Gravitoviscous protoplanetary disks with a dust component. II. Spatial distribution and growth of dust in a clumpy disk

Eduard I. Vorobyov; Vardan G. Elbakyan

REVIEW 3 major objections 5 minor 39 references

Gravitoviscous protoplanetary disks with a dust component. II. Spatial distribution and growth of dust in a clumpy disk

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper argues that giant planets can form inside the inward-migrating clumps of a gravitationally unstable disk before tidal torques destroy the clumps, yielding seeds of 0.25–1.6 Jupiter masses of gas and 1.0–5.5 Earth masses of dust.

desk verdict Solid dust-growth results in fragmenting disks; the protoplanet seed masses are clearly extrapolated and should not be read as simulation outputs. read the letter →

arxiv 1908.10589 v3 pith:4EDSPBFT submitted 2019-08-28 astro-ph.SR astro-ph.EPastro-ph.GA

Eduard I. Vorobyov , Vardan G. Elbakyan This is my paper · ORCID

classification astro-ph.SRastro-ph.EPastro-ph.GA

keywords protoplanetarydisksgravitationalinstabilitydiskfragmentationdustgrowthdust-to-gasratiogiantplanetformationclumpmigrationtidaldownsizing

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 argues that giant planet formation can happen inside the dense gaseous clumps created when a young protoplanetary disk is strongly gravitationally unstable. Using high-resolution two-dimensional thin-disk simulations that track two dust populations, the authors find that dust is efficiently concentrated and grown inside migrating clumps, forming compact central condensations of 70–100 Earth masses. Before tidal torques tear the clumps apart, their centers heat above 2000 K, the temperature at which molecular hydrogen dissociates and a second collapse begins; the authors estimate that this collapse would produce protoplanet seeds of 0.25–1.6 Jupiter masses of gas and 1.0–5.5 Earth masses of dust at orbital distances of tens of au. If true, disk fragmentation offers a direct route to wide-orbit giant planets that are enriched in heavy elements, and the same clump dynamics produces transient dusty rings resembling structures seen in young disks.

What carries the argument

The load-bearing object is the clump's internal structure as computed by a sub-au-resolution thin-disk hydrodynamics code with two dust species: small dust grains that are tightly coupled to gas, and grown dust with a variable maximum radius whose dynamics is set by gas drag, dust self-gravity, and the total gravitational potential. A dust-growth scheme converts small to grown dust and limits growth by a fragmentation barrier. Within a clump, gas friction and the clump's non-Keplerian velocity field drive grown dust inward, building a central condensation. The predicted protoplanet seeds come from applying the centrifugal radius formula $R_{\rm cf}=|J|^2/[G M_c(r')]$ to the clump's surface-density and angular-velocity profiles at the moment its center reaches 2000 K, assuming angular momentum is conserved and that material with $R_{\rm cf}$ smaller than the adopted protoplanet radius forms the seed while the rest forms a circumplanetary disk or envelope.

What would settle it

A numerical experiment that resolves the second collapse, starting from one of the clump profiles shown at the 2000 K moment and actually following the region inside 0.3 au to stellar densities, would settle the matter: if the clump loses its inner material to tidal torques before a bound seed of at least a few tenths of a Jupiter mass forms, or if angular momentum redistribution prevents the centrifugal radius from shrinking below the protoplanet radius, the central claim fails.

Watch

Extended reading notes

Core claim

The central claim is that, in a gravitationally fragmenting disk, dust does not simply trace gas. Over roughly 30 000 years of clump evolution, sub-micron dust is converted into grown dust with radii of several decimeters; grown dust drifts inward under gas friction and accumulates at the clump center, while gas in the outer clump is progressively stripped by tidal torques from the star. The result is a compact, dust-enriched condensation whose interior dust-to-gas ratio can rise above the canonical 1:100 by up to a factor of five. In the two simulated clumps this process continues until the central temperature crosses 2000 K, the dissociation threshold of molecular hydrogen. Assuming angular momentum conservation during the subsequent second collapse, the authors compute centrifugal radii and, adopting a protoplanet radius of 2.5–10 Jupiter radii, derive seed masses of 0.25–1.62 Jupiter masses in gas and 1.0–5.5 Earth masses in dust. They argue these seeds form before the clumps disperse through tidal action, and that later accretion from massive metal-rich disks or envelopes can raise the final masses well above the seed values.

