratios of the fiducial run. back using ϵ0 = 0.1. These are shown as the orange and green curves in Figs. 3—7, respectively. COS turbulence is weakened by dust feedback for ϵ ≳ O(0.1). This is evident from [PITH_FULL_IMAGE:figures/…
Figure 10
Figure 10. Figure 10: Total angular momentum flux in the fiducial run (blue) and the run with stronger feedback using ϵ0 = 0.1. Fluxes are averaged over 100 orbit intervals to improve visibility [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: Space-time plot of the vertically-averaged, local radial pressure gradient for the run with a background global radial pressure gradient Π = 0.05 (red curves in Figs. 3 and 7). radial drift. The SI is then formally active, but we verified it has lower growth rates tha…
Figure 12
Figure 12. Figure 12: Evolution of the gas velocity perturbations for the COS under stronger thermal diffusion Pe = 16π 2 for ϵ0 = 0.01 (blue) and ϵ0 = 0.1 (orange). When Π ̸= 0, dust concentration becomes more diffi￾cult because it drifts in response to the box-wide pres￾sure gradient. Zo…
Figure 14
Figure 14. Figure 14: Maximum dust-to-gas ratios averaged between t ∈ [500, 1000]P as a function of the initial dust-to-gas ratio [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]
Figure 16
Figure 16. Figure 16: Angular momentum fluxes as a function of ini￾tial dust-to-gas ratios. Top: negative of the gas flux; middle: dust flux; bottom: negative of the total flux. Fluxes are av￾eraged over [500, 1000] orbits [PITH_FULL_IMAGE:figures/full_fig_p011_16.png]
Figure 17
Figure 17. Figure 17: Maximum dust-to-gas ratios averaged between t ∈ [500, 2000]P of simulations with varying Stokes numbers. constant. However, this dependence is steeper than one expects from simple diffusion theory. We discuss this in §7.2.2. 6.3. Varying Π [PITH_FULL_IMAGE:figures/fu…
Figure 18
Figure 18. Figure 18: Maximum dust-to-gas ratios averaged between t ∈ [500, 1000]P as a function of the background radial pres￾sure gradient. pressure perturbations associated with the COS relative to the background gradient. Zonal flows form in all sim￾ulations, and AMFs are similar (not …
Figure 19
Figure 19. Figure 19: Vertically and time-averaged (between t ∈ [500, 1000]P) angular momentum flux difference associated with dust and gas velocity fluctuations (blue), and its value according to the model given by Eq. 48 with δvgy given via Eq. 46 (orange). The close match shows that the…
Figure 20
Figure 20. Figure 20: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_20.png]
Figure 21
Figure 21. Figure 21: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_21.png]
Figure 22
Figure 22. Figure 22: Linear growth of the COS simulated by dedalus (lines), compared with analytic growth rates (asterisks). Dust drag is treated via the full differential velocity equation (blue solid) or the TVA (orange dashed). Left panel: a dust-poor disk with ϵ0 = 0.01 (only the exac…
Figure 23
Figure 23. Figure 23: Linear growth of the SI simulated by dedalus (lines), compared with analytic growth rates (asterisks). Dust drag is treated via the full differential velocity equation (blue solid) or the TVA (orange dashed) [PITH_FULL_IMAGE:figures/full_fig_p019_23.png]
Figure 24
Figure 24. Figure 24: Maximum dust concentration factors at different resolutions, using the fiducial setup for the physical parameters (§5.1). C. RESOLUTION STUDY Our fiducial resolution of Nx × Nz = 2048 × 1024 is limited by computational cost. Here, we perform lower￾resolution runs to t…

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Works this paper leans on

56 extracted references · 13 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

  3. [3]

    ذ uA DPYY]Y mXWlY em

    thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

    2021

  4. [4]

    Balbus , S. A. 2003, , 41, 555, 10.1146/annurev.astro.41.081401.155207

    work page arXiv 2003

  5. [5]

    J., & Latter , H

    Barker , A. J., & Latter , H. N. 2015, , 450, 21, 10.1093/mnras/stv640

    doi:10.1093/mnras/stv640 2015

  6. [6]

    A., Pei , S., & Marcus , P

    Barranco , J. A., Pei , S., & Marcus , P. S. 2018, , 869, 127, 10.3847/1538-4357/aaec80

    doi:10.3847/1538-4357/aaec80 2018

  7. [7]

    2024, Annual Review of Astronomy and Astrophysics, https://doi.org/10.1146/annurev-astro-071221-052705

    Birnstiel, T. 2024, Annual Review of Astronomy and Astrophysics, https://doi.org/10.1146/annurev-astro-071221-052705

    doi:10.1146/annurev-astro-071221-052705 2024

  8. [8]

    J., Vasil , G

    Burns , K. J., Vasil , G. M., Oishi , J. S., Lecoanet , D., & Brown , B. P. 2019, arXiv e-prints, arXiv:1905.10388. 1905.10388

    arXiv 2019

Show all 56 references
  1. [9]

