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Quantifying the Impact of the Dust Torque on the Migration of Low-mass Planets II: The Role of Pebble Accretion in Planet Growth within a Global Planet Formation Model

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper argues that the dust torque from drifting pebbles can dominate and reverse inward migration for low-mass planets forming inside the water ice-line, so planet formation models should include it.

desk verdict First genuine global implementation of dust torque in a pebble-accretion formation model, with a real caveat: the headline inner-disk outward migration is computed at the boundary of the torque grid, so the direction is plausible but the quantitative tracks are conditional. read the letter →

arxiv 2501.16169 v2 pith:FK4FDN6J submitted 2025-01-27 astro-ph.EP

Octavio M. Guilera , Pablo Benitez-Llambay , Marcelo M. Miller Bertolami , Martin E. Pessah This is my paper · ORCID
classification astro-ph.EP
keywords protoplanetarydisksplanetarymigrationdusttorquepebbleaccretionplanetformationwatericelineplanet-diskinteractions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to show that the torque exerted by dust and pebbles on a growing planet is not a negligible correction: inside the water ice-line it can dominate the total torque early in a planet's life and push the planet outward, reversing the usual inward migration. Using a global disk model that evolves gas, dust, and pebbles and lets planets grow by pebble and gas accretion, the authors find that this outward push changes final masses, formation timescales, and sometimes composition. For planets born beyond the ice line, the dust torque merely slows inward migration because the dust-to-gas ratio drops quickly there. If true, models of terrestrial and low-mass planet formation that ignore the dust torque will misplace planets and misestimate their growth histories.

What carries the argument

The load-bearing object is the dust torque map of BLP18, a two-dimensional grid of the torque as a function of planet mass and particle Stokes number (the dimensionless measure of how strongly a particle is coupled to the gas), computed for a reference disk and scaled by the local dust-to-gas ratio relative to 0.01. In the global model the total torque is Γtot = Γg + Γd, with Γg from Jiménez & Masset (2017) and Γd obtained by bilinear interpolation in planet mass and mass-weighted mean Stokes number, rescaled by ϵP/ϵ0. The mechanism that carries the argument is the inward drift of ice-rich pebbles: beyond the ice line particles grow to larger Stokes numbers and drift rapidly, enriching the inner disk in dust, which raises the positive dust torque there. A conservative clamp at the minimum grid values (St = 0.01 and the lowest tabulated planet mass) avoids extrapolation, so the inner-disk results rest on the torque at the grid boundary.

What would settle it

Run a 3D hydrodynamical simulation of a roughly 0.1–0.4 M⊕ planet at 0.5–1 au with dust Stokes numbers of $10^{-4}$ to $10^{-3}$, a dust-to-gas ratio around 0.1, and free planetary migration; if the net torque is negative or the planet does not migrate outward despite the enhanced dust, then the clamping of the torque map to St = 0.01 is the cause and the central result fails.

Watch

Extended reading notes

Core claim

The central claim is that the dust torque, computed from the asymmetric distribution of pebbles around an embedded planet, can be a dominant component of the total torque for low- and intermediate-mass planets forming inside the water ice-line. As pebbles drift inward from the outer disk, they raise the dust-to-gas mass ratio in the inner region by more than an order of magnitude within the first million years; the positive dust torque then exceeds the negative gas Lindblad torque up to planet masses of roughly 0.4 M⊕ in the fiducial case, producing outward migration. The outcome depends on the destination: in the fiducial and massive disks, outward-moving planets reach regions of lower dust-to-gas ratio, grow less efficiently, and end up less massive; in a metal-rich disk, they stay in high-ratio regions, reach larger masses, and can acquire envelopes. When the torque prescriptions include pebble accretion, the effect strengthens for low-mass, low-Stokes-number planets, allowing them to cross the ice line and accrete icy pebbles. The paper concludes that dust torque should not be ignored in planet formation models.

