Late gas released in the young Kuiper belt could have significantly contributed to the carbon enrichment of the atmospheres of Neptune and Uranus

Paul Huet; Quentin Kral; Tristan Guillot

REVIEW 4 major objections 4 minor 88 references

Late gas released in the young Kuiper belt could have significantly contributed to the carbon enrichment of the atmospheres of Neptune and Uranus

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Late gas accreted from a massive young Kuiper belt can account for most, and potentially all, of the carbon enrichment observed in the atmospheres of Uranus and Neptune.

desk verdict A plausible new scenario for the C/H of Uranus and Neptune, but the headline claim rests on a fixed CO ice fraction and an untested mixing assumption; worth a careful referee. read the letter →

arxiv 2506.03412 v1 pith:HEIZXHU3 submitted 2025-06-03 astro-ph.EP

Paul Huet , Quentin Kral , Tristan Guillot This is my paper

classification astro-ph.EP

keywords lategasKuiperbeltUranusNeptuneatmosphericcarbonenrichmentC/Hratiodebrisdiscplanetaccretion

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 asks whether the atmospheres of Uranus and Neptune could have become carbon-rich not during planet formation but later, from gas released by a massive young Kuiper belt. It builds a one-dimensional viscous model of that belt's gas, released by collisions and by slow sublimation of CO ice, spreading toward the planets, and computes how much carbon each giant accretes. The central result is that a primordial Kuiper belt of about 50 Earth masses can deliver enough CO to raise Uranus's atmospheric [C/H] to roughly 13–33 times protosolar and Neptune's to 20–58, values that overlap the observed 44–74 and 55–92 once formation-time enrichment is added. If this is right, the super-solar carbon of the ice giants does not require both planets to have formed at the CO ice line, and late gas becomes a general mechanism for raising the metallicity of giant and sub-giant exoplanets.

What carries the argument

The load-bearing machinery is a one-dimensional viscous multi-species gas disc model that carries CO, atomic carbon, and atomic oxygen from the belt toward the planets. Gas is produced by collisional grinding of planetesimals (dominant for a heavy primordial belt) and by slow sublimation of CO ice inside warming Kuiper belt objects, then it viscously spreads inward while CO photodissociates under interstellar radiation with self- and carbon shielding. Each planet removes gas through sink cells with an accretion efficiency of 0.1–0.8, and the delivered carbon mass is converted to an atmospheric ratio through $C/H = (\mu_H/\mu_C)(M_C/M_H)$ using the observed H/He envelope masses of Uranus and Neptune.

What would settle it

Send an entry probe into Uranus, or measure its deep CH4 profile by microwave spectroscopy, and compare the deep carbon abundance with the value the model predicts from late-gas accretion; if the carbon is not mixed uniformly through the 1.25–3.5 Earth-mass H/He envelope, the observed C/H will fall well below the predicted 13–33 times protosolar.

Watch

Extended reading notes

Core claim

The paper's central claim is that accretion of CO gas released from a massive primordial Kuiper belt can account for a large part, and potentially all, of the observed C/H enrichment of Uranus and Neptune. In the fiducial simulation, a 50-Earth-mass belt with an accretion efficiency of 0.5 delivers up to about 0.1 Earth masses of CO to each ice giant within 100 Myr; mixed through the light hydrogen–helium envelopes, this gives [C/H] of 20–58 times protosolar for Neptune and 12.9–33.3 for Uranus. Since sulfur is observed to be enriched relative to hydrogen but less than carbon, the paper argues part of the carbon came from early formation and that the required extra enrichment is roughly 20 times protosolar for both planets, a value the model reaches for belt masses above 20–30 Earth masses. The authors conclude that "our model may explain by itself the observed values of [C/H] on the ice giants."

Load-bearing premise

The calculation assumes that the carbon delivered by the gas mixes evenly through the whole hydrogen–helium envelope of each ice giant; if it sinks or is trapped deeper instead, the same amount of accreted carbon would show up as a much smaller enrichment at the surface.

Editorial extensions

If this is right

In the fiducial compact configuration, the model alone produces [C/H] values of 12.9–33.3 for Uranus and 20–58.3 for Neptune after 100 Myr, which overlap the observed ranges once formation-time enrichment is included.
Belt masses below roughly 20–30 Earth masses (light or extended configurations) give only a few times protosolar enrichment, so explaining the observed carbon enrichment requires a massive primordial Kuiper belt of the kind recent Nice-model extensions assume.
Saturn receives a small late-gas contribution of up to about 2 times protosolar [C/H] and Jupiter at most 0.16, consistent with their observed modestly super-solar carbon abundances.
The same mechanism should operate in extrasolar systems, where sub-Jupiter planets with light envelopes are predicted to show carbon (and, for warm planets, oxygen) enrichment inversely proportional to envelope mass.