    2023, in Astronomical Society of the Pacific Conference Series, Vol

    Dra \.z kowska , J., Bitsch , B., Lambrechts , M., et al. 2023, in Astronomical Society of the Pacific Conference Series, Vol. 534, Protostars and Planets VII, ed. S. Inutsuka , Y. Aikawa , T. Muto , K. Tomida , & M. Tamura , 717, 10.48550/arXiv.2203.09759

    2023 doi arXiv

  2. [10]

    P., Birnstiel , T., Huang , J., et al

    Dullemond , C. P., Birnstiel , T., Huang , J., et al. 2018, , 869, L46, 10.3847/2041-8213/aaf742

    2018 doi

  3. [11]

    2017, arXiv e-prints, arXiv:1705.03319

    Fromang , S., & Lesur , G. 2017, arXiv e-prints, arXiv:1705.03319. 1705.03319

    2017 arXiv

  4. [12]

    1965, , 130, 125

    Goldreich , P., & Lynden-Bell , D. 1965, , 130, 125

    1965

  5. [13]

    2011, , 415, 3591, 10.1111/j.1365-2966.2011.18971.x

    Jacquet , E., Balbus , S., & Latter , H. 2011, , 415, 3591, 10.1111/j.1365-2966.2011.18971.x

    2011

  6. [14]

    2024, arXiv e-prints, arXiv:2404.15933, 10.48550/arXiv.2404.15933

    Klahr , H. 2024, arXiv e-prints, arXiv:2404.15933, 10.48550/arXiv.2404.15933

    2024 doi arXiv

  7. [15]

    Klahr , H., Baehr , H., & Melon Fuksman , J. D. 2023, arXiv e-prints, arXiv:2305.08165, 10.48550/arXiv.2305.08165

    2023 doi arXiv

  8. [16]

    2014, , 788, 21, 10.1088/0004-637X/788/1/21

    Klahr , H., & Hubbard , A. 2014, , 788, 21, 10.1088/0004-637X/788/1/21

    2014 doi

  9. [17]

    N., Kratter , K

    Krapp , L., Youdin , A. N., Kratter , K. M., & Ben \' tez-Llambay , P. 2020, , 10.1093/mnras/staa1854

    2020 doi

  10. [18]

    Latter , H. N. 2016, , 455, 2608, 10.1093/mnras/stv2449

    2016 doi

  11. [19]

    N., & Papaloizou , J

    Latter , H. N., & Papaloizou , J. 2017, , 472, 1432, 10.1093/mnras/stx2038

    2017 doi

  12. [20]

    2023, , 522, 5892, 10.1093/mnras/stad1349

    Lehmann , M., & Lin , M.-K. 2023, , 522, 5892, 10.1093/mnras/stad1349

    2023 doi

  13. [21]

    2024, , 970, 15, 10.3847/1538-4357/ad496c

    ---. 2024, , 970, 15, 10.3847/1538-4357/ad496c

    2024 doi

  14. [22]

    Lesur , G., & Papaloizou , J. C. B. 2010, , 513, A60, 10.1051/0004-6361/200913594

    2010 doi

  15. [23]

    2023, in Astronomical Society of the Pacific Conference Series, Vol

    Lesur , G., Flock , M., Ercolano , B., et al. 2023, in Astronomical Society of the Pacific Conference Series, Vol. 534, Protostars and Planets VII, ed. S. Inutsuka , Y. Aikawa , T. Muto , K. Tomida , & M. Tamura , 465

    2023

  16. [24]

    Lesur , G. R. J., & Latter , H. 2016, , 462, 4549, 10.1093/mnras/stw2172

    2016 doi

  17. [25]

    A., Wendroff , B., & Liska , R

    Li , H., Colgate , S. A., Wendroff , B., & Liska , R. 2001, , 551, 874, 10.1086/320241

    2001 doi

  18. [26]

    M., Lovelace , R

    Li , H., Finn , J. M., Lovelace , R. V. E., & Colgate , S. A. 2000, , 533, 1023, 10.1086/308693

    2000 doi

  19. [27]

    2019, , 485, 5221, 10.1093/mnras/stz701

    Lin , M.-K. 2019, , 485, 5221, 10.1093/mnras/stz701

    2019 doi

  20. [28]

    2021, , 907, 64, 10.3847/1538-4357/abcd9b

    ---. 2021, , 907, 64, 10.3847/1538-4357/abcd9b

    2021 doi

  21. [29]

    2022, , 926, 14, 10.3847/1538-4357/ac3bb9

    Lin , M.-K., & Hsu , C.-Y. 2022, , 926, 14, 10.3847/1538-4357/ac3bb9

    2022 doi

  22. [30]

    Lin , M.-K., & Youdin , A. N. 2015, , 811, 17, 10.1088/0004-637X/811/1/17

    2015 doi

  23. [31]

    2023, , 526, 80, 10.1093/mnras/stad2629

    Liu , H., & Bai , X.-N. 2023, , 526, 80, 10.1093/mnras/stad2629

    2023 doi

  24. [32]

    2019, , 488, 5290, 10.1093/mnras/stz2035

    Lovascio , F., & Paardekooper , S.-J. 2019, , 488, 5290, 10.1093/mnras/stz2035

    2019 doi

  25. [33]

