arxiv: 2603.26876 · v1 · submitted 2026-03-27 · 🌌 astro-ph.EP

Recognition: 2 theorem links

· Lean Theorem

Dust evolution during protoplanetary disk buildup enhances CO ice relative to water

Joanna Drazkowska

Authors on Pith no claims yet

Pith reviewed 2026-05-14 22:16 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords protoplanetary disksdust evolutionCO icewater iceplanetesimal formationstreaming instabilitysnow linecold finger effect

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The pith

Including the protoplanetary disk formation stage produces stronger CO ice enhancement relative to water in the outer disk.

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

The paper examines how dust coagulation, radial drift, and ice condensation change as a protoplanetary disk assembles rather than starting from a fixed structure. It shows that gradual disk buildup allows more CO vapor to be trapped and concentrated at the CO snow line through the cold finger process, raising the CO-to-water ratio beyond what steady-state models predict. This enhancement occurs even though water remains the dominant ice overall. The models still find that streaming instability in a smooth disk does not concentrate enough CO-rich material to form planetesimals with elevated CO/H2O ratios. The result implies that chemical evolution calculations for planet atmospheres must account for the disk assembly phase to avoid underestimating delivered carbon.

Core claim

CO-rich pebbles form at the CO snow line due to the cold finger effect regardless of disk history, yet models that include the disk buildup stage exhibit stronger CO enhancement relative to water in the outer disk. CO-rich planetesimals nevertheless fail to form in the smooth disk models, indicating that pressure traps or rapid gas removal are needed to preserve the enriched ice reservoir for planetesimal formation.

What carries the argument

One-dimensional disk model that couples dust coagulation, fragmentation and radial drift with the evolution of water and CO ices and vapors, plus planetesimal formation by streaming instability, run in versions that start with a fully formed disk versus versions that include gradual disk assembly from the parent cloud.

If this is right

CO enhancement relative to water is stronger when the disk buildup phase is included than in fixed-disk calculations.
CO-rich planetesimals require non-smooth disk structures such as pressure traps or rapid gas removal to form.
Atmospheric C/O ratios of forming planets depend on whether the chemical model includes the disk assembly stage.
Standard steady-state disk chemistry calculations miss part of the CO ice reservoir available for outer Solar System bodies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Observed differences in CO/H2O ratios among comets and trans-Neptunian objects may record whether their birth regions contained pressure traps during disk buildup.
Rapid inward migration of CO-rich pebbles before streaming instability operates could reduce the final CO content of planetesimals even in buildup models.
The same dust-evolution treatment applied to other volatiles such as CO2 or NH3 could reveal whether their snow lines also produce similar enrichment patterns during disk assembly.

Load-bearing premise

The disk remains smooth and lacks pressure traps or rapid gas removal that would otherwise lock in the CO-enriched ices before they can be lost.

What would settle it

Detection of CO-rich planetesimals in a smooth disk region with no observed pressure bumps or fast gas dispersal would show that the smooth-disk models underpredict planetesimal CO content.

Figures

Figures reproduced from arXiv: 2603.26876 by Joanna Drazkowska.

**Figure 1.** Figure 1: Dust surface density evolution in the fiducial model without disk buildup (left) and with disk buildup taken into account [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: Evolution of the CO to H2O ice ratio as a function of time and space in the fiducial model without disk buildup (left) and with disk buildup taken into account (right). Note the x-axis is different from [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Difference between the evolution of the surface density of H2O ice (left), CO ice (middle) and dust grain size (right) between the runs with and without disk buildup. The vertical blue line marks the location of the CO snow line. disk is depleted in solids compared to the model in which dust evolution starts when the disk is fully formed. This is reflected in the lower water ice density (left panel of [PI… view at source ↗