Reading between the lines

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

Because the paper takes its accretion efficiency of 0.5 from protoplanetary-disc studies, running dedicated hydrodynamic simulations in the low-density debris-disc regime would provide an ab initio value of faccr and is the most direct test of the model's headline enrichment numbers.
The mechanism makes a compositional fingerprint beyond carbon: late gas raises C/H and O/H without raising S/H, so a confirmed pattern of carbon enrichment exceeding sulfur enrichment in Uranus and Neptune, or in warm sub-Jupiters, would discriminate this channel from pebble-accretion enrichment, which tends to enrich heavy elements together.
The model implicitly requires the delivered CO to arrive while each planet's atmosphere is still hot enough to mix it and before hydrogen–helium phase separation sequesters the carbon; exoplanets observed at ages of tens of millions of years could test whether the enrichment scales with envelope mass, as Figure 14 of the paper predicts.

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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

You should read this paper if you care about ice giant metallicities. The core idea—CO gas released from a massive young Kuiper belt spreading inward and being accreted by Uranus and Neptune—is new as a quantitative model, and the comparison with S/H-derived limits on the extra carbon is a genuinely useful step. The authors run a proper viscous evolution code with CO photodissociation and planetary accretion, and they test belt mass, accretion efficiency, viscosity, belt lifetime, and compact versus extended geometries. They are honest about many uncertainties, and the light-belt case correctly shows that a present-day-mass Kuiper belt contributes almost nothing.

The main weakness is not what they test; it's what they fix. The collision-driven gas release rate is Mdot_CO = -f_ice * Mdot_belt, with f_ice fixed at 0.1. The final [C/H] scales linearly with f_ice. If the primordial CO ice fraction is 0.03—plausible, given the current Kuiper belt's depletion—the fiducial Neptune prediction drops from 20-58 to 6-17, below the ~21 extra carbon that their own S/H tracer says is needed. The 'explain by itself' claim then fails, and even the 'significant contribution' claim sits within a factor of a few of failing. The same applies to the assumption that all ice in collisional fragments is released as gas; they never vary the release efficiency.

The other load-bearing assumption is mixing: they deposit the accreted carbon uniformly into the full 1.25-4.15 M_Earth H-He atmosphere. If the carbon sinks or is only partially mixed, the atmospheric C/H would be much lower. That's a first-order unknown for icy giants, and the paper doesn't test it.

None of this kills the paper. The scenario is plausible, the model is a reasonable first quantitative pass, and the exoplanet prediction—warm sub-Jupiters enriched in C and O relative to N and S—is testable with JWST and the ELT. The authors flag many of these uncertainties themselves, which is to their credit. I'd send this to review, but with a request that they (1) run a sensitivity series over f_ice and collisional release efficiency, and (2) quantify how much of the accreted carbon must be mixed into the observable atmosphere to match the data. Without that, the strong claim is not yet supported. With it, the result would be much more robust.

Referee Report

4 major / 4 minor

Summary. The manuscript develops a one-dimensional multi-species viscous accretion model to quantify the carbon enrichment of the atmospheres of Uranus and Neptune from CO gas released by a massive primordial Kuiper belt. The model includes collisional and sublimation gas release, photodissociation, viscous spreading, and parameterized planetary accretion. With a 50 M_Earth belt and accretion efficiency 0.5, the predicted post-100 Myr [C/H] is 12.9–33.3 for Uranus and 20–58.3 for Neptune, which the authors argue can explain a substantial fraction, potentially all, of the observed super-solar [C/H]. They also use S/H and D/H ratios to estimate the additional enrichment needed from late gas, concluding that a belt of 20–30 M_Earth is required. The paper claims the mechanism is universal and predicts a correlation between envelope mass and C/O enrichment in exoplanets.

