Radial Drift and Concurrent Ablation of Boulder-Sized Objects

Remo Burn; Ulysse Marboeuf; Willy Benz; Yann Alibert

REVIEW 3 major objections 4 minor 117 references

Radial Drift and Concurrent Ablation of Boulder-Sized Objects

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Meter-sized boulders can carry water ice about ten percent closer to the star than the classical snowline.

desk verdict A solid, honest parameter study of a neglected size regime, but the headline 10% snowline smearing is conditional on boulders surviving erosion, and the abstract oversells the disk-independence. read the letter →

arxiv 1908.02513 v1 pith:3YDI4XFZ submitted 2019-08-07 astro-ph.EP

Remo Burn , Ulysse Marboeuf , Yann Alibert , Willy Benz This is my paper · ORCID

classification astro-ph.EP

keywords protoplanetarydiskswatersnowlineradialdriftboulder-sizedbodiessublimationdustmantleHertz-Knudsen-Langmuirplanetformation

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 tries to establish that boulder-sized solids, roughly 1 m to 100 m across, are not simply lost from a protoplanetary disk: they drift inward faster than the water snowline recedes, cross it, and shed water ice as they ablate, so that ice can be present up to about ten percent closer to the star than the classical snowline location. A reader should care because disk composition, planetesimal formation, and the water budgets of forming planets are usually computed with a sharp snowline set by temperature and pressure alone; if this result holds, that boundary is smeared inward by a dynamical process that depends on the presence and size distribution of boulders. The paper also shows that for an unmantled body made of dust and water ice, a simple analytic surface-sublimation formula matches a full cometary-nucleus thermal model, because bodies below about 100 m reach internal thermal equilibrium in about a year.

What carries the argument

The argument runs on a race between two speeds: the radial drift speed of a solid body, computed from gas-drag stopping times in the Epstein, Stokes, and quadratic regimes, and the inward speed of the water snowline during disk evolution. On the ablation side, the Hertz-Knudsen-Langmuir formula $\phi(T)=P_s(T)/\sqrt{2\pi m_{\mathrm{H_2O}} R_g T}$ gives the free surface sublimation rate of water ice; because heat conduction equilibrates bodies below roughly 100 m within about a year, this surface formula alone tracks the full cometary-nucleus model. The feedback that carries the result is the drift-ablation loop: sublimation shrinks the radius, a smaller radius drifts faster, down to the fastest meter-size bodies, and faster drift brings the body into hotter regions, accelerating ablation until the body reaches the 10 cm disintegration limit.

What would settle it

The claim would be settled by measuring the impact-erosion lifetime of meter-sized icy bodies in the relevant velocity regime: if such bodies lose more than a few percent of their mass per year, they would disintegrate before crossing the snowline and the predicted ten-percent inward water-ice zone would not form; if erosion is much slower, the zone is expected. A complementary observation is a spatially resolved water-vapor or ice map just inside the snowline of a boulder-rich disk, looking for the predicted inward extension rather than a sharp cutoff.

Watch

Extended reading notes

Core claim

The central claim is that the dynamical snowline for water, the place where drifting solids actually lose their ice, is not the classical temperature-pressure snowline for bodies between about 1 m and 100 m. These bodies drift starward faster than the snowline moves inward, so they cross it; once inside, sublimation shrinks them and the smaller body drifts even faster, with the fastest drift near meter size, so they carry water inward until they shrink to roughly 10 cm and disintegrate. In the paper's terminology, the region polluted with water ice extends to ten percent closer to the star than the snowline location, and this result is nearly independent of disk mass, disk lifetime, and irradiation. A non-eroding dust mantle would let bodies reach about half the classical snowline distance, but the paper argues such mantles are stripped by collisions with pebble-sized objects. For homogeneous dust-water-ice bodies without a mantle, the paper finds the interior is isothermal on timescales of about a year, so the analytic Hertz-Knudsen-Langmuir sublimation expression reproduces the full numerical thermal model.

Load-bearing premise

The load-bearing premise is that a drifting boulder survives intact while it crosses the snowline; the paper's own collision-rate calculation finds that with standard laboratory erosion rates a 10 m body loses roughly $8\times10^{-2}$ percent of its mass per year, making the collision-free assumption valid only for about ten years, far shorter than the hundreds to thousands of years of sublimation modeled.

