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Strong clumping in global streaming instability simulations with a dusty fluid

T0 review · 4 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Global simulations of the streaming instability show dust clumps reaching only 30% of the Hill density after 160 orbits, so gravitational collapse would need roughly 480 to 1000 orbits.

desk verdict Useful first global dust-fluid SI results with an honest extrapolation that gets slightly oversold in the abstract; the 30%-of-Hill-density measurement is the robust part. read the letter →

arxiv 2501.18424 v2 pith:PO7P76KB submitted 2025-01-30 astro-ph.EP

Dominik Ostertag , Mario Flock This is my paper · ORCID
classification astro-ph.EP
keywords streaminginstabilityprotoplanetarydisksdustclumpingplanetesimalformationHilldensitydust-fluidmodelglobaldisksimulations
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

Using a global 2D stratified disk model rather than a local box, this paper asks whether the streaming instability alone can pack dust into clumps dense enough to collapse into planetesimals. With a dust-to-gas mass ratio of Z=0.02, dense clumps appear within 20 orbits, but after 160 orbits the densest clump reaches only about 30% of the local Hill density, the threshold for gravitational collapse. The authors extrapolate the roughly exponential growth of the maximum density and estimate that reaching the Hill density would take about 480 orbits in a massive disk, and up to about 1000 orbits in a less massive or compact disk. If right, the streaming instability is slower and less efficient at building collapse-ready clumps than earlier local simulations indicated, and the clumps it forms are too closely spaced for current observatories to resolve.

What carries the argument

The machinery is a two-fluid hydrodynamic model in which the gas is a stratified disk and the dust is a pressureless fluid with aerodynamic back-reaction and dust diffusion, run at a Stokes number of St=0.01 and a pressure-gradient parameter of Π=0.07. The streaming instability is the aerodynamic drag instability that concentrates dust when dust and gas densities are comparable. The paper measures the maximum dust density in a 2D axisymmetric (R,z) disk and compares it with the local Hill density, $\rho_{\mathrm{Hill}} = 9 M_* / (4\pi R^3)$, which sets the threshold for gravitational collapse. That ratio, maximum clump density over local Hill density, is the quantity that turns a clumping simulation into a statement about when planetesimal formation can begin.

What would settle it

Run the same Z=0.02 setup in a full 3D stratified model, or at least at double resolution in 2D, and track the maximum dust density relative to $\rho_{\mathrm{Hill}}$ for 500 orbits. If the ratio crosses 1 within about 300 orbits, the extrapolated timescale is too slow; if it stays below 0.3 after 160 orbits, the slow-collapse conclusion is supported.

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Extended reading notes

Core claim

The central discovery is that in a realistic global disk, clumping by the streaming instability is real but limited: at a global dust-to-gas ratio Z=0.02, dust clumps form throughout the domain within about 20-25 orbits and reach roughly 30% of the local Hill density after 160 orbits at 10 au. The maximum dust density then appears to grow exponentially once the nonlinear phase sets in, and the paper's extrapolation places gravitational collapse at about 480 orbits, with clumps drifting only about one au inward during that time; for a less massive or compact disk the number rises to about 1000 orbits. A companion run with Z=0.01 shows no strong clumping, matching earlier results. The clumps drift inward more slowly than the background dust because their high dust-to-gas ratio shields them from aerodynamic drag, and their average separation at 10 au is about 0.03 au.

Load-bearing premise

The 480-orbit estimate assumes both that the 2D axisymmetric pressureless-fluid setup captures the same streaming-instability clumping as fully 3D simulations, and that the maximum clump density keeps growing exponentially beyond 160 orbits, a trend the paper itself says no theory guarantees.

Editorial extensions

If this is right

  • Streaming-instability collapse in a massive disk would take roughly 480 orbits, corresponding to tens to hundreds of thousands of years; in less massive or compact disks the estimate doubles to roughly 1000 orbits.
  • Collapse is more likely outside about 10 au, where the Hill density falls with radius faster than the gas midplane density.
  • The dense clumps formed at Z=0.02 are spaced by about 0.03 au at 10 au, far too close to be resolved by current or planned millimeter observatories.
  • A disk with Z=0.01 does not produce strong clumps, placing the clumping threshold for this global setup between 1% and 2% dust-to-gas ratio.
  • The clumps slow their inward drift as they densify, so the one to two au of drift before collapse is probably an upper limit rather than a lower bound.

