A unique solution to overcome the barriers to planetesimal formation at low dust-to-gas ratio

F. A. Gerosa; H. Meheut; J. Bec

REVIEW 4 major objections 7 minor 19 references

A unique solution to overcome the barriers to planetesimal formation at low dust-to-gas ratio

T0 review · 4 major / 7 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Weakly turbulent disks alone may gather pebbles into dense clusters and halt their drift, offering a single-process path to planetesimal formation at ordinary dust-to-gas ratio.

desk verdict A plausible, clearly presented synthesis of the authors' own simulations, identifying a low-turbulence regime where pebbles cluster in anticyclonic eddies and radial drift is reduced or halted; but the leap to a 'unique path' to planetesimal formation is not backed by a density or collapse calculation. read the letter →

arxiv 2508.20070 v1 pith:TQJHPIWL submitted 2025-08-27 astro-ph.EP astro-ph.SR

H. Meheut , F. A. Gerosa , J. Bec This is my paper · ORCID

classification astro-ph.EPastro-ph.SR

keywords protoplanetarydisksplanetesimalformationKeplerianturbulenceradialdriftanticycloniceddiesdustclusteringshearingboxpebbles

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 proposes that the turbulence present in protoplanetary disks, when captured in full rather than approximated by a diffusion coefficient, can itself solve the two classic barriers to planetesimal formation: inward radial drift and insufficient solid concentration. In two-dimensional shearing-box simulations of Keplerian turbulence at low turbulent intensity, centimeter-to-meter solids clump into point clusters inside anticyclonic eddies, and their drift toward the star is slowed or completely stopped. The authors argue this 'Keplerian turbulence clustering' is a distinct mechanism from ordinary turbulent concentration, and that it could allow gravitational collapse to form planetesimals without invoking pressure bumps or the streaming instability. A sympathetic reader would care because it suggests a unique, self-contained route to planet formation in the standard low-dust-to-gas-ratio disk.

What carries the argument

The central mechanism is 'Keplerian turbulence clustering': long-lived anticyclonic vortices in weakly turbulent disks concentrate solid grains toward their centers via the Coriolis force, forming point clusters. The same elongated eddy geometry that traps particles also explains the drift reduction, because the eddies' small radial extent limits the radial acceleration of particles and their long azimuthal extent blocks inward motion. A complementary tool, the Lyapunov dimension of the particle set in phase space, is used to classify the three dynamical behaviors: diffusion, filamentary structures, and point clusters.

What would settle it

A 3D stratified shearing-box simulation with self-gravity and particle back-reaction, using the same forcing and parameter range, that shows the peak dust-to-gas ratio inside anticyclonic eddies never reaches order unity would disprove the claimed route; equivalently, a 2D run with back-reaction included that destroys the point clusters would do the same.

Watch

Extended reading notes

Core claim

The paper reports that when protoplanetary disk turbulence is treated as fully developed Keplerian turbulence with Rossby number below one, three dynamical regimes appear depending on turbulent intensity and particle stopping time. At low turbulent intensity (alpha around 10^-3 to 10^-4), pebble-sized solids concentrate into point clusters inside anticyclonic eddies, where the Coriolis force overcomes centrifugal expulsion; all particles of a given size reach the same position and velocity and evolve as a single particle. In the same regime, the radial drift of centimeter-to-meter solids is reduced by a factor of 0.5 to 1.0 relative to the laminar case, and can be fully arrested when the sol

Load-bearing premise

The path to planetesimal formation assumes that the point clusters seen in 2D, externally forced, incompressible turbulence without back-reaction or self-gravity correspond to real dense clumps in a 3D stratified disk that can gravitationally collapse; if 3D effects dilute the clusters or the concentration never reaches the collapse threshold, the claim fails.