Load-bearing premise

The outward migration result assumes that dust torque maps computed in 2D, without planetary migration and dust back-reaction, and tabulated only down to a Stokes number of 0.01, remain valid when interpolated and linearly scaled to the low Stokes numbers and enhanced dust-to-gas ratios that actually occur inside the water ice-line in the model.

Editorial extensions

If this is right

  • Planets that start inside the water ice-line can migrate outward early in their evolution, with final masses either lower or higher than in dust-free models depending on the dust-to-gas ratio of the region they enter.
  • In metal-rich disks, outward migration can keep inner planets in high dust-to-gas regions, allowing them to grow larger cores and acquire gas envelopes, and in some cases to cross the ice line and incorporate icy pebbles.
  • For planets initially beyond the ice line, the dust torque only delays inward migration and does not substantially alter their formation tracks, because the dust-to-gas ratio falls quickly and formation timescales are short.
  • Including pebble accretion in the torque prescription strengthens the outward migration of low-mass, low-Stokes-number planets inside the ice line, reinforcing the conclusion that dust torque belongs in global planet formation models.

Reading between the lines

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

  • If the dust torque acts as modeled, planet formation models that omit it should predict systematically different final positions and masses for close-in low-mass planets; comparing the model's mass–period distribution against exoplanet demographics would be a direct test.
  • Because the model clamps the Stokes number to 0.01 inside the ice line, where the true mass-weighted mean is 10^-4 to 10^-3, the reported dust torque is a conservative estimate; extending the maps to lower Stokes numbers could strengthen, or if the torque turns over, weaken the outward migration result.
  • The paper's discussion of dust back-reaction suggests the torque may be even larger for Mars-mass planets, so the outward-migration window might extend to smaller embryos than the roughly 0.4 M⊕ threshold found in the fiducial run.
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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

3 major / 5 minor

Summary. This paper incorporates the dust torque from Benitez-Llambay & Pessah (2018, BLP18) into the PLANETALP global planet formation model, which includes axisymmetric disk evolution with viscous accretion and X-ray photoevaporation, dust growth and transport, and concurrent pebble and gas accretion. The authors compute planet formation tracks for three disk models (fiducial Mdisk=0.05 Msun, massive Mdisk=0.1 Msun, and metal-rich Z=0.02), comparing runs with and without the dust torque, and also apply the recent Chrenko et al. (2024) prescriptions that include the dynamical effect of pebble accretion. The main findings are that the dust torque drives substantial outward migration for planets initially inside the water ice line, with consequences for their final masses, formation timescales, and compositions, while planets starting beyond the ice line are only mildly affected. The paper concludes that the dust torque should not be ignored in models of planet formation.

Significance. If the qualitative result holds, this is a valuable step toward including dust-driven torques in global models of planet formation. The paper makes good use of two independent torque prescriptions and consistently applies a conservative no-extrapolation policy, and it is transparent about the limitations of the underlying hydrodynamical maps. The qualitative conclusion that the dust torque can reverse inward migration of low-mass planets inside the ice line is plausible and worth testing with more detailed simulations. However, the quantitative tracks in the inner disk depend critically on clamping the Stokes number to the minimum of the torque grid, which is exactly the regime where the model is least constrained. The significance of the paper will be much stronger if the torque maps are extended to lower Stokes numbers and lower planet masses, or if the clamping is validated by additional simulations.

major comments (3)
  1. [Sec. 2, Dust-to-gas Mass Ratio]
  2. [Sec. 4 and Fig. 11]
  3. [Sec. 5, The Dynamical Impact of Pebble Accretion and Sec. 5, Limitations]
minor comments (5)
  1. [Caption of Fig. 1]
  2. [Captions of Figs. 5 and 10]
  3. [Footnote 3]
  4. [Sec. 5, paragraph on embryo formation]
  5. [Title of Sec. 5]

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: torque inputs are independent hydrodynamical maps; Stokes clamping is a transparent limitation, not a circular step.