Load-bearing premise

The argument assumes, as in Section 3.3, that a clump whose center exceeds 2000 K collapses to a protoplanet quickly enough to beat tidal disruption, and that specific angular momentum is conserved during that collapse; the simulation does not resolve the collapse, and inside 0.3 au the density and rotation profiles are extrapolated to a plateau and to zero rotation at the center.

Editorial extensions

If this is right

Gravitational instability of a massive young disk can end in giant planets at tens of au, not just brown dwarfs or scattered clumps, because tidal stripping reduces the clump to roughly a Jupiter mass before the center collapses.
Planets formed this way start metal-rich: the dust-to-gas ratio in the protoplanetary seeds is 0.011–0.013, above the canonical 0.01, and the dust mass of the seed is 1.0–5.5 Earth masses.
Dusty rings at several tens of au form when clumps are tidally destroyed and are later disturbed by other migrating clumps; these transient rings are plausible analogs of ring-like structures observed around the youngest, most massive protoplanetary disks.
Final planet masses are not fixed by the seed: accretion from a surrounding circumplanetary disk or envelope can increase the mass substantially, although tidal stripping during migration may remove much of that envelope, keeping the planet in the giant-planet regime.
The dust accumulated in clumps before collapse, with central condensations of 70–100 Earth masses, provides a head start for the heavy-element content of the eventual planet.

Reading between the lines

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

If this picture holds, direct imaging surveys of wide-orbit giant planets around young stars should find a population with heavy-element masses in the roughly 1–10 Earth-mass range and envelopes enriched above stellar metallicity, at orbital distances where core accretion struggles to assemble cores fast enough.
In this picture, the solid core of a giant planet may be assembled before the gas envelope by in-clump dust drift rather than by later planetesimal accretion, which would explain how gravitational-instability planets avoid being coreless.
A testable extension is that transient dusty rings from clump dispersal should be more common in disks younger than about 0.5 Myr and should correlate with clump migration events, so surveys of the youngest embedded disks could look for rings that later disappear.
The quoted seed-mass range rests on conservation of angular momentum during collapse; adding magnetic fields or turbulence in a future model would redistribute angular momentum and likely shrink the seeds, so the numbers bracket an idealized, non-magnetic collapse.

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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

This paper is worth your time, but keep the quantitative planet-seed masses in perspective. The genuinely new and solid part is the dust evolution inside gravitationally bound clumps: two thin-disk FEOSAD simulations with sub-au resolution show dust growing to decimeters, the dust-to-gas ratio swinging by factors of ten, and grown dust drifting inward to form a compact 70–100 Earth-mass condensation. Those are forward simulation results, not fitted to a target, and the clump tracking is careful. The finding that dust is retained while gas is tidally stripped is a plausible mechanism for metal-rich giants, and the re-formed dusty rings after clump dispersal are an interesting link to observed ALMA structures, though the match to any specific disk is not established.

The soft spot is Section 3.3. The seed masses of 0.25–1.6 Jupiter masses and 1–5.5 Earth masses come from an extrapolation inside the innermost resolved radius of about 0.3 au, and the critical radius of 0.18 au sits entirely inside that unresolved region. The calculation assumes specific angular momentum is conserved through the second collapse and that the profile flattens smoothly to the center; the quoted mass range only varies the assumed protoplanet radius, not these structural assumptions. Tidal torques during the roughly 7 kyr between crossing 2000 K and dispersal could plausibly change the answer by factors of a few. That said, the authors are transparent about the resolution limit and explicitly call the masses estimates. The weaker qualitative claim—that a clump can form a protoplanet seed before tidally dispersing—does not depend on the exact numbers and is consistent with the simulation showing central temperatures above the H2 dissociation threshold.

Other limitations are minor in this context: only two models are run, there is no convergence study, and the code is not public, but the companion paper documents the method and the two models do agree qualitatively.