Editorial extensions

If this is right

The water ice available to planet formation begins about ten percent closer to the star than the classical snowline whenever meter-to-100 m bodies exist, so sharp-snowline disk models underestimate the inner water reservoir.
The volatile flux carried by drifting boulders can be estimated from the boulder size distribution and composition and should be added to disk chemistry and planet formation models.
For unmantled homogeneous dust-ice bodies up to 100 m, the analytic surface-sublimation formula can replace the full thermal model, reducing computational cost in future simulations.
Because the disintegration location is nearly constant when measured in units of the snowline distance, the predicted inward pollution zone scales across disks with different masses and lifetimes.
If a non-eroding dust mantle is present, icy bodies can reach about half the classical snowline distance, but pebble collisions should remove such mantles, keeping the unmantled result closer to reality.

Reading between the lines

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

If boulders are as abundant as the paper postulates, the water vapor they release just inside the snowline could locally raise the vapor pressure and slow further sublimation, potentially pushing the polluted region deeper inward than ten percent; the paper only tests this with an imposed vapor profile.
A full coagulation-erosion model could remove boulders before they cross the snowline, which would turn the ten-percent zone into an upper limit; the paper identifies collisional erosion as its main uncertainty.
The same drift-and-ablation mechanism should act on other volatiles with their own snowlines, such as CO2 or CO, and because each volatile has a different sublimation temperature, the smearing width should differ by species in a way that may be observable in resolved disk chemistry.
The near time-independence of the result suggests a practical rule for planet formation codes: deposit water at roughly 0.9 times the snowline radius whenever boulders are present, rather than at the snowline itself.

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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

Here's the short version: this is a competent, readable parameter study of a genuinely neglected size regime, and the headline result—that 1–100 m boulders crossing the water snowline by radial drift can carry water ice about 10% closer to the star than the classical snowline—is plausibly real. But the paper's own collision analysis in Sect. 4.1 gives erosion timescales around 10 yr, far shorter than the 100–1000 yr sublimation/drift phase. That means the central mechanism only operates if the solid surface density is low or the erosive effect is weaker than the Windmark et al. fit. The authors are transparent about this, but the abstract and conclusion oversell the 10% as almost disk-independent, when the non-irradiated disk case gives only 3%.

What is actually new: previous pebble-drift models stopped at around decimeter sizes, and Schorghofer's asteroid study was static. This is the first time the 1–100 m drift+ablation regime gets a quantitative treatment. The analytic Hertz-Knudsen-Langmuir surface sublimation formula is validated against the full cometary nucleus model with internal heat conduction and vapor diffusion, and the agreement in the no-mantle, pre-heated limit is solid. The parameter study covers disk mass, lifetime, irradiation, and mantle thickness; the disk-variation results are mostly robust at the percent level, and the snowline-normalized scaling is a nice way to decouple the result from disk evolution. There are no fitted parameters in the central claim; it comes out of the time-dependent simulation. The collision section deserves credit for showing its work and stating the survival problem explicitly.

The soft spots are real but not fatal to the paper as a parameter study. First, the collision timescale problem is load-bearing: if boulders don't survive to drift across the snowline, the 10% water delivery doesn't occur. The paper can't fix that without a full treatment of the solid size distribution and collisional evolution. Second, the abstract's "almost independently" overstates the disk dependence. Third, no code or data is released, which makes re-use harder. None of these make the modeling careless—the analysis is internally consistent within its stated assumptions.

Who should read it: anyone modeling disk composition, pebble/planetesimal formation, or water delivery to terrestrial planet formation regions. It deserves serious peer review, with a request to correct the summary generalization and to state the collision-survival condition front and center rather than in a caveat.

Referee Report

3 major / 4 minor

Summary. This manuscript couples an α-disk evolution model to the radial drift of spherical, dusty-water-ice bodies and to two treatments of sublimation—an analytic Hertz-Knudsen-Langmuir surface-ablation formula and the full Marboeuf et al. (2012) cometary nucleus model—to ask how far inward of the classical H2O snowline drifting boulders can carry water ice. The authors find that bodies with radii between roughly 1 m and 100 m drift inward faster than the snowline moves and, in the absence of a dust mantle, shrink to 10 cm at distances about 10% inside the snowline, with the ratio remaining stable as the disk evolves. Disk mass, lifetime, and photo-evaporation affect this inward penetration at the percent level, but the non-irradiated disk case gives only about 3% inward penetration. The analytic sublimation formula is shown to reproduce the full thermal model for homogeneous bodies up to about 100 m in radius, and the authors separately assess dust-mantle, water-vapor, frictional-heating, and collision effects, identifying collisions with small impactors as the main limitation on the mechanism.