Editorial extensions

If this is right

If this mechanism operates, planetesimals could form in weakly turbulent disk regions without any external pressure bump, removing a common requirement in current formation scenarios.
The radial drift barrier would be relaxed for the pebble sizes most vulnerable to loss, since their inward velocity is reduced by up to a factor of two and can vanish entirely in the cluster regime.
The collision/fragmentation barrier may be mitigated because particles inside a point cluster share the same velocity and position, reducing relative velocities within the cluster.
The mechanism reproduces standard turbulent concentration at higher turbulent intensities, so it extends rather than replaces existing results, and its clustering is distinct from that of Hogan & Cuzzi (2001).
The formation of point clusters at arbitrarily low dust-to-gas ratio, in the absence of back-reaction, implies that the concentration step does not need a preconditioning of the dust-to-gas ratio.

Reading between the lines

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

A testable implication the paper leaves unexplored is the actual density contrast inside the point clusters: if the local dust-to-gas ratio in these clusters reaches the order-unity threshold, gravitational collapse would follow directly; the paper does not report that ratio explicitly.
If the mechanism survives vertical stratification, as the authors' unpublished 3D simulations suggest, then low-viscosity 'dead zones' of disks would become preferred sites for planetesimal formation rather than quiet regions where formation stalls.
The toy model of elongated eddies implies a quantitative prediction: the drift reduction should scale with eddy aspect ratio, so simulations or observations that constrain eddy shapes in low-Rossby-number turbulence could test the mechanism independently of cluster formation.
Including particle back-reaction could go either way: the streaming instability might add to the concentration, or the feedback might disrupt the eddies; the robustness of the mechanism to back-reaction remains the main untested margin.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a conference proceedings paper that repackages the authors' own published simulations (Gerosa et al. 2023, 2024) under a new astrophysical framing. The new element is the identification of a 'Keplerian turbulence' regime at low Rossby number, where point clusters form in anticyclonic eddies and the radial drift of pebbles is reduced by a factor of 0.5-1.0, or even fully arrested for the clustered particles. That is a genuinely interesting result, and the paper is honest that it is a 'novel perspective' rather than new simulations. The 2D assumption is justified with reference to Taylor-Proudman columnar vortices and to unpublished 3D simulations (Gerosa et al., in prep.), which is a reasonable though unverifiable position for a proceedings paper.

The main soft spot is exactly what the stress-test note flags: the paper never converts the observed clustering into a volume density or mass. It says that gravitational collapse requires 'up to four orders of magnitude' concentration, but it never measures whether the point clusters achieve that. The clusters are mathematical points in the Lagrangian sense; their physical density depends on particle radius and stopping time, which are not modeled. The paper also neglects back-reaction and self-gravity, so the step from a passive overdensity to a collapsing cloud is absent. Combined with the lack of error bars on the drift reduction and the 2D setup, the advertised 'unique path' is an extrapolation, not a demonstrated result.

That said, this is a short SF2A contribution, and the authors clearly state their simplifications and point to their prior work for the full method. The physics is plausible and the parameter-space map (Lyapunov dimension classification) is a useful organizing principle. The paper does not commit the sin of hiding its limitations; it openly says that streaming instability and back-reaction are neglected, and that 3D confirmation is forthcoming.

My verdict: worth a serious referee if expanded into a full journal paper with a density calculation, but as written it is a conference abstract with an overconfident title. I'd bring it to a reading group, and I'd cite the earlier Gerosa papers rather than this one. If it lands on my editorial desk, I would send it out—on the strength of the underlying simulations and the potential importance of the regime—but I would expect the referee to require the quantitative collapse threshold and either the 3D results or a clear statement that they are still preliminary.