This paper is for people working on gravitational instability planet formation, dust evolution in disks, and ALMA ring interpretations. It deserves a serious referee. My recommendation would be to send it to peer review and, in revision, ask for a sensitivity test of the seed masses to the interior extrapolation and to angular momentum loss, or for the authors to soften the quantitative claims to order-of-magnitude. As is, the headline numbers overstate what the simulation shows, but the underlying dust physics is a genuine step forward.

Referee Report

3 major / 5 minor

Summary. The paper presents 2D thin-disk simulations of gravitationally unstable protoplanetary disks with a two-component dust model (small sub-micron grains and grown dust with a variable maximum radius) using the FEOSAD code. Two prestellar core collapse models are evolved for about 0.6 Myr. The authors find that the disks are highly time-variable, with spiral arms, dusty rings, and gravitationally bound clumps that form, migrate inward, lose gas through tidal torques, and disperse. Inside the clumps, small dust is efficiently converted to grown dust, which drifts inward and forms compact central condensations of 70–100 Earth masses. Before tidal dispersal, the central gas temperature exceeds 2000 K in both tracked clumps, and the authors argue that a second collapse could form protoplanets at tens of au. Using azimuthally averaged clump profiles near the time of the 2000 K crossing, they estimate protoplanetary seed masses of 0.25–1.6 Jupiter masses of gas and 1.0–5.5 Earth masses of dust, and they connect tidally disrupted clumps to the formation of dusty rings. The paper closes with a caveat list in Section 3.4.

Significance. If the quantitative planet-formation claim holds, the paper would provide a concrete pathway for forming metal-rich giant planets at tens of au via gravitational instability, linking clump migration, dust growth, and dusty ring formation. The simulations are forward models with no fitting to the derived dust or planet properties, and the dust dynamics inside migrating clumps are analyzed in unusual detail for a thin-disk code. The authors are also explicit about many limitations in Section 3.4. The main weakness is that the central quantitative result—the protoplanet seed masses—is not a direct simulation output but a post-processing estimate based on extrapolated inner profiles and an assumed conservation law, so the strength of the paper's headline claim currently exceeds what the numerics can support.

major comments (3)

[Section 3.3, Figure 10, Eq. (14)] The seed masses in Table 3 are not direct outputs of the simulation. The azimuthally averaged clump profiles have their innermost resolved point at r ≈ 0.3 au, stated in Section 3.3, while the critical radius Rcrit = 0.18 au that separates the protoplanet seed from the circumplanetary disk lies inside this unresolved region. The profiles are extended to r = 0 by assuming vφ = 0 at the center and constant surface-density plateaus, and Eq. (14) then evaluates Rcf = |J|^2/[G Mc(r')] using these extrapolated profiles. Because almost all of the claimed seed mass is interior to 0.18 au, the quantitative masses in Table 3 are determined primarily by the assumed extrapolation rather than by the simulation. At minimum, the paper should report how the seed masses change under alternative plausible inner extrapolations, or present a higher-resolution test of the inner clump structure.
[Section 3.3, Figures 8 and 9] The timing argument for the second collapse is not fully supported. In model 1 the central temperature reaches 2000 K at τ = 22.8 kyr and the clump disperses after τ = 30 kyr, leaving roughly 7 kyr for the second collapse to occur; the calculation assumes that the specific angular momentum J is strictly conserved during this interval, with no account taken of tidal torques from the central star or the surrounding disk. Since Rcf scales as J^2, even a modest change in J during this window would shift Rcrit and the resulting seed mass. The authors should either justify the conservation assumption quantitatively or show that the conclusion is robust to plausible angular-momentum loss during the pre-dispersal phase.
[Section 3.3, Table 3] The quoted range 0.25–1.6 MJup and 1.0–5.5 M⊕ is presented as the spread of possible seed masses, but the only parameter varied in the calculation is the assumed protoplanet radius Rp.p. (2.5, 5, and 10 RJup). No sensitivity test is given for the plateau extrapolation, for the assumed flat surface-density profile, or for the conservation of J, so the range underestimates the model uncertainty. The abstract and conclusions should present these values as illustrative estimates tied to the adopted assumptions rather than as robust limits.

minor comments (5)