Reading between the lines

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

  • The 480- and 1000-orbit numbers are extrapolations, not simulated outcomes; if the exponential growth stalls, the true collapse times are longer, while if axisymmetry suppresses 3D modes, they could be shorter.
  • A testable next step is to let clumps continue for hundreds more orbits in a disk with a wider radial domain to check whether the traffic-jam self-shielding keeps drift this slow while density approaches the Hill value.
  • The optical-depth calculation suggests that unresolved clumps could still leave a detectable signature as optically thick spots in a mostly optically thin disk at long wavelengths; searching for such contrast in inclined disks is a way to constrain the instability observationally.
  • If real disks carry even weak turbulence, clump lifetimes and densities may drop below this no-turbulence estimate, pushing planetesimal formation further out in radius or to higher metallicities.
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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 Letter reports global 2D axisymmetric (R,z) FARGO3D simulations of the streaming instability in a stratified protoplanetary disk at 9.3–10.7 au, treating dust as a pressureless fluid with aerodynamic backreaction and dust diffusion. For Z = Σd/Σg = 0.01 the authors confirm weak clumping; for Z = 0.02 dense clumps form within about 20 orbits. The measured maximum dust density reaches roughly 30% of the local Hill density after 160 orbits, and the authors extrapolate this growth exponentially to estimate that Hill density is reached after about 480 orbits, or about 1000 orbits for less massive or compact disks after rescaling by a factor of 6.5. They then compare five observed disk midplane density profiles to the Hill density, estimate a clump separation of about 0.03 au at 10 au, and conclude that such structures are unresolved by ALMA and ngVLA, predicting efficient planetesimal formation outside 10 au.

Significance. If the measured clump densities and the extrapolated collapse times are confirmed, the paper is significant: it provides one of the first global, stratified dust-fluid tests of streaming-instability clumping and argues that SI-driven planetesimal formation is less efficient than inferred from local 3D simulations. The study's strengths include the use of a public code (FARGO3D), a direct comparison of the simulated maximum density to the Hill density, an honest caveat in Section 4 about the lack of a theory for the maximum-density evolution, and a falsifiable observability prediction for ALMA/ngVLA. However, the central quantitative claim rests on an unvalidated exponential extrapolation, and the numerical method lacks a convergence test, a specification of the dust-diffusion treatment, and a 3D validation; these issues currently prevent the timescales from being accepted as established.