Significance. If the central result is accepted, the paper provides a concrete, quantitative mechanism for smearing the water snowline and for delivering water to terrestrial-planet-forming regions, with implications for disk chemistry, planetesimal formation, and exoplanet compositions. A genuine strength is that the 10% inward penetration is not a fitted parameter: it emerges from the coupled drift-sublimation simulations and is stable across several disk parameters. The validation of the analytic surface-sublimation expression against the full cometary nucleus model is also nontrivial, because the latter includes heat conduction and vapor diffusion that the former omits. The authors are transparent about their assumptions, including the collision caveat. The significance is nevertheless contingent on the survival of boulders against collisional erosion over the 10^2–10^3 yr drift phase: the paper's own Section 4.1 estimates a nominal erosion timescale of about 10 yr, so the headline claim currently applies to a restricted regime unless erosion is explicitly included in the trajectory calculation.

major comments (3)

[Sec. 4.1] The collision analysis in Section 4.1 is load-bearing for the central claim. The authors state that the nominal 10 m target encounters about 4e-4 of its own mass per year in small impactors and, using the Windmark et al. (2012) erosion fit, loses about 8e-2% of its mass per year, making the collision-free assumption valid only on timescales of about 10 yr. This is one to two orders of magnitude shorter than the 10^2–10^3 yr sublimation/drift phase that produces the 10% inward penetration. Since erosion directly reduces the body's radius and mass, it can shorten the distance actually traveled before disintegration; this is not a peripheral parameter but a condition on the validity of the headline result. I recommend that the authors either add an erosion term to the radius-evolution equation (e.g., Eq. 14) and recompute the disintegration locations, or explicitly present the 10% result as conditional on the low-solid-surface-density or reduced-erosion regimes named in Section 4.1. The abstract and Conclusions currently state the 10% result without carrying this caveat forward.
[Sec. 3.3.2 / Fig. 10] The abstract and Conclusion item 1 state that the 10% inward penetration holds 'almost independently' of disk properties, but the non-irradiated disk in Fig. 10 reaches only about 3% inside the snowline, as acknowledged in Section 3.3.2. A factor-of-three difference between 10% and 3% is not a 'percent-level' effect relative to the headline value. The claim should be qualified to irradiated disks with the nominal pressure-gradient profile, or the reported range of inward penetration should be given explicitly (e.g., 3–10% depending on irradiation and pressure gradient).
[Sec. 3.3.1 / Fig. 8] The '10%' inner boundary is defined by the adopted 'complete disintegration' radius of 10 cm, after which the body is assumed to have a very short lifetime. Since the total inward drift is integrated from the initial radius down to this cutoff, the reported inward penetration depends on the choice of R_stop = 10 cm. A convergence check with a smaller cutoff radius (e.g., 1 cm) or a stated estimate of the residual drift time below 10 cm would make the headline distance more robust. I expect the effect to be small because sub-meter bodies drift more slowly, but the sensitivity is not currently quantified.

minor comments (4)

[Sec. 3.1 heading] The heading contains a typo: 'Comparision' should be 'Comparison'.
[Fig. 7(a) caption] The caption for Fig. 7(a) should explain that the log-ratio is artificially set to 12 once the snowline starts moving outward; currently this is stated only in the main text.
[Sec. 4.4] The sentence describing the no-vapor case as an 'upper boundary for the dynamical snowline location' is easy to misread. Since the presence of vapor slows sublimation and lets the body penetrate further inward, the no-vapor result is an outer (more conservative) limit on the dynamical snowline; please rephrase for clarity.
[Sec. 2.4.2] The initial placement of bodies at 10% outside the snowline is justified as a relaxation condition, but the manuscript does not explicitly state that the pre-sublimation drift from farther out has no effect on the resulting disintegration position because sublimation is inactive below the 150 K threshold. A sentence stating this explicitly would remove a possible concern about the initial condition.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 10% inward-snowline penetration is a simulation output from independent drift and sublimation physics, not a fitted or self-referential quantity.