[Section 3.3] The word 'protoplantery' in the last paragraph of Section 3.3 should be 'protoplanetary'.
[Section 3.4] In the final paragraph, 'circumlanetary disks' should be 'circumplanetary disks'.
[Section 2.2, Eq. (4)] The superscript n appearing on Σn d,tot in Eq. (4) is not defined; please clarify the discretization notation or remove the superscript.
[Figure 3] The time–space diagrams would be easier to read if color bars were provided for each panel, since the text refers to 'high surface density speckles' and 'sharp horizontal spikes' that depend on the color scale.
[Section 3.1] In the discussion of the re-formed dusty ring after clump dispersal, the text compares the ring mass of about 80 M⊕ with the clump dust mass of 88.3 M⊕; a direct statement of the expected mass conservation would help the reader judge whether the difference is significant.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central results are emergent simulation outputs, and the seed-mass estimates are explicitly labeled post-hoc calculations using standard conservation laws.

full rationale

The paper's main claims—clump formation, dust growth to decimeter sizes, dust-to-gas variations, and compact central dust condensations of 70–100 Earth masses—are direct outputs of the forward FEOSAD thin-disk simulations, with no parameter fitted to those target quantities. The protoplanetary seed masses in Table 3 are not disguised simulation outputs either: Section 3.3 explicitly presents them as estimates obtained from Eq. (14), Rcf(r') = |J|^2/[G Mc(r')], using assumed conservation of specific angular momentum and an adopted protoplanet radius Rp.p. = 5 RJup, with a sensitivity study varying Rp.p. = 2.5 and 10 RJup. This is a standard post-processing estimate, not a quantity fed into the model as an input, so it is not circular by construction. The extrapolation of clump profiles inside 0.3 au, with constant surface-density plateaus and v_phi = 0 at the center, is a resolution limitation and an assumption about the unresolved interior; it affects the reliability of the quantitative seed masses but does not make the derivation equivalent to its inputs. Self-citations to the FEOSAD method paper (Vorobyov et al. 2018) and to the authors' earlier clump migration study (Vorobyov & Elbakyan 2018) are present, but the load-bearing dynamics of the clumps examined here are resolved and displayed in the paper itself (Figures 6-9), so those citations are not used in place of independent evidence for the central claim. No uniqueness theorem, ansatz, or self-definitional reduction is invoked. The honest finding is no significant circularity; the quantitative seed masses carry a correctness risk from unresolved interior extrapolation, but that is outside the circularity definition.

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

The central claim about protoplanet formation rests on the assumed 2000 K collapse threshold, conservation of angular momentum, and an extrapolation of unresolved clump interior profiles, in addition to standard thin-disk modeling choices and several adopted parameters.

free parameters (6)

Mcore = 1.32 and 0.99 solar masses
Initial core mass chosen to produce massive disks prone to gravitational instability and fragmentation.
beta = 0.88% and 0.77%
Rotational-to-gravitational energy ratio chosen to promote disk formation and fragmentation.
Tinit = 20 and 15 K
Initial gas temperature of the cloud core; sets the background temperature for the disk.
alpha_viscosity = 1e-2
Shakura-Sunyaev viscosity parameter assumed constant throughout the disk.
ufrag = 30 m/s
Dust fragmentation velocity threshold adopted in the dust growth model.
Rp_protoplanet = 5 Jupiter radii (varied 2.5 and 10)
Assumed radius of the seed protoplanet used to split clump material into seed versus disk and envelope.

assumptions (5)

domain assumption Thin-disk approximation with local hydrostatic equilibrium and negligible vertical motions
Used to vertically integrate the hydrodynamics; limits applicability to disks with scale height less than 10 to 20 percent of radius.
standard math Ideal gas equation of state with gamma = 5/3
Used for pressure and energy throughout the simulations.
standard math Specific angular momentum is conserved during the second collapse
Used to compute centrifugal radii and split the clump into protoplanetary seed versus disk and envelope.
domain assumption Second collapse is triggered when central temperature exceeds 2000 K
Based on hydrogen dissociation; invoked to argue that protoplanet formation occurs before tidal dispersal.
domain assumption Initial cloud core profiles follow Basu (1997) with the specific forms of Eqs. (9) and (10)
Assumed initial surface density and angular velocity distributions for the collapsing core.