major comments (4)
  1. [Section 3.1 and Fig. 3; Section 4] The 480-orbit collapse time is obtained by extrapolating an exponential fit to the envelope of the maximum dust density, and Section 4 explicitly concedes that no theory predicts how the maximum local dust density evolves and that there is no guarantee the profile remains exponential. Because the maximum is set by different clumps at different times, the fitted e-folding time is not tied to a single physical object, and no uncertainty is assigned to the extrapolation. The 1000-orbit estimate for rescaled, less massive disks in Section 4 inherits this uncertainty, as do the derived inward-drift limits and the conclusion that SI clumping is less efficient than previously thought. Please either run the simulation toward the Hill-density crossing, provide a physically motivated model for the envelope, or present 480–1000 orbits explicitly as an illustrative extrapolation rather than a quantitative prediction.
  2. [Section 2 and Table 1] The pressureless-dust-fluid method is used with the FARGO3D dust module, but the dust-diffusion prescription and its coefficient are never stated. In a pressureless fluid, peak densities are controlled by physical or numerical diffusion, and without specifying the diffusion treatment the reported 30% of Hill density after 160 orbits is not a fully determined simulation result. No resolution-convergence study is presented either. A convergence sequence (for example, at half and double the current resolution) and a clear statement of the diffusion coefficient (including an explicit zero if no diffusion is applied) are required to support the central density measurement.
  3. [Section 2] The simulations are 2D axisymmetric in (R,z), and the meridional domain is only ±0.014 rad about the midplane, corresponding to about ±0.14 au (roughly ±0.2 gas scale heights) at 10 au. The setup therefore excludes azimuthal and non-axisymmetric streaming-instability modes and contains only a weak vertical gas stratification, yet the clumping statistics are compared with 3D local shearing-box calculations. Please justify the vertical domain size and show that the axisymmetric dust-fluid model reproduces the clumping behavior of a 3D calculation (for example, a local shearing-box run with the same Z, St, and Π) before the measured densities and extrapolated timescales are transferred to real disks.
  4. [Appendix B] The dust-refilling prescription resets the dust density to its initial value in the outer damping zone whenever it falls below 25% of the initial value, and Eq. (B.5) continuously damps the gas density toward the initial state over the entire domain. This is a persistent artificial mass source at the outer boundary that can feed the inwardly drifting clumps and directly affect the growth of ρdust,max. The sensitivity to the 25% threshold, the refilling location, and the damping timescale is not tested, and the text's own reference to possible outer-boundary artifacts in the choice of the 9.4–10.4 au window makes this a live concern.
minor comments (4)
  1. [Section 3.1] The clump drift velocity is said to be 'fitted by eye'; please provide a quantitative fit with an uncertainty estimate.
  2. [Section 3.1] The sentence 'The chosen domain is meant not to exclude clumps that are an artifact from the outer boundary' is ambiguous; if the intent is to exclude such clumps, please reword accordingly.
  3. [Section 4] The final sentence of Section 4 ends with the dangling word 'resolve' after mentioning the method of Scardoni et al. (2024); the sentence is incomplete and should be finished.
  4. [Abstract and Conclusions] The phrase 'using disk parameters from GM Aur, HD163296, IM Lup, MWC 480, and TW Hya' overstates what is done: Fig. 4 compares analytic midplane density profiles to the Hill density, while the simulation uses one canonical profile at 10 au. Please rephrase to 'consistent with the midplane densities of...'.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the clumping result is simulation-produced and externally benchmarked, while the 480-orbit collapse time is an acknowledged extrapolation rather than a construction from inputs.

full rationale

Walking the derivation chain, the clumping measurement (Sect. 3, Fig. 3) is generated by a FARGO3D simulation whose initial conditions are taken from Flock & Mignone (2021); the Hill-density threshold (Eq. 1) is an external physical yardstick; the Zcrit conversion from Li & Youdin (2021) is used only to place the run in parameter space; and the 480/1000-orbit collapse times are obtained by extrapolating the simulated maximum dust density, with the exponential form explicitly stated to have no theoretical guarantee: 'no theory has predicted yet how the maximum local dust density evolves in time due to non-linear streaming instability... there is no guarantee that the profile will continue to be of exponential shape' (Sect. 4). None of these steps defines the target result in terms of the input or fits a parameter to the target quantity. The only self-citation that appears is Flock & Mignone (2021) for the disk setup and damping/refilling recipes; that setup does not encode the clumping outcome, so it is not load-bearing for the central claim. The extrapolation from 30% to 100% of Hill density is an acknowledged model-form assumption and a genuine numerical prediction from simulation output, not a circular reduction. Because the paper is benchmarked against independent local simulations (Li & Youdin 2021; Lim et al. 2024b) and uses an external criterion (Hill density), the central claim has independent content. Score 2 reflects only the minor non-load-bearing self-citation, not any circular derivation.

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

The paper introduces no new physical entities. The central claims rest on five chosen simulation parameters, two domain assumptions about the fluid treatment and geometry, one ad hoc exponential extrapolation, one representativeness assumption about observed disk profiles, and the standard Hill-density collapse criterion.