    Lovelace , R. V. E., Li , H., Colgate , S. A., & Nelson , A. F. 1999, , 513, 805, 10.1086/306900

    1999 doi

  26. [34]

    2014, , 789, 77, 10.1088/0004-637X/789/1/77

    Lyra , W. 2014, , 789, 77, 10.1088/0004-637X/789/1/77

    2014 doi

  27. [35]

    2011, , 527, A138+, 10.1051/0004-6361/201015568

    Lyra , W., & Klahr , H. 2011, , 527, A138+, 10.1051/0004-6361/201015568

    2011 doi

  28. [36]

    Lyra , W., & Umurhan , O. M. 2019, , 131, 072001, 10.1088/1538-3873/aaf5ff

    2019 doi

  29. [37]

    B., Umurhan , O

    Lyra , W., Yang , C.-C., Simon , J. B., Umurhan , O. M., & Youdin , A. N. 2024, , 970, L19, 10.3847/2041-8213/ad5af6

    2024 doi

  30. [38]

    Magnan , N., Heinemann , T., & Latter , H. N. 2024, , 10.1093/mnras/stae1978

    2024 doi

  31. [39]

    S., Pei , S., Jiang , C.-H., et al

    Marcus , P. S., Pei , S., Jiang , C.-H., et al. 2015, , 808, 87, 10.1088/0004-637X/808/1/87

    2015 doi

  32. [40]

    S., Pei , S., Jiang , C.-H., & Hassanzadeh , P

    Marcus , P. S., Pei , S., Jiang , C.-H., & Hassanzadeh , P. 2013, Physical Review Letters, 111, 084501, 10.1103/PhysRevLett.111.084501

    2013 doi

  33. [41]

    C., & Kataoka , A

    Miotello , A., Kamp , I., Birnstiel , T., Cleeves , L. C., & Kataoka , A. 2023, in Astronomical Society of the Pacific Conference Series, Vol. 534, Protostars and Planets VII, ed. S. Inutsuka , Y. Aikawa , T. Muto , K. Tomida , & M. Tamura , 501, 10.48550/arXiv.2203.09818

    2023 doi arXiv

  34. [42]

    P., Gressel , O., & Umurhan , O

    Nelson , R. P., Gressel , O., & Umurhan , O. M. 2013, , 435, 2610, 10.1093/mnras/stt1475

    2013 doi

  35. [43]

    Ormel , C. W. 2024, arXiv e-prints, arXiv:2411.14643, 10.48550/arXiv.2411.14643

    2024 doi arXiv

  36. [44]

    R., Julien , K., & Stewart , G

    Petersen , M. R., Julien , K., & Stewart , G. R. 2007 a , , 658, 1236, 10.1086/511513

    2007 doi

  37. [45]

    R., Stewart , G

    Petersen , M. R., Stewart , G. R., & Julien , K. 2007 b , , 658, 1252, 10.1086/511523

    2007 doi

  38. [46]

    2017, in Astrophysics and Space Science Library, Vol

    Pinilla , P., & Youdin , A. 2017, in Astrophysics and Space Science Library, Vol. 445, Formation, Evolution, and Dynamics of Young Solar Systems, ed. M. Pessah & O. Gressel , 91, 10.1007/978-3-319-60609-5\_4

    2017 doi

  39. [47]

    Pringle , J. E. 1981, , 19, 137, 10.1146/annurev.aa.19.090181.001033

    1981

  40. [48]

    2015, , 804, 35

    Raettig, N., Klahr, H., & Lyra, W. 2015, , 804, 35. http://stacks.iop.org/0004-637X/804/i=1/a=35

    2015

  41. [49]

    2013, , 765, 115, 10.1088/0004-637X/765/2/115

    Raettig , N., Lyra , W., & Klahr , H. 2013, , 765, 115, 10.1088/0004-637X/765/2/115

    2013 doi

  42. [50]

    2021, arXiv e-prints, arXiv:2103.04476

    ---. 2021, arXiv e-prints, arXiv:2103.04476. 2103.04476

    2021 arXiv

  43. [51]

    I., & Sunyaev , R

    Shakura , N. I., & Sunyaev , R. A. 1973, , 24, 337

    1973

  44. [52]

    2013, , 764, 20, 10.1088/0004-637X/764/1/20

    Shi , J.-M., & Chiang , E. 2013, , 764, 20, 10.1088/0004-637X/764/1/20

    2013 doi

  45. [53]

    J., & Latter , H

    Teed , R. J., & Latter , H. N. 2021, , 507, 5523, 10.1093/mnras/stab2311

    2021 doi

  46. [54]

    2024, , 962, 173, 10.3847/1538-4357/ad15fe

    Wu , Y., Lin , M.-K., Cui , C., et al. 2024, , 962, 173, 10.3847/1538-4357/ad15fe

    2024 doi

  47. [55]

    2007, , 662, 613, 10.1086/516729

    Youdin , A., & Johansen , A. 2007, , 662, 613, 10.1086/516729

    2007 doi

  48. [56]

    N., & Goodman , J

    Youdin , A. N., & Goodman , J. 2005, , 620, 459, 10.1086/426895

    2005 doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.