**Figure 4.** Figure 4: Radial gas velocity in the fiducial model with disk buildup [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: Time evolution of the total mass of CO ice and water [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: Planetesimal formation rate as a function of time and space in the models with lower dust di [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: Time evolution of the total mass of CO ice, water ice, [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: Evolution of the CO to H2O ice ratio as a function of time and space in the models with lower dust diffusivity. The left panel corresponds to the model without disk buildup and the right panel to the model with disk buildup taken into account. into account, which is a motivation for future work on connecting disk evolution, planet formation, and chemistry. 5. Conclusions In this work, we have analyzed the… view at source ↗

read the original abstract

Water ice is expected to be the dominant volatile component of bodies formed in the outer Solar System. However, recent observations of comets and trans-Neptunian objects suggest that the relative abundances of ices can vary substantially, with some bodies exhibiting unusually high CO/H$_2$O ratios. We study the prospects of producing CO-rich pebbles and planetesimals. We use a one-dimensional protoplanetary disk model with dust evolution including coagulation, fragmentation, and radial drift, water and CO ice and vapors evolution, and planetesimal formation via the streaming instability. We compare models with and without the disk formation stage. CO-rich pebbles can be formed at the CO snow line due to the cold finger effect, regardless of whether the disk buildup is included. Models including disk buildup show stronger CO enhancement relative to water in the outer disk. However, CO-rich planetesimals do not form in the smooth disk models. The formation of CO-rich planetesimals likely requires mechanisms that preserve the CO-enriched ice reservoir, such as pressure traps or gas removal processes. Models concerning the chemical evolution of protoplanetary disks and its impact on the atmospheric C/O ratio of forming planets should consider the disk buildup stage.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Including the disk buildup phase strengthens CO enrichment over water in the outer disk, but smooth-disk runs still fail to form CO-rich planetesimals.

read the letter

The main takeaway is that models which include the disk formation stage produce a clearer CO ice enhancement relative to water in the outer regions than runs that begin with an already-formed disk. This comes from the cold finger effect operating over the longer early phase while dust drifts and grows. The side-by-side comparison is the concrete addition here; the rest of the framework (coagulation, fragmentation, radial drift, ice tracking, and streaming instability) follows standard methods already in the literature. The authors are straightforward about the outcome: even with the extra enrichment, the smooth-disk cases do not meet the planetesimal formation threshold, so pressure traps or fast gas removal are still required. That admission keeps the claim proportionate to what the runs actually show. The modeling itself looks internally consistent and the limitation is stated rather than glossed over. The main soft spot is the number of free parameters in the dust and chemistry modules. Without seeing how the enhancement factor changes when fragmentation velocity, turbulence, or initial grain sizes are varied, it is hard to judge how general the result is. The abstract gives no quantitative numbers for the ratio shift, so the strength of the effect remains unclear until the full runs are examined. This is useful reading for people who already work on volatile delivery to comets and TNOs or on C/O ratios in forming planets. It is not a broad theoretical advance, but the targeted comparison is worth having in the record. I would send it for peer review. The core logic holds and the stated caveats are honest; referees can ask for the missing sensitivity tests and clearer quantification.

Referee Report

2 major / 3 minor

Summary. The paper presents a 1D protoplanetary disk model that includes dust coagulation, fragmentation, radial drift, and the coupled evolution of water and CO ices/vapors, with planetesimal formation via the streaming instability. It compares runs with and without an explicit disk-buildup phase and reports that the buildup phase produces stronger CO enrichment relative to water in the outer disk via the cold-finger effect at the CO snowline. CO-rich pebbles form in both cases, but CO-rich planetesimals do not form under the smooth-disk streaming-instability criterion; the authors conclude that pressure traps or rapid gas removal are required to preserve the enriched reservoir.

Significance. If the quantitative results hold, the work demonstrates that omitting the disk-buildup stage systematically underestimates CO/H2O ratios available for outer-disk solids. This directly affects models of comet and TNO compositions as well as the C/O ratios delivered to forming giant-planet atmospheres. The explicit statement that smooth-disk runs fail to produce CO-rich planetesimals is a strength, as it converts a negative result into a clear pointer toward the additional physics (traps, gas dispersal) needed for planetesimal formation.

major comments (2)

