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Atmospheric C/O Ratios of Sub-Neptunes with Magma Oceans: Homemade rather than Inherited

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Magma-ocean chemistry, not the protoplanetary disk, sets sub-Neptune C/O ratios.

desk verdict A genuinely new metal-carbon sink in a magma-ocean equilibrium model that can make sub-Neptune C/O ratios very low, but the vertical-transport step needed to connect deep C/O to transmission spectra is only shown to work under strong mixing. read the letter →

arxiv 2504.20450 v2 pith:Q653IWBE submitted 2025-04-29 astro-ph.EP

Aaron Werlen , Caroline Dorn , Hilke E. Schlichting , Simon L. Grimm , Edward D. Young This is my paper · ORCID
classification astro-ph.EP
keywords sub-NeptunesC/Oratiomagmaoceanchemicalequilibriumcarbonsequestrationexoplanetatmospheresmetal-silicatepartitioningJWST
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 argues that the atmospheric carbon-to-oxygen ratio (C/O) of a sub-Neptune is not a fossil of where the planet formed in the protoplanetary disk. Instead, it is set by chemical equilibrium between the hydrogen-dominated atmosphere and the molten rock and metal deep inside the planet. Using a global chemical equilibrium calculation across gas, silicate, and metal phases, the authors show that the resulting C/O can range from orders of magnitude below solar to a few times solar depending on planet mass, atmospheric mass fraction, and temperature. A key new ingredient is carbon partitioning into iron metal, which can sequester much of the carbon and drive atmospheric C/O far below the disk value, especially for small envelopes. If right, this means JWST C/O measurements can probe the interior chemistry of sub-Neptunes rather than their formation location.

What carries the argument

The central object is the global chemical equilibrium framework: a set of linearly independent chemical reactions among 26 species distributed across three phases, iron metal, silicate melt, and gas, solved with Gibbs free-energy equilibrium conditions, phase mass-balance, and elemental conservation. The paper's extension adds a carbon partitioning reaction between metal and silicate, $\mathrm{C_{metal}} + \mathrm{O_{metal}} \rightleftharpoons \mathrm{CO_{silicate}}$, letting carbon be drawn out of the atmosphere into the metal phase. The same equilibrium framework is then coupled to one-dimensional atmosphere models with photochemistry and vertical mixing to check how the deep composition is transmitted to observable pressures.

What would settle it

Measure atmospheric C/O in several sub-Neptunes spanning at least a factor of a few in inferred atmospheric mass fraction from bulk density and compare with the predicted monotonic rise of C/O with envelope mass fraction; seeing no such correlation, or finding C/O values that track the planet's likely formation radius instead of its interior state, would falsify the equilibrium-driven picture.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the atmospheric C/O ratio in sub-Neptunes emerges from the chemical exchange between the atmosphere and the underlying magma ocean rather than being inherited from the protoplanetary disk. The authors compute global chemical equilibrium among gas, silicate melt, and iron metal, including a new reaction that lets carbon partition from silicate into metal. Across a grid of 2 to 10 Earth-mass planets with atmospheric mass fractions of 0.1 to 10 percent, they find atmospheric C/O spans several orders of magnitude below solar to a few times solar, with carbon sequestration into the metal phase producing large depletions at low atmospheric mass fractions. They further show, with coupled one-dimensional radiative-convective and photochemical models, that the deep-equilibrium C/O is largely preserved in the observable atmosphere under strong vertical mixing, so a measured C/O far below the host star's value would indicate that iron metal in the magma ocean has locked away a large fraction of the carbon.

Load-bearing premise

The whole result rests on the assumption that the atmosphere, magma ocean, and metal phase stay in full chemical equilibrium long enough to re-set the envelope's composition; if gas transport or a solidifying interior shut that exchange down, the atmosphere could keep a disk-inherited C/O fingerprint.

Editorial extensions

If this is right

  • Observed sub-Neptune C/O ratios, especially values far below the host star's, should be read as diagnostics of interior conditions rather than formation location.
  • Planets with small atmospheric mass fractions and low masses are the most likely to show strongly sub-stellar C/O, because most of the carbon is sequestered into the metal phase.
  • Under strong vertical mixing the deep C/O is preserved at observable pressures, so transmission and emission spectroscopy can both probe the interior, whereas under weak mixing the C/O varies with altitude and transmission measurements would sample a different value than the deep one.
  • If carbon is excluded from the metal phase, atmospheric C/O stays close to the initial disk value, so the metal phase is the main agent that decouples atmospheric composition from the disk.
  • Atmospheric retrievals that impose disk-based C/O priors may be biased for sub-Neptunes with magma oceans.