Referee Report

4 major / 7 minor

Summary. This short proceedings paper reports two-dimensional incompressible shearing-box simulations of forced Keplerian turbulence with Lagrangian dust particles. For low turbulent intensity (α ~ 10^-3–10^-4) and pebble-sized stopping times, it identifies a 'point-cluster' regime in which particles of a given stopping time converge to the same position and velocity inside anticyclonic eddies, and a companion set of simulations in which a constant azimuthal force is applied to the particles to model pressure-gradient drift. The authors show that the radial drift can be reduced or halted in this regime. They conclude that Keplerian turbulence alone can overcome the drift and fragmentation barriers and provide a unique path to planetesimal formation at canonical dust-to-gas ratio. The manuscript is explicitly a synthesis and re-interpretation of the authors' earlier work (Gerosa et al. 2023, 2024), with a 3D extension cited as in preparation.

Significance. The proposed mechanism, if quantitatively confirmed, would be a valuable addition to planetesimal-formation scenarios because it would show that a weakly turbulent disk can concentrate solids without invoking pressure bumps or the streaming instability. The paper has real strengths: it uses direct numerical simulations of the flow rather than diffusion models; it classifies particle behavior with a Lyapunov-dimension diagnostic; it recovers the known high-turbulence behavior (diffusion, turbulent concentration, enhanced drift), which gives confidence in the numerical setup; and it reports a parameter sweep over Stokes and Rossby numbers. The central limitation is that the step from Lagrangian clustering to a physical, gravitationally collapsible density enhancement is not made. Because of that missing quantitative link, the significance currently rests on an extrapolation rather than on a demonstrated result.

major comments (4)

[§3.1, Fig.1] The point-cluster regime is not converted into the quantity that actually matters for the paper's central claim, namely the local dust volume density or dust-to-gas ratio. The text states that 'all the particles of a family reach the same position with the same velocity' (Sec. 3.1), but in a Lagrangian simulation this is a mathematical concentration in phase space. The Introduction quotes a required enhancement of 'up to four orders of magnitude,' yet no measurement of the density contrast in the clusters, no estimate of the mass within a Hill radius, and no comparison to the Roche density are given. Without this, 'a unique path to planetesimal formation' is not established by the data presented.
[§3.2, Fig.2] The drift-reduction result has no associated error bars, ensemble statistics, or convergence study. The verbal summary 'reduced by a factor between 0.5 and 1.0' is ambiguous and does not specify whether the ratio plotted is v_turb/v_laminar or 1 - v_turb/v_laminar, nor how it depends on Stokes number and α. The statement that drift is 'fully arrested' is only supported by the point-cluster coincidence with zero relative velocity. Please provide the measured values, their uncertainties, and the exact definition of the plotted quantity, since this is one of the two pillars of the claim that the drift barrier is overcome.
[§2, last paragraph; §4, last paragraph] The transition from this idealized setup to protoplanetary disks is not yet documented. The simulations are 2D, driven by an external forcing at a single wavenumber, neglect particle back-reaction, and do not include stratification or self-gravity. The justification for 2D relies on a paper in preparation (Gerosa et al., in prep). Moreover, if the clusters actually achieve the factor of 10^4 concentration quoted in the Introduction, the local dust-to-gas ratio would exceed unity and the neglect of back-reaction would be inconsistent at the cluster scale. Please provide a published 3D check or a quantitative argument for why these approximations do not change the conclusion, and estimate the local dust-to-gas ratio implied by the clustering.
[Abstract and §4] The title/abstract claim of a 'unique' solution or 'unique path' is stronger than what is shown. The manuscript demonstrates one possible mechanism in a simplified model; it does not compare the efficiency or robustness of this path with pressure-bump plus streaming-instability scenarios, nor does it prove that point clusters form from global disk initial conditions. I recommend either adding a comparative discussion or softening the uniqueness claim (e.g., 'a direct path' or 'a single mechanism').

minor comments (7)

