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REVIEW 3 major objections 5 minor 20 references

C/O ratios in self-gravitating protoplanetary discs with dust evolution

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper shows that the carbon-to-oxygen ratio of the gas and ices in self-gravitating protoplanetary discs evolves with dust dynamics, producing a narrow C/O fingerprint for gravitational instability and a wide one for streaming…

desk verdict Solid modeling study of C/O in self-gravitating discs, but the GI/SI dichotomy in Figure 10 is softer than the abstract claims because it compares different phase quantities to observations. read the letter →

arxiv 2412.05099 v1 pith:HMCNA27M submitted 2024-12-06 astro-ph.EP astro-ph.SR

Tamara Molyarova , Eduard Vorobyov , Vitaly Akimkin This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords carbon-to-oxygenratioprotoplanetarydiscsdustevolutionsnowlinesgravitationalinstabilitystreamingexoplanetatmospheresvolatiletransport
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 argues that the carbon-to-oxygen ratio ($C/O$) of planet-forming material is not just a chemical snapshot but a diagnostic of how planets form. In two self-gravitating disc models evolved for 0.5 Myr with dust growth, drift, and freeze-out/sublimation of H$_2$O, CO$_2$, CO, and CH$_4$, the $C/O$ ratio of gas and ices becomes strongly non-uniform. Regions where gravitational instability (GI) can operate have a narrow total $C/O$ range of about 0.3–0.6, centred near the initial value of 0.34, while regions where streaming instability (SI) can operate show a wide range from 0 to 1.4. This split matches the observed two populations of exoplanets: directly imaged planets cluster around 0.5–0.8, while transiting hot Jupiters scatter widely. If correct, atmospheric $C/O$ becomes a practical way to tell whether a giant planet formed by disc fragmentation or by core accretion with migration.

What carries the argument

The central object is the coupled hydrodynamics–dust–ice model FEOSAD, treated as a thin disc with self-gravity, temperature-dependent viscosity, dust growth and drift, and a phase-transition network for four volatiles. The mechanism carrying the argument is the combination of radial drift of icy grains, which transports oxygen-rich ices inward and concentrates them at snowlines, and the criterion-based identification of GI ($Q\le1$) versus SI regions (the Li–Youdin threshold). The paper then compares the $C/O$ distributions in those regions with observed exoplanet populations and cometary compositions.

What would settle it

Observe the $C/O$ ratios of a dozen directly imaged giant planets at separations beyond 10 au: if their $C/O$ ratios scatter as widely as those of transiting hot Jupiters instead of clustering near 0.3–0.6, the gravitational-instability fingerprint proposed here would be falsified.

Watch

Extended reading notes

Core claim

Using the FEOSAD thin-disc hydrodynamics code with self-gravity, two-temperature dust, and a four-species volatile model (H$_2$O, CO$_2$, CO, CH$_4$) that allows freeze-out, thermal desorption, and photodesorption, the authors simulate disc formation and evolution to 0.5 Myr for two core masses. They show that dust drift and the feedback of icy mantles on fragmentation create rings, spirals, and multiple snowlines, and that the total $C/O$ ratio anticorrelates with the dust-to-gas ratio because oxygen-rich ices dominate in dust-rich regions. Weighting all disc regions where the Toomre criterion ($Q \le 1$) is met, they find that the $C/O$ distribution for gravitational instability has a narrow peak near 0.5, while the regions meeting the Li–Youdin criterion for streaming instability give a broad gas-phase $C/O$ range of roughly 0.2–1.4 and low ice-phase values. They argue this dichotomy is consistent with the observed separation between directly imaged exoplanets (narrow, lower $C/O$) and transiting hot Jupiters (wide $C/O$), and that the ice-phase $C/O\approx 0.2$–0.3 between the CO, CO$_2$, and CH$_4$ snowlines matches Solar System comets.

Load-bearing premise

The modelling restricts chemistry to freezing and desorption of four ices; if gas-phase or surface reactions (e.g. CO converting to CO$_2$, methanol forming, volatile trapping in mantles) materially alter the midplane composition, the assigned $C/O$ fingerprints would shift.