Reading between the lines

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

  • If the equilibrium assumption holds, the scatter in observed sub-Neptune C/O ratios could be mapped onto a scatter in interior metal content or thermal state, turning atmospheric retrievals into a crude tomographic probe of the planet's deep interior.
  • The metal-phase carbon sink suggests that a sub-Neptune with a larger iron core fraction would show a lower atmospheric C/O for the same envelope mass, a correlation that could be tested with planets of known mass-radius composition.
  • The strong sensitivity to silicate-metal equilibrium temperature implies that C/O measurements might also constrain the depth at which metal-silicate equilibration occurred, placing a constraint on the thermal state of the magma ocean during the era when the atmosphere formed.
  • A direct test for a sample of sub-Neptunes spanning a range of masses and atmospheric mass fractions inferred from bulk density is that the model predicts a monotonic increase of C/O with atmospheric mass fraction; if observations instead show no such trend, the assumption of global equilibrium would need to be revisited.
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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 / 6 minor

Summary. The paper investigates whether the atmospheric C/O ratios of sub-Neptunes are set by formation (inherited from the protoplanetary disk) or by chemical equilibrium between the atmosphere and an underlying magma ocean. The authors use the global chemical equilibrium framework of Schlichting & Young (2022), extended with an explicit metal–silicate reaction for carbon partitioning (reaction 1), to compute bulk atmospheric C/O ratios across a grid of planetary masses, atmospheric mass fractions, and two thermal states. They find that including carbon in the metal phase strongly lowers the atmospheric C/O ratio at low atmospheric mass fractions, while excluding it yields nearly constant, often super-solar C/O. They then couple one representative 6 M_Earth case to 1D atmospheric models (HELIOS, FastChem, VULCAN, HELIOS-K) with photochemistry and two vertical mixing strengths, finding that the C/O ratio is altitude-independent for K_zz = 10^7 cm2/s but varies significantly for K_zz = 10^4 cm2/s. The paper concludes that atmospheric C/O is 'homemade rather than inherited' and that observed low C/O ratios imply iron metal in the magma ocean has sequestered carbon.

Significance. If the central claim holds, the paper would change how observed sub-Neptune C/O ratios are interpreted: they would report on interior conditions and magma-ocean chemistry rather than formation location. This is a timely and relevant contribution given JWST transmission spectra of sub-Neptunes such as TOI-270d. The paper's strengths are its internally consistent equilibrium network, the inclusion of a physically motivated carbon metal-silicate exchange reaction, and sensitivity tests over carbon partitioning fits and silicate-metal equilibrium temperature. The coupling to 1D atmospheric models with photochemistry is also valuable. The main significance, however, is conditional on the vertical transport step, because the observable atmosphere may not preserve the deep equilibrium C/O ratio under realistic mixing conditions.

major comments (3)
  1. [§3.3 and Figure 4] The conclusion in §5 that 'the deep C/O ratio is largely preserved in the observable atmosphere' is not supported by the low-Kzz case shown in Figure 4. In the low-mixing scenario, gravitational settling and photochemistry deplete CO, CO2, CH4, and H2O above about 10^-2 bar, and the C/O ratio in the transmission region (10^-3 to 10^-5 bar) deviates from the deep equilibrium value. Since the TOI-270d C/O measurement cited in §1 is from transmission spectroscopy and no constraint on Kzz is provided, the inference that a low observed C/O implies iron metal carbon sequestration is not supported. The authors should either demonstrate preservation at realistic Kzz values, provide constraints on Kzz from the models, or present the interior-probe conclusion as explicitly conditional on strong vertical mixing.
  2. [§2.5 and Figure 1] The conclusion that atmospheric C/O is 'not inherited from the protoplanetary disk' is not supported by the model as presented, because the initial envelope C/O is fixed to the solar value and not varied. In global chemical equilibrium, the final atmospheric C/O depends on the total planetary C/O inventory (core plus envelope), so a different disk C/O would shift the results. Moreover, Figure 1 shows that at high atmospheric mass fractions the atmospheric C/O approaches the initial disk value, which is the inherited regime. The authors should qualify the conclusion to state that magma ocean interactions can strongly modify a solar-composition envelope at low atmospheric mass fractions, rather than claiming inheritance is erased, and ideally test sensitivity to the initial envelope C/O.
  3. [Equations (2)–(4) and §5] The central claim assumes global chemical equilibrium across the metal, silicate, and gas phases on timescales shorter than atmospheric evolution, but no timescale or kinetic argument is presented. If the magma ocean solidifies or transport timescales prevent re-equilibration, the atmospheric C/O could retain a disk-inherited fingerprint. The paper's conditional 'if there is a magma ocean' is acknowledged in places, but §5 states the 'not inherited' conclusion without that caveat. The authors should add a discussion of the relevant equilibration timescales and clearly state the conditions under which the homemade scenario applies.
minor comments (6)
  1. [§3.3] The statement 'As CH4 overtakes CO as the main carbon carrier, the C/O ratio rises slightly at high altitudes' appears to contradict the earlier statement that the C/O ratio decreases above ~10^-2 bar in the low-mixing case; please clarify the vertical profile.
  2. [§2.4 and Figure 1 caption] There are minor grammar issues: 'a AMOI' should be 'an AMOI', and 'a atmosphere' should be 'an atmosphere'.
  3. [§2.1, Eq. (2)] Please specify that the pressure term is included only for gas-phase species, so that the summation notation is unambiguous.
  4. [§2.2] The absence of pressure corrections to the Gibbs free energies, especially for reaction (1), is a potential source of uncertainty in the carbon partitioning results; the sensitivity tests in Appendix A do not cover this assumption.
  5. [§4] The phrase 'SiH4 reduces the atmosphere' is unclear; please specify whether it reduces the atmospheric mass, metallicity, or something else.
  6. [§2.4] The atmospheric models do not include helium; this may affect the mean molecular weight and hence gravitational settling in the 1D calculations, and a brief justification or caveat would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the C/O outputs are computed from an explicit equilibrium network with externally anchored partitioning, not fitted to the C/O values being interpreted.