Significance. The scenario is original and potentially important: it links the Nice model's massive primordial Kuiper belt to the long-standing problem of the ice giants' high metallicities, and it provides a falsifiable prediction for exoplanet atmospheric composition. The authors document a numerical model with a sensitivity study over belt mass, accretion efficiency, viscosity, architecture, and depletion timescale, and they explicitly discuss several limitations (e.g., O/H, terrestrial planets, migration). If the central numbers survive a wider parameter exploration, the paper would establish a new channel for giant-planet atmospheric enrichment. However, the key quantitative conclusion currently rests on a few favorable but unvaried assumptions.

major comments (4)

[Sec. 2.3, Sec. 4.2.2, Table 3] The gas production rate is set by Ẍ_CO = −f_ice Ẍ_belt with f_ice fixed at 0.1, and the collisional rate scales as e^{5/3} with a chosen mean eccentricity of 0.25; neither f_ice nor eccentricity is varied in the sensitivity runs, yet the predicted [C/H] in Eq. (13) is directly proportional to f_ice and strongly dependent on e. If f_ice were 0.03 (a plausible lower value) or e were 0.1 (the typical assumed range), the fiducial Neptune [C/H] would drop to roughly 6–17 or 4–12, respectively, below the observed 55–92 and below the S/H-derived extra of about 21. The 'explain by itself' claim therefore depends on undiagnosed favorable multipliers; the authors should either extend the sensitivity grid to these parameters or soften the claim.
[Sec. 3.3.1, Table 3] The statement that the model 'may explain by itself the observed values of [C/H] on the ice giants' is not supported for Uranus, whose fiducial maximum of 33.3 is below the observed minimum of 44; for Neptune, the maximum of 58.3 only marginally overlaps the observed minimum of 55. The abstract's 'could account entirely' is correspondingly overstated. The predicted ranges should be described as capable of explaining the lower end of the observed enrichment or a substantial fraction of it, rather than the full values.
[Sec. 2.7, Eq. (13)] The conversion from accreted carbon mass to atmospheric [C/H] assumes complete and uniform mixing of the carbon throughout the full H/He envelope (1.25–3.5 M_Earth for Uranus, 1.6–4.15 M_Earth for Neptune). If mixing is incomplete, or if a significant fraction of the accreted carbon is sequestered at depth, the same accreted mass would yield a different observable [C/H]; the paper does not test the mixing efficiency or discuss the fate of carbon below the observable atmosphere. Please add a discussion or a dedicated test of this assumption.
[Sec. 2.6.1] In the compact-architecture (Nice-model) runs, the planets are held at fixed positions (5–16 au) throughout the simulation, even though the scenario explicitly invokes outward migration of Neptune to 30 au. The claim that planet positions do not affect the results is not backed by a controlled test; the accretion rate depends on the local surface density and radial velocity via Eqs. (7)–(8), which vary with radius. A sensitivity run with migrating planets, or at least with the extended configuration at the same belt mass, would be needed to substantiate this point.

minor comments (4)

[Sec. 3.1.1] The assumption that the S/C ratio in early accreted planetesimals equals the protosolar value (S/C|ppd ~ S/C|proto) is plausible but unquantified; please add a brief discussion of how the inferred extra [C/H] changes if this ratio differs by, say, a factor of 2.
[Sec. 3.1.2 vs. Sec. 3.1.1] The D/H-based estimate of the extra [C/H] gives values about a factor of 2 higher than the S/H-based estimate, yet the paper does not explain why the S/H-based value is preferred when drawing conclusions in Section 4.
[Throughout] A number of typos and formatting issues need cleaning: 'Received 21 Mars 2025' (March), 'Figure 3.3.1' (likely Figure 8), 'e5/3' formatting in Sec. 4.2.2, and the Jupiter row of Table A.1 where the lower and upper bounds are listed in reverse order (1.16e-6 – 1.29e-7).
[Sec. 3.2] The references 'Figure A' and 'Fig. A.3' are ambiguous; please use the explicit figure numbers (e.g., A.1, A.2, A.3).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted [C/H] values are computed from literature-based physical inputs and compared against, not fitted to, the observed C/H and S/H of Uranus and Neptune.