Editorial extensions

If this is right

  • Planets formed by gravitational instability should have atmospheres with $C/O$ clustered near 0.3–0.6, while planets formed by streaming instability and migration can show $C/O$ anywhere from 0 to 1.4.
  • Directly imaged exoplanets likely formed via GI in the outer disc, whereas transiting hot Jupiters' wide $C/O$ spread reflects migration through varied disc conditions.
  • Comets with ice-phase $C/O$ 0.2–0.3 formed between the CO and CO$_2$ snowlines, whereas carbon-rich comets likely originated at the snowlines themselves.
  • Dust-to-gas ratio and total $C/O$ are anticorrelated, so planetesimals assembled in dust-rich rings should start with low $C/O$ unless they later accrete carbon-rich gas.

Reading between the lines

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

  • If gas-phase and surface reactions (CO-to-CO$_2$ conversion, methanol formation, volatile trapping) were added, the boundaries of the $C/O$ zones would likely shift, but the qualitative anticorrelation and the GI/SI separation may survive; rerunning the same model with a reduced chemical network is a testable extension.
  • The narrow GI peak near 0.5 depends on excluding refractory carbon and on the assumed initial volatile abundances; including carbon-rich rock cores would raise the baseline $C/O$ and could move the GI peak closer to the observed directly imaged value.
  • This claim implies that atmospheric $C/O$ measurements, combined with orbital separation and age, could identify individual planets formed by disc fragmentation, a prediction testable with current or near-future JWST spectroscopy of wide-orbit planets.
  • The ice-phase match to comets suggests that most Solar System comets formed between snowlines, while carbon-rich comets like C/2016 R2 require formation at a carbon-rich snowline; linking specific comets to specific zones is a testable prediction.
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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. The paper uses the thin-disc hydrodynamic code FEOSAD, including self-gravity, thermal balance, dust growth and drift, and turbulent diffusion, to follow the phase transitions (freeze-out, thermal desorption, photodesorption) of H2O, CO2, CH4, and CO in two self-gravitating protoplanetary disc models over 0.5 Myr. The authors map the resulting C/O ratio in the gas, in the ice, and in total, and connect these distributions to potential planet formation sites. They identify regions where gravitational instability (GI) and streaming instability (SI) criteria are satisfied, and claim that GI regions have a narrow C/O range (≈0.3–0.6, total) matching directly imaged exoplanets, while SI regions have a wide C/O range (≈0–1.4, gas phase) matching transiting hot Jupiters. They also report an anticorrelation between dust-to-gas ratio and total C/O, and an ice-phase C/O of ≈0.2–0.3 between the CO2, CH4, and CO snowlines consistent with Solar System comets.

Significance. If the GI/SI C/O dichotomy survives scrutiny, it would provide a useful observational diagnostic for distinguishing planet formation mechanisms from atmospheric compositions. The paper's strengths include a global 2D model with self-consistent dust dynamics and phase transitions, explicit consideration of disc substructures and multiple snowline geometries, two different core masses, and quantitative comparisons with exoplanet population data. The authors are also transparent about the model's simplifications, such as the absence of gas-phase and surface chemistry and the thin-disc approximation. However, the central claim is currently built on an inconsistent definition of the observable C/O between the two formation channels, and on a simplified chemical scheme whose quantitative ranges are not shown to be robust. These issues need to be addressed before the main diagnostic can be accepted.