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Cite this review

Pith. "Pith review of Gravitoviscous protoplanetary disks with a dust component. II. Spatial distribution and growth of dust in a clumpy disk." pith.science (2026). https://pith.science/paper/4EDSPBFT

@misc{pith2026190810589,
  author       = {Pith},
  title        = {Pith review of: Gravitoviscous protoplanetary disks with a dust component. II. Spatial distribution and growth of dust in a clumpy disk},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4EDSPBFT}},
  note         = {Machine review of arXiv:1908.10589}
}

abstract

Spatial distribution and growth of dust in a clumpy protoplanetary disk subject to vigorous gravitational instability and fragmentation is studied numerically with sub-au resolution using the FEOSAD code. Hydrodynamics equations describing the evolution of self-gravitating and viscous protoplanetary disks in the thin-disk limit were modified to include a dust component consisting of two parts: sub-micron-sized dust and grown dust with a variable maximum radius. The conversion of small to grown dust, dust growth, friction of dust with gas, and dust self-gravity were also considered. We found that the disk appearance is notably time-variable with spiral arms, dusty rings, and clumps, constantly forming, evolving, and decaying. As a consequence, the total dust-to-gas mass ratio is highly non-homogeneous throughout the disk extent, showing order-of-magnitude local deviations from the canonical 1:100 value. Gravitationally bound clumps formed through gravitational fragmentation have a velocity pattern that deviates notably from the Keplerian rotation. Small dust is efficiently converted into grown dust in the clump interiors, reaching a maximum radius of several decimeters. Concurrently, grown dust drifts towards the clump center forming a massive compact central condensation (70-100 $M_\oplus$). We argue that protoplanets may form in the interiors of inward migrating clumps before they disperse through the action of tidal torques. We foresee the formation of protoplanets at orbital distances of several tens of au with initial masses of gas and dust in the protoplanetary seed in the (0.25-1.6) $M_{\rm Jup}$ and (1.0-5.5) $M_\oplus$ limits, respectively. The final masses of gas and dust in the protoplanets may however be much higher due to accretion from surrounding massive metal-rich disks/envelopes.

Figures

Figures reproduced from arXiv: 1908.10589 by the authors.

**Figure 1.** Gas surface density maps in model 1 shown for the inner 1200 × 1200 au2 box at nine evolutionary times. The time is counted from the formation of the central star. The disk forms at t = 12.4 kyr. The insets in the upper-right corner of each panel present the dust-to-gas mass ratios for all azimuthal grid points at a specific radial distance from the star. The red arrows indicate the position of an inward-migrating c… view at source ↗

**Figure 2.** Similar to [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Time-space diagrams showing the temporal evolution of the following azimuthally averaged quantities: surface density of gas (top row), surface density of grown dust (second row), gas temperature (third row), and maximum radius of grown dust (bottom row). The left and right columns correspond to model 1 and model 2, respectively. unstable stages of disk evolution. As [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Spatial maps of the grown dust surface density in the inner 200 × 200 au2 box shown in model 1 at six consecutive times. The yellow arrows indicate the inward-migrating clump. The insets shows the azimuthal variations in the dust-to-gas ratio at a given radial distance…

**Figure 6.** Figure 6: Azimuthally averaged radial distributions of the grown dust (red lines) and small dust (blue lines) surface densities, total dust to gas ratio (green lines), maximum radius of dust grains (thin black solid lines), ratio of grown to total dust surface densities (dashed …

**Figure 5.** Figure 5: Top panel: Gas surface density distribution (in log g cm−2 ) in the vicinity of the clump at t = 144.1 kyr in model 1. The superimposed black arrows show the velocity field of the gas. Bottom panel: Grown dust surface density distribution (in log g cm−2 ) in the vicini…

**Figure 8.** Figure 8: Top panel. Gas and total dust masses (red and black solid lines, respectively) of the clump vs. time. The red and black dashed lines show the gas and total dust mass inside the inner 2 au of the clump, respectively. Middle panel. The radial distance of the clump from …

**Figure 9.** Figure 9: Similar to [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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