full rationale

The derivation chain is self-contained. Gas production in Secs. 2.2-2.3 uses the assumed ice fraction f_ice=0.1 (Mumma & Charnley 2011) and the collisional mass-loss rate from Löhne et al. (2008) with size distributions from Bottke et al. (2023); viscous spreading, photodissociation (Eqs. 9-12) and planetary accretion (Eqs. 7-8, with faccr=0.5 from independent hydrodynamic simulations) are standard or externally benchmarked. Eq. 13 converts the simulated accreted carbon mass to [C/H] using atmospheric masses from Guillot et al. (2023), and the results in Table 3 are compared with observed [C/H]. No equation inverts the observed C/H to set belt mass, f_ice, faccr, or alpha; the 50 M_Earth belt is justified by Nice-model literature (Griveaud et al. 2024), and the S/H-based 'extra C/H' target (Eq. 16) is computed from observations before any simulation is run and is not fed back into the model. The self-citations (Kral et al. 2017, 2019, 2020, 2021, 2024) supply the debris-disc gas/accretion modeling infrastructure, but they do not assume the conclusion that late gas explains the ice giants' C/H, and that infrastructure is independently calibrated against exo-Kuiper belt observations. The paper's admitted simplifications, such as fixed planet positions during depletion and the assumption that accreted CO mixes uniformly in the H/He atmosphere (Sec. 2.7), are parameter/mixing sensitivities and not circular reductions. The strongest criticism is that results scale linearly with f_ice and depend on the unmixed-atmosphere assumption, but a fixed undiagnosed multiplier is a robustness concern, not a case where the prediction is equivalent to its input by construction.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central claim depends on a set of scenario parameters (belt mass, accretion efficiency, viscosity, ice fraction, thermal conductivity, eccentricity, depletion timescale, S/C ratio in solids) that are taken from literature or assumed rather than derived from first principles. The axioms listed are the key modeling choices that connect gas production, spreading, accretion, and mixing into the observed C/H. No new physical entities are introduced.

free parameters (8)

Initial Kuiper belt mass M0 = 50, 20, 5, 0.1 M_Earth
Scenario parameter drawn from Nice model and alternative formation models; the 50 M_Earth case is the one that matches the observed C/H.
Accretion efficiency faccr = 0.1, 0.5, 0.8
Assumed from protoplanetary disc hydro simulations; not computed for debris disc conditions.
Viscous alpha = 1e-3 to 1e-2
From debris disc gas literature; authors argue it does not affect final accreted mass.
CO ice fraction fice = 0.1
From cometary ice-to-refractory ratio.
Thermal conductivity K = 1e-10 m2/s
From cold KBO observations.
Eccentricity e = 0.25
Assumed for the primordial belt; gas production scales roughly as e^(5/3).
Depletion e-folding time tfold = 10 or 100 Myr
From Nice model and extended scenarios.
S/C ratio in accreted solids = assumed equal to protosolar
Used to derive the required 'extra' C/H from S/H observations.

assumptions (6)

domain assumption All CO ice in colliding planetesimals is released as gas
Sec. 2.3 assumes M_CO = -fice * M_belt_dot; exposed surface area argument.
domain assumption Accreted CO mixes uniformly in the full H/He atmosphere
Sec. 2.7, Eq. 13.
domain assumption The S/C ratio in solids accreted during planet formation equals the protosolar value
Sec. 3.1.1, Eq. 16.
standard math The gas disc is axisymmetric and evolves via 1D viscous diffusion with a constant alpha
Sec. 2.1; standard viscous accretion disc theory (Lynden-Bell & Pringle 1974).
domain assumption Planet positions are fixed during gas accretion
Sec. 2.6; migration not modeled, authors argue positions weakly affect results.
domain assumption Photodissociation is driven by ISRF with self-shielding and carbon shielding prescriptions
Sec. 2.5.

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Cite this review

Pith. "Pith review of Late gas released in the young Kuiper belt could have significantly contributed to the carbon enrichment of the atmospheres of Neptune and Uranus." pith.science (2026). https://pith.science/paper/HEIZXHU3

@misc{pith2026250603412,
  author       = {Pith},
  title        = {Pith review of: Late gas released in the young Kuiper belt could have significantly contributed to the carbon enrichment of the atmospheres of Neptune and Uranus},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HEIZXHU3}},
  note         = {Machine review of arXiv:2506.03412}
}