[§2] The abstract says turbulence is 'fully captured rather than modeled with a turbulent diffusion or turbulent viscosity parameter,' but §2 states that the onset of turbulence is not captured and that a turbulent state is sustained by an imposed external forcing. Please revise to avoid overstatement.
[§3.1, Fig.1] The text refers to '2nd panel,' '3rd panel,' and '4th panel,' but the figure panels are not labeled; add panel letters and color bars with a vorticity scale.
[§3.1] The conversion from turbulent Stokes number to Keplerian Stokes number is given by reference to Sengupta et al. (2024) but no formula is provided; please state the relation used.
[§2] Please state the Reynolds number and the resolution relative to the forcing scale and the Kolmogorov scale, so the reader can assess whether the flow is fully resolved.
[§4] The invocation of Taylor (1922) to justify 2D columnar vortices in 3D disks is an oversimplification; the Taylor-Proudman theorem is modified by stratification, vertical boundaries, and shear. Please qualify.
[References] The entry 'Simon, J. B., Birnstiel, J. B., & Nesvorný, D. 2024' appears to have a wrong author name ('J. B. Birnstiel'?) and the arXiv number is missing; please check.
[§1 and §4] The manuscript would benefit from a sentence stating which simulations are new to this paper and which are re-analyzed from Gerosa et al. (2023, 2024), given that the text says 'We present numerical simulations.'

Circularity Check

1 steps flagged · score 3.0 of 10

Main results are numerical outputs from the authors' own published simulations; the only load-bearing self-citation is an unpublished 3D confirmation used to bridge 2D results to real disks.

self citation load bearing [Section 4, Discussion and conclusion (last paragraph)]
"Indeed, as demonstrated by our 3D simulations, the formation of strong clusters of particles that take the form of vertical lines or surfaces, in the absence of vertical stratification, is confirmed for Keplerian turbulence (Gerosa et al., in prep)."

The paper's central claim that the 2D point-cluster mechanism operates in real 3D disks, which is essential for the 'unique path to planetesimal formation,' is supported only by an unpublished, inaccessible self-citation. The adjacent external citation (Taylor 1922) establishes columnar vortices in rotating flows, not dust clustering in protoplanetary turbulence. Thus the load-bearing evidence for the 3D reality of the mechanism reduces to the authors' own forthcoming paper; no independent confirmation is provided, making this a self-referential support step rather than a definitional equivalence.

full rationale

No equation-level or definitional circularity was found: the turbulent alpha parameter is measured from the simulated Reynolds stress rather than fitted to the clustering output; the drift-reduction factor is a simulation result compared with the analytic laminar drift; and the point clusters are computed particle positions, not assumed densities. The paper is largely a synthesis of the authors' previously published, peer-reviewed simulations (Gerosa et al. 2023, 2024), which is a normal and non-circular mode of scientific communication. The clearest circularity concern is the use of the authors' own in-preparation 3D simulations to validate the 2D-to-3D extrapolation, an unpublished self-citation that is load-bearing for the astrophysical conclusion. Additionally, the 'unique' mechanism is acknowledged to be the known Coriolis concentration in anticyclonic eddies, so the novelty is partly a renaming. These concerns warrant a moderate score of 3, not a higher one, because the core 2D results and drift measurements retain independent numerical content.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper's central claim rests on a 2D forced-turbulence model with a chosen forcing scale, no back-reaction, and no self-gravity. The clustering and drift reduction are outputs of this idealized setup, so the main burden is carried by the modeling assumptions rather than fitted parameters.

free parameters (2)

Turbulent forcing wavenumber k_f = 4
Sets the scale of the largest turbulent eddies; the paper hypothesizes this corresponds to H/10. Clustering efficiency and drift suppression depend on this choice.
Drift-driving azimuthal force magnitude = not stated
A constant azimuthal force is added to model the radial drift; its magnitude is not specified in the text, but it sets the laminar drift baseline against which turbulence effects are measured.

assumptions (4)

domain assumption Turbulent velocity fluctuations are subsonic, so an incompressible approximation is valid
Invoked in Section 2 to justify the simulation framework; excludes compressible effects and shocks that could alter clustering or drift.
domain assumption The turbulence is two-dimensional and columnar, consistent with the Taylor-Proudman theorem
Section 2 and Discussion: 2D may not capture vertical mixing, vertical stratification, or 3D instabilities that could disrupt the point clusters.
domain assumption Back-reaction of particles on the gas and the streaming instability are neglected
Section 2: these processes could either reinforce or destroy the clusters; the paper isolates purely kinematic effects.
ad hoc to paper A sustained turbulent state is imposed via external forcing; the onset of turbulence is not modeled
Section 2: forced turbulence may not reproduce the spatial structure of self-consistently driven turbulence (e.g., MRI), and the forcing scale is a free parameter.