full rationale

The dust torque is imported from the BLP18 hydrodynamical simulations and from Chrenko et al. (2024) via the interpolation maps built in Guilera et al. (2023). These are external computations with stated physical assumptions, and they are not fitted to reproduce the migration tracks reported here. The scaling of the dust torque by the local dust-to-gas ratio (epsilon_P/epsilon_0) and the bilinear interpolation in planet mass and mass-weighted Stokes number are declared inputs in Section 2; no parameter is adjusted to force the outward migration of inner planets. The only reduction-by-construction in the manuscript appears in Appendix A, where the multi-species torque sum inside the ice line is identical to the mean-Stokes-number torque because every dust species is clamped to the table minimum St=0.01. The paper states this explicitly and uses it only as a consistency check, not as the source of the headline result. The more serious issue is that the inner-disk outward migration is evaluated at the boundary of the BLP18 torque grid rather than with resolved data for St~1e-4-1e-3; this is a correctness and robustness limitation, acknowledged in Section 5, but it is not circularity because the torque value at St=0.01 is an external input rather than a parameter fitted to the target tracks. Self-citations to BLP18 and Guilera et al. (2023) are load-bearing as data sources, but BLP18 is an independent hydrodynamical result and Chrenko et al. (2024) provides a separate, partially independent confirmation, so the argument does not reduce to an unverified self-citation chain. Accordingly, no specific circular step meeting the quoted-evidence standard is present.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central result is a synthesis of prior torque maps (BLP18, Chrenko et al. 2024) with a global disk and planet formation model. No new physical entities are introduced. The main burden lies in the transferability of 2D torque prescriptions to the 1D global model, especially at Stokes numbers below the computed grid.

free parameters (2)
  • Stokes number floor St_min = 0.01
    When the local mass-weighted mean Stokes number falls below the minimum of the BLP18 torque grid, the model uses the minimum grid value. This affects the inner disk, where actual Stokes numbers are 1e-4 to 1e-3, and is central to the outward migration result.
  • Maximum planet mass cutoff = 10 Earth masses
    Growth is halted at 10 Earth masses because the dust torque becomes inefficient beyond this mass. This bounding choice prevents the model from exploring higher-mass outcomes but is not fitted to data.
assumptions (5)
  • domain assumption BLP18 torque maps are transferable to 1D global tracks
    The dust torque is taken from 2D hydro maps without pebble accretion or migration, via bilinear interpolation in mass and Stokes number (Section 2).
  • domain assumption Dust torque scales linearly with local dust-to-gas ratio
    The dust torque is computed as (epsilon_P/epsilon_0) times the interpolated map value, with epsilon_0 = 0.01, following BLP18 (Section 2).
  • ad hoc to paper Stokes number clamping is valid in the inner disk
    For Stokes numbers below 0.01, the model adopts the minimum grid value, which is an extrapolation not directly tested against hydrodynamical simulations.
  • domain assumption Dust growth is governed by fragmentation and drift limits
    The dust size distribution uses threshold fragmentation velocities of 1 m/s inside and 10 m/s outside the water ice line, following Birnstiel et al. 2012 and experimental results.
  • domain assumption Pebble accretion follows standard 2D/3D prescriptions with isolation mass
    Pebble accretion and pebble isolation mass prescriptions are taken from Lambrechts et al. 2014, Bitsch et al. 2018, and Ataiee et al. 2018, as described in Section 2.