major comments (3)
  1. [Section 4, Figure 10] The comparison between GI and SI regions and observed exoplanet C/O ratios uses different C/O definitions: for GI the total volatile C/O is plotted, while for SI the gas-phase and ice-phase C/O are plotted separately. Observed atmospheric C/O is a single gas-phase quantity, so this is not a like-for-like comparison. A GI planet's atmospheric C/O equals the local total C/O only if all accreted solids are vaporized and mixed into the envelope; otherwise it is closer to the gas-phase value. Similarly, an SI-formed planet's atmospheric C/O depends on its solid-to-gas accretion ratio, which is not specified. The apparent narrow GI peak and broad SI gas-phase tail could therefore arise in part from the phase choice rather than from a genuine formation-mechanism difference. I request that Figure 10 be recomputed using a common observable (e.g., gas-phase C/O for both mechanisms, or a simple envelope-formation model that mixes gas and solids with an explicit accretion ratio), and that the conclusions be re-evaluated accordingly.
  2. [Section 2.3 and Discussion] The chemical model includes only freeze-out, thermal desorption, and photodesorption of four species, with no gas-phase or surface reactions. The authors correctly note in the Discussion that CO-to-CO2 conversion, methanol formation, and volatile trapping in ice mantles can substantially change C/O ratios. Since the paper makes a quantitative prediction (GI total C/O ≈0.3–0.6, SI gas-phase C/O ≈0–1.4), it is important to quantify how sensitive these ranges are to the missing chemistry. A simple post-processing test, such as converting a fraction of CO ice to CO2 in the relevant regions or adopting a methanol abundance, would show whether the GI/SI dichotomy survives. Without such a test, the claimed C/O fingerprints are statements about the simplified chemistry, not robust predictions of the physical disc.
  3. [Section 3.5 and Figure 9] The GI C/O distribution in Figure 10 is derived from all regions with Q_Toomre ≤ 1, but the actual GI clumps are under-resolved: the authors state that the clump lifetime is too short for differentiation because of insufficient numerical resolution, and that focused higher-resolution studies are needed. If GI planets form preferentially inside clumps, the material C/O in those clumps may differ from the surrounding Q ≤ 1 regions. The paper should either provide a resolution/convergence test demonstrating that the clump C/O is adequately captured, or justify why the disc-averaged total C/O in GI-unstable regions is representative of the material that ends up in a GI-formed planet.
minor comments (5)
  1. [Introduction, Section 1] There are several typos and grammatical slips: "the disc matter can be roughly divided into three component" should be "three components"; "annual structures" in Section 3.1 should be "annular structures"; "circumcise" in Section 3.1 should be "circumscribe"; "protorstar" in Section 3.4 should be "protostar"; "he most important" in Section 2.3 should be "the most important"; "drown dust" in Section 4 should be "grown dust"; "boader" in Section 3.3 should be "border"; "V ariations" in Section 3.3 should be "Variations"; "preset" in Section 3.3 should be "present"; "two-dimentional" in Section 3.5 should be "two-dimensional"; and "F ormation" in the References should be "Formation".
  2. [Figure 3 caption] The caption of Figure 3 reads "Same as Figure 3 but for model M2" but it should refer to Figure 2; please correct the cross-reference.
  3. [Section 3.3, Figure 4 caption] In the caption of Figure 4, "By the age of 490 yr" in the text should read "490 kyr"; the time unit is inconsistent with the rest of the paper.
  4. [Section 3.1] The sentence "The most prominent dust rings are located in the vicinity of the water snowline: the ring outside the primary snowline at 5 – 8 au (depending on the time) and the ring at 1 – 2 au, inside the primary snowline, which at later times also contains water ice and additional snowlines" is somewhat confusing because the second ring is first described as inside the primary snowline and then as containing water ice. Please rephrase for clarity.
  5. [Section 4, Figure 10] The observed exoplanet C/O data from Hoch et al. (2023) are plotted at arbitrary y-axis positions; the figure would be clearer if the data points were shown in a separate panel or with a legend explaining the arbitrary offset.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: simulated C/O values are emergent model outputs compared with independent exoplanet and cometary datasets.

full rationale

The paper's central C/O predictions are not fitted to the exoplanet data they are compared with. The model starts from protostellar ice abundances (Karin I. Öberg et al. 2011) and evolves gas, dust, and four volatiles through freeze-out, sublimation, advection, and dust dynamics; the resulting gas/ice/total C/O distributions are emergent outputs. The GI and SI regions are identified a priori using dynamical criteria (Toomre Q ≤ 1 and the Li & Youdin 2021 streaming-instability threshold), and the C/O values in those regions are then post-processed, not tuned to match Hoch et al. (2023). The comparison to observed exoplanet C/O uses published, independent data. Self-citations to Molyarova et al. (2021) and Vorobyov et al. (2024) supply the model machinery and the SI post-processing method; they are not uniqueness theorems and do not by themselves force the C/O dichotomy. The one weak citation, 'Molyarova et al., in prep', is used for the snowline accumulation mechanism, but the same mechanism is also attributed to the published Molyarova et al. (2021), and the C/O conclusions do not logically reduce to that citation. The choice to plot total C/O for GI and gas/ice C/O separately for SI is an interpretive assumption about how each formation mechanism incorporates matter; this affects the strength of the comparison but is not a reduction of the output to the input by construction. The dust-to-gas vs total C/O anticorrelation is explicitly acknowledged as a logical consequence of low-C/O ices being attached to dust, not presented as an independent empirical law. No equation reduces to another by definition, and no fitted parameter is renamed as a prediction.