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Cite this review

Pith. "Pith review of A unique solution to overcome the barriers to planetesimal formation at low dust-to-gas ratio." pith.science (2026). https://pith.science/paper/TQJHPIWL

@misc{pith2026250820070,
  author       = {Pith},
  title        = {Pith review of: A unique solution to overcome the barriers to planetesimal formation at low dust-to-gas ratio},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TQJHPIWL}},
  note         = {Machine review of arXiv:2508.20070}
}

read the original abstract

In the incremental growth model, planetesimal formation constitutes the least understood step in the process of planetary formation. The two main difficulties in this regard are the collision/fragmentation and the drift barriers. Numerous solutions have been proposed to overcome these barriers, but often need a conjunction of processes to reach the conditions for planetesimal formation. We present numerical simulations, in which the protoplanetary disk turbulence is fully captured rather than modeled with a turbulent diffusion or turbulent viscosity parameter. When the turbulent cascade is taken into account, and in the case of weakly turbulent disks, not only can solid grains be highly concentrated in clusters, but their radial drift can also be slowed or even halted. These results open a unique path to planetesimal formation starting at disk canonical dust-to-gas ratio, namely Keplerian turbulence.

Figures

Figures reproduced from arXiv: 2508.20070 by the authors.

**Figure 1.** Left: Examples of outcomes of dust structures formed in protoplanetary disk turbulence. The gas vorticity is plotted in colors, and particle positions during the statistically steady state in black. On the 4th panel, the unique particle cluster is highlighted with a circle. Right: Summary of the different dynamical behaviors of particles in protoplanetary disk turbulence, classified according to the Lyapunov dimensi… view at source ↗

**Figure 2.** Left: Drift velocity modification by protoplanetary disk turbulence. Right: Toy-model of particles circumventing elongated eddies resulting in reduced drift velocity. The vorticty of the flow is plotted in colors and the particles positions during a statistically steady state in black. The radial drift towards the star is oriented from right to left. ily converted (in the Epstein regime) to the corresponding particl… view at source ↗

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

& Sommeria, J

Barge, P. & Sommeria, J. 1995, A&A, 295, L1

1995

[2] [2]

2024, Annual Review of Astronomy and Astrophysics, 62, 157

Birnstiel, T. 2024, Annual Review of Astronomy and Astrophysics, 62, 157

work page 2024

[3] [3]

Chavanis, P. H. 2000, A&A, 356, 1089

work page 2000

[4] [4]

Gerosa, F. A. 2024, PhD thesis, Universit´ e Cˆ ote d’Azur, HAL:tel-04835433

work page 2024

[5] [5]

A., Bec, J., M´ eheut, H., & Kapoor, A

Gerosa, F. A., Bec, J., M´ eheut, H., & Kapoor, A. U. 2024, Astronomy & Astrophysics, 685, L4

work page 2024

[6] [6]

Clusters of heavy particles in two-dimensional Keplerian turbulence

Gerosa, F. A., Meheut, H., & Bec, J. 2023, EPJPlus, 138, arXiv:2210.13147

work page Pith review arXiv 2023

[7] [7]

F., Gammie, C

Hawley, J. F., Gammie, C. F., & Balbus, S. A. 1995, ApJ, 440, 742

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[8] [8]

Hogan, R. C. & Cuzzi, J. N. 2001, Physics of Fluids, 13, 2938

work page 2001