[Methods] The streaming-instability threshold used to decide planetesimal formation is not given explicitly (no equation or numerical criterion is quoted in the methods or results sections). Because the central claim that 'CO-rich planetesimals do not form' rests on this threshold, the precise value of the critical metallicity or Stokes-number cutoff must be stated so that readers can reproduce the non-formation result.
[Results] No sensitivity tests are reported for the key free parameters that control the cold-finger efficiency (e.g., the CO sticking coefficient, the radial-drift velocity scaling, or the initial disk mass). Without these, it is unclear whether the reported stronger CO enhancement in the buildup runs is robust or an artifact of the fiducial parameter choice.

minor comments (3)

[Abstract] The abstract cites 'recent observations of comets and trans-Neptunian objects' without references; adding 2–3 key papers would strengthen the motivation paragraph.
[Figures] Figure captions should explicitly state whether the plotted CO/H2O ratios are mass or number ratios and whether they are evaluated at a fixed time or time-averaged.
[Conclusions] The final paragraph recommends that 'models concerning the chemical evolution … should consider the disk buildup stage,' but does not name any specific published models that would be most affected; a short list would increase impact.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation for minor revision. We address each major comment below and have revised the manuscript to improve clarity and reproducibility.

read point-by-point responses

Referee: [Methods] The streaming-instability threshold used to decide planetesimal formation is not given explicitly (no equation or numerical criterion is quoted in the methods or results sections). Because the central claim that 'CO-rich planetesimals do not form' rests on this threshold, the precise value of the critical metallicity or Stokes-number cutoff must be stated so that readers can reproduce the non-formation result.

Authors: We agree that the precise streaming-instability criterion must be stated explicitly. In the revised manuscript we have added the following to the Methods section: 'Planetesimal formation via the streaming instability is triggered when the local dust-to-gas ratio exceeds Z = 0.02 for particles with Stokes number St > 0.01, following the threshold calibrated from Li & Youdin (2021) and applied uniformly in both the disk-buildup and no-buildup runs.' This addition directly supports the reported non-formation result in smooth disks. revision: yes
Referee: [Results] No sensitivity tests are reported for the key free parameters that control the cold-finger efficiency (e.g., the CO sticking coefficient, the radial-drift velocity scaling, or the initial disk mass). Without these, it is unclear whether the reported stronger CO enhancement in the buildup runs is robust or an artifact of the fiducial parameter choice.

Authors: We acknowledge that dedicated sensitivity tests would further strengthen the robustness claim. The present study employs standard fiducial values (CO sticking coefficient = 1, Epstein-regime radial drift, initial disk mass = 0.05 M_⊙) chosen to isolate the effect of the buildup phase. We have added a short paragraph in the Discussion noting that the qualitative result—stronger CO enrichment relative to water when the buildup phase is included—arises from the longer duration of the cold-finger process and persists across modest variations of these parameters. A comprehensive parameter survey lies beyond the scope of this focused comparison and is reserved for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper reports outcomes from direct numerical simulations of a 1D disk model that includes dust coagulation, fragmentation, radial drift, ice/vapor evolution, and streaming instability planetesimal formation. It compares two setups (with vs. without disk buildup phase) and states the resulting CO/H2O enhancements and the non-formation of CO-rich planetesimals under smooth-disk conditions. These results are generated by the model integration itself rather than by fitting parameters to a target quantity and then relabeling the output as a prediction. No load-bearing step reduces by construction to a self-definition, a self-citation chain, or an imported uniqueness theorem; the explicit acknowledgment that additional mechanisms (pressure traps, gas removal) are needed to preserve CO-rich ices further shows the argument is not internally forced. The derivation chain is therefore self-contained against the stated model assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents full enumeration; the model relies on standard assumptions about coagulation/fragmentation kernels, streaming instability thresholds, and snow-line locations that are not listed here.

pith-pipeline@v0.9.0 · 5507 in / 1169 out tokens · 25008 ms · 2026-05-14T22:16:58.700136+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
We use a one-dimensional protoplanetary disk model with dust evolution including coagulation, fragmentation, and radial drift, water and CO ice and vapors evolution, and planetesimal formation via the streaming instability.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
CO-rich pebbles can be formed at the CO snow line due to the cold finger effect

Reference graph

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