abstract

Exo-Kuiper belts have been observed for decades, but the recent detection of gas in some of them may change our view of the Solar System's youth. Late gas produced by the sublimation of CO (or CO$_2$) ices after the dissipation of the primordial gas could be the norm in young planetesimal belts. Hence, a gas-rich Kuiper belt could have been present in the Solar System. The high C/H ratios observed on Uranus and Neptune could be a clue to the existence of such late gas that could have been accreted onto young icy giants. The aim of this paper is to estimate the carbon enrichment of the atmospheres of Uranus and Neptune caused by the accretion of the gas released from a putative gas-rich Kuiper belt. We find that assuming a primordial Kuiper belt with a mass of tens of earth masses leads to significant CO gas accretion onto the giants, which can lead to high C/H ratios, especially for Uranus and Neptune. Our model shows that a relatively massive gas-rich Kuiper belt could have existed in the Solar System's youth, significantly enriching the atmospheres of Uranus and Neptune with carbon. Late gas accretion and its effect on outer giant planets metallicities could be a universal scenario, also occurring in extrasolar systems. Observations of sub-Jupiter exoplanets could provide very useful information to better constrain this scenario, with an enrichment in carbon and oxygen (for warm-enough planets) compared to other elements that should be inversely proportional to their envelope mass.

Figures

Figures reproduced from arXiv: 2506.03412 by the authors.

**Figure 1.** Schematic presenting a description of our set of 9 simulations. The heavy belt cases are at the top (compact configuration) and middle (extended configuration), and the light cases are at the bottom. J, S, U, and N are Jupiter, Saturn, Uranus, and Neptune, respectively. The different simulations differ in terms of the locations of planets, accretion efficiency, the viscosity of the gas, and the belt’s mass. For t… view at source ↗

**Figure 2.** Estimations of the contribution of late gas to the atmospheric [C/H] ratios for Jupiter (J), Saturn (S), Uranus (U), and Neptune (N) calculated from the observed [C/H] and [S/H] (see subsection 3.1.1). The crosses show the mean values and the bars show the uncertainties, noting that the minimal values go to zero. 3.1.2. Using the D/H ratio to estimate carbon enrichment from planetary formation The D/H ratios of Ura… view at source ↗

**Figure 3.** CO mass production rate in the belt as a function of time for all LKB (light KB) simulations [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: Surface density of CO (in variations of blue) and neutral carbon (in variations of orange) at different times for the LKB-fid simulation. The color goes from darker to brighter for increasing time as indicated by the color bar. The gray vertical bars represent the pla…

**Figure 5.** Figure 5: Neutral carbon cumulated accreted mass for each planet as a function of time for the LKB-fid simulation. Finally, regardless of the circumstances, we find that for the LKB simulations the accreted masses on both Uranus and Neptune turn into a small C/H value when compa…

**Figure 7.** Figure 7: Surface density of CO (in variations of blue) and neutral carbon (in variations of orange) at different times for the HKB-fid simulation. The color goes from darker to brighter for increasing time as indicated by the color bar. The gray vertical bars indicate the pla…

**Figure 3.3.** Figure 3.3: 1 shows the CO mass captured onto the 4 gi [PITH_FULL_IMAGE:figures/full_fig_p012_3_3.png]

**Figure 8.** Figure 8: CO accreted mass for each planet as a function of time for the compact configuration of HKB simulations (HKB-fid left, HKB-2 middle, HKB-3 right). for observations as explained in the beginning of the result section. To account for that, in [PITH_FULL_IMAGE:figures/fu…

**Figure 9.** Figure 9: [C/H] for the HKB-fid simulation as a function of time. The filled areas correspond to predictions for Uranus (purple) and Neptune (blue). The uncertainties are shown via the extension of the filled areas and are due to uncertainties on the respective atmospheric mass…

**Figure 11.** Figure 11: [C/H] for the simulation HKB-fid as a function of time for Jupiter and Saturn. The uncertainties are shown by the extent of the filled-in areas and are due to the uncertainties over the respective atmospheric mass in which the CO can mix (i.e. between a diluted 60 M⊕…

**Figure 10.** Figure 10: [C/H] for the simulation HKB-2 (top) and HKB-3 (bottom) as a function of time. 3.3.2. The extended architecture In the compact architecture context, the planets and KB need to start in a compact configuration with a massive planetary belt to end up with the present-d…

**Figure 12.** Figure 12: [C/H] for the simulation HKB-4 (top) and HKB-5 (bottom) as a function of time. 4.2. The primordial belt model to explain the metallicity of Uranus and Neptune 4.2.1. The gas viscosity The α viscosity in debris discs is expected to be rather high compared to protoplan…

**Figure 13.** Figure 13: Accretions rates for the HKB-fid simulations compared to the maximum capture rate onto planets due to atmospheric cooling. As stated earlier, the other physical mechanism that may impact the theoretical accretion rate is the complex hydrodynamical flow. Previous numer…

**Figure 14.** Figure 14 [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]

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