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

The central result depends on several chosen model inputs: initial volatile abundances set the baseline C/O, viscosity and fragmentation parameters set the dust structure, and the chemistry is intentionally limited to phase transitions. No new physical entities are introduced. These choices are reasonable and mostly sourced from the literature, but they are not independently measured within the paper.

free parameters (5)
  • Initial volatile ice abundances = H2O 100, CO2 29, CO 29, CH4 5 relative to H2O; baseline C/O = 0.34
    Table 1. Adopted from protostellar ice observations by Karin I. Öberg et al. 2011, not derived in the paper. All C/O values and the GI/SI ranges scale with this choice.
  • Turbulent viscosity parameters = alpha_MRI = 1e-3, alpha_dz = 1e-5 (or 1e-1 above 1300 K), Sigma_MRI = 100 g cm^-2
    Section 2.1, Eq. (5). These control dead zone extent, snowline motion, and ring formation. Values are chosen from literature, not fitted to the target C/O results.
  • Fragmentation velocities = vfrag = 0.5 m/s for bare grains, 5 m/s for icy grains
    Section 2.2. Adopted from Okuzumi and Tazaki 2019. Controls dust growth and the dust rings that drive the C/O anticorrelation.
  • Interstellar UV field strength = Genv = 5.5 G0
    Section 2.3. Assumed elevated unattenuated UV field; sets photodesorption snowlines in the outer disc and affects the outer C/O distribution.
  • Initial ice-to-rock mass ratio = 0.08
    Section 2.3. Chosen so that ice mantles do not change the mass and radius of dust grains. This simplification changes the relative contribution of ices to the total C/O ratio.
assumptions (6)
  • domain assumption Thin-disc, vertically integrated approximation for gas and dust dynamics
    Section 2.1. All equations are 2D in the disc plane. The paper acknowledges that vertical settling and molecular-layer C/O gradients are not captured.
  • domain assumption Gas and dust temperatures are equal and set by the midplane temperature
    Section 2.1 and Eq. (4). Snowline positions and freeze-out rates depend on this equality.
  • domain assumption Chemistry is restricted to adsorption and thermal/photodesorption of four volatile species
    Section 2.3 and Discussion. No gas-phase or surface reactions, no methanol, no volatile trapping. The authors list these as limitations.
  • domain assumption Initial state has all ices on small grains and no gas-phase volatiles
    Section 2.3. The volatile evolution starts from this state, which sets the early C/O distribution.
  • domain assumption No late Bondi-Hoyle infall from the ambient medium
    Section 2.2. The authors note recent work on continuing infall but exclude it from these simulations, which could affect disc mass and C/O evolution.
  • domain assumption GI and SI criteria identify actual planet-forming regions
    Section 4 and Figure 9. Gravitational instability is identified by Q <= 1 and streaming instability by the Li and Youdin 2021 criterion. The C/O distributions for planet formation rely on these external criteria.

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Pith. "Pith review of C/O ratios in self-gravitating protoplanetary discs with dust evolution." pith.science (2026). https://pith.science/paper/HMCNA27M

@misc{pith2026241205099,
  author       = {Pith},
  title        = {Pith review of: C/O ratios in self-gravitating protoplanetary discs with dust evolution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HMCNA27M}},
  note         = {Machine review of arXiv:2412.05099}
}
abstract