full rationale

The central result (1–100 m boulders cross the snowline and disintegrate near 0.9 r_snowline) follows from time integration of a standard α-disk drift formula (Eq. 8, based on Weidenschilling/Adachi/Nakagawa) and a sublimation law (Eq. 12, Hertz-Knudsen-Langmuir). The snowline position is computed independently from disk temperature and pressure, and the sublimation threshold is fixed a priori. The 10% figure is not an input parameter: bodies are initially placed 10% outside the snowline only to relax initial transients, and the final disintegration radii (Fig. 8) vary with body size (0.5 m disintegrates near 1.0, larger bodies near 0.9), so the result is not the initial condition echoed back. The comparison between the analytic ablation model and the Marboeuf et al. (2012) comet code is partly by construction—both share Eq. (12) at the surface—but the full model adds heat conduction, vapor diffusion, and mantle physics, so the agreement is a nontrivial test of the internal-isothermality assumption rather than a tautology. The paper's own Sect. 4.1 collision estimate (erosion timescale ~10 yr vs. sublimation phase 100–1000 yr) is a serious physical-validity caveat, but it is an environmental assumption, not a circular derivation: it states that the result holds only if erosion is suppressed, which is a falsifiable condition rather than a fit of the predicted distance. No fitted parameter is renamed as a prediction, and no load-bearing conclusion depends on an unverified self-citation; the cited Marboeuf et al. (2012) model is used with its equations stated and is not doing the work of the 10% result alone.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model uses standard disk and comet physics; no new particles or forces are introduced. The hand-chosen thresholds (R_stop, T_threshold, initial offset, mantle thickness) are the main free inputs that shape the reported numbers, and the physics assumptions above are all stated and largely justified, though the collision-erosion and no-mantle assumptions are recognized as uncertain.

free parameters (4)

R_stop (complete disintegration radius) = 0.1 m
Radius at which a shrinking body is declared completely disintegrated (Sect. 3.3.1). Chosen by hand because centimeter-sized icy bodies at these temperatures have very short lifetimes. This choice directly defines the reported distance to the star at 'complete disintegration' and therefore the 10% value.
T_threshold (sublimation activation temperature) = 150 K
Temperature above which the sublimation models are started (Sect. 2). Chosen by hand; controls how much radial drift occurs before water ice begins to sublimate.
Initial body offset from snowline = 10% beyond snowline (1.1 x rsnowline)
Initial position chosen to let the body relax to the environment (Sect. 2.4.2). The authors argue initial conditions are forgotten by the time sublimation starts, but this is an input choice that could affect trajectories in short runs.
Constant dust mantle thickness = 5 cm nominal; 0.5 and 10 cm variants
For the 'constant mantle' cases (Sect. 3.3.3), mantle thickness is imposed by hand because it is weakly constrained by observations. This parameter controls how far inward mantle-covered bodies can drift (down to ~0.5 rsnowline).

assumptions (5)

domain assumption Body is a homogeneous sphere of dust and crystalline water ice, with no other volatiles, amorphous ice, or clathrates.
Sect. 2.4.2. The composition directly sets the sublimation rate and drift behavior. The authors choose crystalline ice and dust/ice ratio of 1, citing Marboeuf et al. (2014).
domain assumption The body's surface temperature equals the local midplane gas temperature and the interior is isothermal for radii below 100 m on circular orbits.
Sect. 2.2.2 and 3.4. The cometary nucleus model uses the local gas temperature as surface boundary; thermal equilibrium is justified by short conduction timescales. This is what makes the analytic model valid.
domain assumption Water vapor partial pressure around the body is zero, so sublimation follows the free Hertz-Knudsen-Langmuir rate.
Sect. 2.2.2, 2.3, 4.4. The authors neglect disk vapor and the body's own coma; they test an artificial vapor profile and note it pushes disintegration further inward, so the zero-vapor case is an upper boundary for the dynamical snowline.
domain assumption Collisional erosion is negligible during the drift and sublimation phase.
Sect. 4.1. The paper's own estimate using Windmark et al. (2012) gives erosion of about 8e-2 %/yr, which would invalidate the no-collision assumption on ~10 yr timescales. The authors flag this and restrict the validity of their main results to cases with reduced solid surface density or weaker erosion.
domain assumption No dust mantle forms on the body in the nominal cases; all freed dust is lost.
Sect. 2.2.3 and 3.3.3. Dust mantle formation is modeled in separate cases (unstable, constant). The main 10% result applies only to mantle-free bodies; a permanent mantle changes the disintegration location to ~0.5 rsnowline.

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Cite this review

Pith. "Pith review of Radial Drift and Concurrent Ablation of Boulder-Sized Objects." pith.science (2026). https://pith.science/paper/3YDI4XFZ