free parameters (5)
  • Dust-to-gas surface density ratio Z = 0.01 and 0.02
    The two chosen values bracket the strong-clumping threshold. Z=0.02 is the value on which the central clumping result depends.
  • Stokes number St = 0.01
    Sets the drag regime and the clumping behavior. Chosen to match Flock & Mignone (2021) and to remain in the pressureless-fluid regime St<0.1.
  • Pressure gradient parameters Pi and eta = Pi=0.07, eta=0.0049
    Set the dust-gas drift speed that drives the streaming instability and clump drift; central to the simulated dynamics.
  • Gas surface density Sigma0 = 390 g/cm^2
    Chosen so the midplane density at 10 au matches observed massive disks; no uncertainty propagation is provided.
  • Dust refilling threshold in outer damping zone = 25% of initial density
    Appendix B resets dust density to the initial value whenever it falls below 25% of that value, continuously adding dust at the outer boundary; no sensitivity run is shown.
assumptions (5)
  • domain assumption Dust as a pressureless fluid is valid for St=0.01
    Invoked in Section 2, relying on Weber et al. (2019). Neglects dust pressure and finite particle-size effects.
  • domain assumption 2D axisymmetric geometry captures the streaming instability clumping dynamics
    Section 2 states the setup is 2D-axisymmetric in (r,theta); no 3D validation or convergence study is shown, so the suppression of azimuthal modes is untested.
  • ad hoc to paper Exponential extrapolation of maximum clump density beyond 160 orbits
    Section 4 admits no theory predicts the maximum-density evolution and there is no guarantee the exponential shape continues, yet the 480 and 1000 orbit collapse estimates depend on it.
  • domain assumption Observed disk profiles of Martire et al. (2024) and Yoshida et al. (2022) are representative for Class II disks
    Used in Section 3.2 to identify sweet spots for planetesimal formation; no ensemble treatment or uncertainty propagation is presented.
  • standard math Hill density marks the gravitational collapse threshold
    Equation (1), following Klahr & Schreiber (2020), is a standard criterion in planet formation.

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Cite this review

Pith. "Pith review of Strong clumping in global streaming instability simulations with a dusty fluid." pith.science (2026). https://pith.science/paper/PO7P76KB

@misc{pith2026250118424,
  author       = {Pith},
  title        = {Pith review of: Strong clumping in global streaming instability simulations with a dusty fluid},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PO7P76KB}},
  note         = {Machine review of arXiv:2501.18424}
}
read the original abstract

Context: How planets form in protoplanetary disks and what drives the formation of their seeds is still a major unknown. It is an accepted theory that multiple processes can trap dusty material in radially narrow rings or vortex-like structures, preventing the dust from drifting inwards. However, the relevant process for clumping this dusty material until it collapses under gravity still needs to be identified. One promising candidate is the streaming instability arising from the aerodynamic interaction between dust and gas once they reach similar densities. Aims: We investigate with a global disk model based on recent observational constraints if streaming instability can form dust clumps, which might gravitationally collapse. Further, our goal is to verify the observability of the produced structures using ALMA or ngVLA. Methods. For the first time, we present global 2D (R, z) hydrodynamic simulations using FARGO3D in which the dust is treated as a pressureless fluid. The disk model assumes stratification, realistic boundary conditions, and meaningful resolution to resolve the fast-growing modes. We choose two values for the total dust-to-gas mass ratio Z = 0.01 and Z = 0.02, compare the maximum clump density to the local Hill density, and compute the optical depth of the dust disk. Results: With a dust-to-gas mass ratio of Z = 0.01, we confirm previous streaming instability simulations, not showing the ability to form strong concentrations of dust clumps. With Z = 0.02, dense clumps form within 20 orbits, however reaching only 30% of the Hill density even following disk parameters from the massive protoplanetary disks GM Aur, HD163296, IM Lup, MWC 480, and TW Hya, which all share astonishingly similar surface density profiles.

Figures

Figures reproduced from arXiv: 2501.18424 by the authors.

Figure 1
Figure 1. Comparison between a dust fluid simulation with a metalicity of Z=0.01 (top) and Z = 0.02 (bottom) after 100 orbits at 10 au [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Evolution of the disk with Σd/Σg = 0.02. Top: 2D dust density after 160 orbits, bottom: Evolution of the surface density ratio over 160 orbits. The white dashed line shows the theoretical radial drift with a constant drift velocity of vr,clump = 30 cm s−1 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Evolution of the maximum dust density between 9.4 and 10.4 au over 160 orbits for the considered simulations. The black line indicates the density ratio clumps must reach to collapse under their gravity. The chosen domain is meant not to exclude clumps that are an artifact from the outer boundary. 9) a method to convert from Zcrit(St = 0.01, Π = 0.05) ≈ 0.016 to Zcrit(St = 0.01, Π = 0.07) ≈ 0.022. Because this value… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Comparison between five midplane gas density profiles (grey, orange) and their critical Hill densities (blue). For reference, the red dot indicates our work’s central location and gas density. A similar plot (albeit with only one gas density profile) was already shown …

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Cited by 1 Pith paper

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