Elemental abundances, particularly the C/O ratio, are seen as a way to connect the composition of planetary atmospheres with planet formation scenario and the disc chemical environment. We model the chemical composition of gas and ices in a self-gravitating disc on timescales of 0.5\,Myr since its formation to study the evolution of C/O ratio due to dust dynamics and growth, and phase transitions of the volatile species. We use the thin-disc hydrodynamic code FEOSAD, which includes disc self-gravity, thermal balance, dust evolution and turbulent diffusion, and treats dust as a dynamically different and evolving component interacting with the gas. It also describes freeze-out, sublimation and advection of four volatile species: H$_2$O, CO$_2$, CH$_4$ and CO. We demonstrate the effect of gas and dust substructures on the distribution of volatiles and C/O ratios, including the formation of multiple snowlines of one species, and point out the anticorrelation between dust-to-gas ratio and total C/O ratio emerging due to the contribution of oxygen-rich ice mantles. We identify time and spatial locations where two distinct trigger mechanisms for planet formation are operating and differentiate them by C/O ratio range: wide range of the C/O ratios of $0-1.4$ for streaming instability, and a much narrower range $0.3-0.6$ for gravitational instability (with the initial value of 0.34). This conclusion is corroborated by observations, showing that transiting exoplanets, which possibly experienced migration through a variety of disc conditions, have significantly larger spread of C/O in comparison with directly imaged exoplanets likely formed in gravitationally unstable outer disk regions. We show that the ice-phase C/O$\approx0.2-0.3$ between the CO, CO$_2$ and CH$_4$ snowlines corresponds to the composition of the Solar system comets, that represent primordial planetesimals.

Figures

Figures reproduced from arXiv: 2412.05099 by the authors.

Figure 1
Figure 1. Surface density of gas and grown dust, Toomre Q-parameter, maximum dust radius, temperature and viscous α-parameter in model M1 at selected time moments: 160 kyr, 80 × 80 au; 350 kyr, 35 × 35 au; 490 kyr, 9 × 9 au. The contours indicate the position of the water snowline. Note that at the panels with multiple water snowlines, water is frozen outside the outer line and inside an inner dust ring at 1 – 2 au. these fea… view at source ↗
Figure 1
Figure 1. Inside the primary water snowline, the values of [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Radial distribution of azimuthally averaged surface densities of the volatiles in the gas and in the ice at various time instances in M1 (Mcore = 0.66 M⊙). Pale lines indicate the total surface density of species. The upper panels show surface densities of gas, small dust and grown dust, and the midplane temperature. 10-3 10-2 10-1 100 101 102 103 104 101 102 103 gas grown dust small dust Σ, g cm-2 160 kyr Tmp, K 10… view at source ↗
Figures from the paper (8 more)
Figure 3
Figure 3. Figure 3: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]
Figure 4
Figure 4. Figure 4: Radial profiles of the C/O ratio at 490 kyr in models M1 (left) and M2 (right). The plots show C/O in total (black), in the gas (red), and in the ice (blue). The C/O ratio in the ice (gas) is only shown for radial distances where the mass of the volatiles in the ice (g…
Figure 5
Figure 5. Figure 5: Evolution of central source luminosity and C/O ratio in models M1 (Mcore = 0.66M⊙, left) and M2 (Mcore = 1M⊙, right). The upper panels show stellar and accretion luminosity depending on time. Below are, successively, total C/O ratio, C/O in the gas, and C/O in the ice,…
Figure 6
Figure 6. Figure 6: Distributions of C/O ratios and gas/dust surface densities. Model M1 160 kyr (upper left) and 300 kyr (upper right); model M2 250 kyr (lower left) and 490 kyr (lower right). Dotted lines mark the positions of the snowlines for H2O (dark purple), CO2 (magenta), CH4 (gre…
Figure 7
Figure 7. Figure 7: Averaged radial profiles of dust-to-gas ratio, the total C/O ratio, and CO2 and H2O in the gas and in the ice in model M2 at 490 kyr. The horizontal lines in the upper panel show the reference values for the C/O ratio (0.34) and dust-to-gas ratio (0.01) [PITH_FULL_IMA…
Figure 8
Figure 8. Figure 8: Dependence between total C/O ratio and dust-to-gas mass ratio in models M1 (upper panel) and M2 (lower panel). Three time instances are shown. The dashed line shows the fitted log-linear dependence for 490 kyr. shown in upper panels of [PITH_FULL_IMAGE:figures/full_fi…
Figure 9
Figure 9. Figure 9: The disc regions where the conditions for GI and SI are fulfilled in model M1. The regions and times where there is no instability are shaded in white. In the upper panel, the colour indicates the minimum value of QToomre at a given radius, if QToomre ≤ 1. In the lower…
Figure 10
Figure 10. Figure 10: Distribution of C/O ratios in the regions where gravitational and streaming instabilities are triggered. For GI, total C/O ratio is shown, for SI, the C/O ratios in the ice and in the gas. Black and grey points show the observed C/O ratios in two populations of exopla…

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.