@misc{pith2026190802513,
  author       = {Pith},
  title        = {Pith review of: Radial Drift and Concurrent Ablation of Boulder-Sized Objects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3YDI4XFZ}},
  note         = {Machine review of arXiv:1908.02513}
}

read the original abstract

Context. The composition of a protoplanetary disk at a given location does not only depend on temperature and pressure but also on the time dependent transport of matter, such as radial drift of solid bodies, which could release water and other volatile species before disintegration or accretion onto a larger body with potentially considerable implications for the composition of planets. Aims. We perform a parameter study focused on the water depletion of different sized bodies able to cross the water snowline by gas induced radial drift. Methods. Either the analytical Hertz-Knudsen-Langmuir sublimation formula assuming equilibrium temperature within the body or a more involved, numerical model for the internal thermal evolution is coupled with an alpha-disk model. Different properties of the disk and the embedded body are explored. Results. Bodies with radii up to 100 meter drift faster towards the central star than the water snowline, hence, cross it. The region that can be reached before complete disintegration - and is therefore polluted with H2O ice - extends to 10 percent closer to the star than the snowline location. The extent of this polluted region could be multiple times larger in the presence of a dust mantle, which is, however, unlikely to form due to frequent collisions with smaller-than centimeter sized objects. Conclusions. Given a significant abundance of meter sized boulders in protoplanetary disks, the transport of water by radial drift of these bodies towards regions closer to the star than the snowline is not negligible and this flux of volatiles can be estimated for a given distribution of solid body sizes and compositions. A simple expression for surface sublimation is applicable for a homogeneous body consisting of only dust and water ice without a dust mantle.

Figures

Figures reproduced from arXiv: 1908.02513 by the authors.

**Figure 2.** Tortuosity of a path through a porous structure. In (A) a path through the material is shown, in (B) the length of the pore L and the distance between the endpoints X is indicated. Tortuosity is defined as L/X. Image adapted from O’Connell et al. (2010) under a creative common licence (http://creativecommons.org/licenses/by/2.0). of a gaseous disk, there is no direct irradiation, since the disk is opaque. Instead, … view at source ↗

**Figure 3.** Almost linear decrease in radius over time (green line, left axis) for a fixed surface temperature of 169 K using the cometary nucleus model. The derivative dR/dt is plotted in orange (right axis). 2.4. Initial conditions 2.4.1. Disk The initial gas surface density of the disk is given by a power law with exponential outer cut-off boundary (as proposed by Andrews et al. 2010) and a normalization constant Σ0, corres… view at source ↗

Figures from the paper (12 more)

**Figure 5.** Figure 5: As [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 4.** Figure 4: shows the results for a test case, in which we placed a body with an initial radius of 10 m and the composition shown in table 2 into the nominal disk (see table 1). The initial semimajor axis is set to 6 AU at time zero of the disk evolution. We find almost indisting…

**Figure 6.** Figure 6: Surface density evolution for the nominal disk. The dashed, blue line shows the snowline position. In the nominal disk model we calculated the drift speed (see Sect. 2.1.3) of solid bodies in the size range from 10−2 m to [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Drift velocity and regime in an irradiated disk with photoevaporation. All the bodies with sizes in the red area in Fig. (a) cross the snowline, since they drift faster than it moves towards the central star. The snowline is determined using tabulated values for the…

**Figure 8.** Figure 8: Comparison of locations of complete disintegration of different sized bodies without a dust mantle. In panel (a) the distance to the star is measured in AU and the dots represent the locations where the body shrank to a size of 10 cm. The dashed, cyan line indicates t…

**Figure 9.** Figure 9: Remaining mass fraction in the overall population of bodies crossing the snowline (1 kg ≤ m ≤ 1 × 109 kg) with shaded bands indicating the standard deviation due to the evolving disk. The mass shown is an integral over a distribution of masses with the indicated power-…

**Figure 10.** Figure 10: Mean relative locations of complete disintegration in different disks for initially 10 m sized bodies with and without constant dust mantles. As in [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

**Figure 11.** Figure 11: Sublimation comparison of a 10 m sized bodies with different dust mantle thicknesses and removal processes. The legend is ordered in increasing sublimation time. The smooth line marks the location of the body in time (left axis), while the dots at the end of the lin…

**Figure 13.** Figure 13: Interior Temperature of an initially 10 m sized body covered by a 10 cm thick dust mantle. The number of layers is reduced to 15 compared to nominal runs for better visibility and 60 timesteps are merged into one block. The uppermost, dark framed layer shows the dus…

**Figure 15.** Figure 15: Collisional energy calculated with the Stokes collision rate, integrated over impactor masses larger than the indicated minimum mass. The energy is measured in units of the energy required to heat the body by one Kelvin. The target properties and impactor mass distrib…

**Figure 14.** Figure 14: Collision rates of the nominal target body (table 2) with a radius of 10 m integrated over impactor masses larger than the indicated minimum mass. Results are shown for three different slopes of the impactor mass distribution and in panel (b) additionally for three d…

**Figure 16.** Figure 16: Evolution of a 10 m sized body in the nominal disk calculated with the analytical surface ablation model, with and without water vapor pressure. The water vapor increases exponentially depending on the local disk temperature up to a maximum of one percent of the loc…

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Pith tools

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

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