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Cite this review

Pith. "Pith review of Quantifying the Impact of the Dust Torque on the Migration of Low-mass Planets II: The Role of Pebble Accretion in Planet Growth within a Global Planet Formation Model." pith.science (2026). https://pith.science/paper/FK4FDN6J

@misc{pith2026250116169,
  author       = {Pith},
  title        = {Pith review of: Quantifying the Impact of the Dust Torque on the Migration of Low-mass Planets II: The Role of Pebble Accretion in Planet Growth within a Global Planet Formation Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FK4FDN6J}},
  note         = {Machine review of arXiv:2501.16169}
}
read the original abstract

Although dust constitutes only about 1% of the mass of a protoplanetary disk, recent studies demonstrate that it can exert a significant torque on low- and intermediate-mass planetary cores. We compute and quantify for the first time the influence of the dust torque on the evolution of growing planetary embryos as they move in a protoplanetary disk while growing via gas and pebble accretion. Our global model evolves the gaseous disk via viscous accretion and X-ray photoevaporation, while accounting for dust growth and evolution including coagulation, drift, and fragmentation. Our research indicates that dust torque significantly influences planetary migration, particularly driving substantial outward migration for planets forming within the water ice-line. This effect occurs due to an increased dust-to-gas mass ratio in the inner disk, resulting from inward pebble drift from outer regions. In contrast, for planets initially located beyond the water ice-line, the dust torque mitigates inward migration but does not significantly alter their paths, as the dust-to-gas ratio diminishes rapidly due to rapid pebble drift and the brief timescales of planet formation in these areas. These findings underscore the pivotal role of dust torque in shaping the migration patterns of low- and intermediate-mass planets, especially when enhanced dust concentrations in the inner disk amplify its effects

Figures

Figures reproduced from arXiv: 2501.16169 by the authors.

Figure 1
Figure 1. Time evolution maps of the gas surface density (top), particle mass-weighted mean Stokes numbers (mid￾dle), and dust-to-gas mass ratio, ϵ = Σdust/Σdust (bottom). and its metallicity, we consider in addition two com￾plementary disk models: i) the fiducial case with a more massive disk, Mdisk = 0.1M⊙ and ii) the fidu￾cial case with an initial metallicity ϵ(t = 0 yr) = 0.02 3 . In what follows, we compute planet format… view at source ↗
Figure 3
Figure 3. Individual torque components and the total torque on the planet, as a function of the planet mass for the planet initially located at 0.5 au in the fiducial run. of the dust torque are not significant. This is due to two different reasons. On the one hand, the dust-to-gas mass ratio decreases rapidly beyond the water ice-line, leading to a rapid decline of the positive dust torque4 On the other hand, as we show in G… view at source ↗
Figure 4
Figure 4. Planet mass versus time for the planets ini￾tially located at 0.5 and 1 au (solid and dashed lines). The black/red lines indicate whether the dust torque is consid￾ered/ignored [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Planet formation tracks for the planets initialed located at 0.5 au and 1 au overlaid on the time evolution map of the dust-to-gas ratio, ϵ = Σd/Σg. ratio is highest; significantly boosting the pebble accre￾tion rates. However, when the dust torque is taken into accoun…
Figure 6
Figure 6. Figure 6: Time evolution maps of the particle mass￾weighted mean Stokes numbers (top) and the dust-to-gas mass ratio ϵ = Σd/Σg (bottom) for the case of a massive disk with Mdisk = 0.1M⊙ [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Time evolution maps of the particle mass￾weighted mean Stokes numbers (top) and the dust-to-gas mass ratio ϵ = Σd/Σg (bottom) for the case of a metallic disk with an initial dust-to-gas ratio ϵ = 0.02. we present the planet formation tracks for the fiducial case, contr…
Figure 10
Figure 10. Figure 10: Top panel: planet formation tracks for the plan￾ets initialed located at 0.5 au and 1 au overlaid on the time evolution map of the dust-to-gas ratio (ϵ = Σd/Σg). Bottom panel: planet formation track for the planet initialed located at 2 au overlaid on the time evoluti…
Figure 11
Figure 11. Figure 11: Planet formation tracks for the fiducial disk – as in [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: Comparison of the planet formation tracks for the case of an initial disk metallicity of 0.02. The red curves correspond to the case where the total torque is given solely by the gaseous torque (where we use the recipes from Jim´enez & Masset 2017). The black and blue…

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Pith tools

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