full rationale

The atmospheric C/O ratios are obtained by solving the global chemical equilibrium conditions (Eqs. 2-4) with stated initial elemental abundances and thermodynamic data; no C/O value is fitted to the observed C/O ratios discussed in the introduction. The carbon-in-metal reaction is anchored to independent experimental partitioning data (Blanchard et al. 2022), and the no-metal comparison isolates its effect rather than assuming the conclusion. The Schlichting & Young (2022) and Young et al. (2023) work supplies the modeling framework and initial compositions, but the paper's central claim is not a restatement of those citations: it is a conditional model prediction that if atmosphere and magma ocean reach equilibrium, the atmospheric C/O is set by that equilibrium. This conditional is an assumption with external thermodynamic content, not a tautology. The paper's own low-Kzz results (Fig. 4) show that the transmission-region C/O can diverge from the deep equilibrium value, making the Section 5 statement that the deep C/O is 'largely preserved' stronger than the low-mixing case supports; this is a robustness limitation, not a circular reduction of the derivation. No self-definitional, fitted-input, uniqueness-imported, ansatz-smuggling, or renaming circularity was found.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central computation rests on a global equilibrium model whose inputs are mostly prior thermodynamic data and experimental partition coefficients. The main author-chosen controls are the initial carbon content in metal, the thermal states (AMOI and SME temperatures), the initial envelope composition, and the vertical mixing coefficient in the coupled case. No new physical entities are introduced.

free parameters (4)
  • Initial metal carbon content = 6.5 mol% C in metal (0.5 wt% core carbon)
    Chosen to represent reactive carbon in the core; sets the core C/O of 0.02 and controls how much carbon can be sequestered into metal, the main driver of atmospheric C/O depression in Figure 1.
  • Initial envelope composition = 99.9% H2, 0.1% CO2 (solar C/O = 0.5)
    Sets the disk-inherited baseline C/O; the headline result is framed as a departure from this input.
  • AMOI and SME temperatures = 3000 K / 3500 K and 4000 K / 4500 K
    Two thermal states bracket the hot magma ocean; SME temperature changes atmospheric C/O by up to two orders of magnitude (Figure 6), so quantitative results are sensitive to this grid input.
  • Vertical mixing coefficient Kzz = 10^4 and 10^7 cm2/s
    Two scenarios for the single coupled 1D atmospheric model; determines whether the observable C/O matches the deep equilibrium value.
assumptions (6)
  • domain assumption Global chemical equilibrium is reached among metal, silicate, and gas phases.
    Section 2.1 solves Equations (2)-(4) with all phases equilibrated; if kinetics or transport prevent this, the atmospheric C/O would not be set by the magma ocean.
  • domain assumption Ideal mixing in all phases except Si and O in metal.
    Section 2.2 states ideal mixing is assumed, simplifying activity coefficients to mole fractions.
  • domain assumption Pressure corrections to Gibbs free energies of silicate and metal species are negligible.
    Section 2.2 follows Schlichting and Young (2022) in omitting pressure corrections; the authors note this needs more robust assessment.
  • domain assumption Carbon partitioning data from Blanchard et al. (2022) apply at sub-Neptune metal-silicate conditions.
    Section 2.3 adopts this experimental fit over Fischer et al. (2020) and Grewal et al. (2019); the resulting carbon sink strength depends on this choice.
  • domain assumption CH4 dissolution into silicate melt is negligible.
    The discussion states CH4 is not included as a silicate species and cites low solubilities; this removes a potential additional carbon sink.
  • domain assumption Standard-state Gibbs free energies of formation from Schlichting and Young (2022) are accurate.
    Section 2.2 relies on the internally consistent thermodynamic dataset; uncertainties are not propagated.

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Cite this review

Pith. "Pith review of Atmospheric C/O Ratios of Sub-Neptunes with Magma Oceans: Homemade rather than Inherited." pith.science (2026). https://pith.science/paper/Q653IWBE

@misc{pith2026250420450,
  author       = {Pith},
  title        = {Pith review of: Atmospheric C/O Ratios of Sub-Neptunes with Magma Oceans: Homemade rather than Inherited},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q653IWBE}},
  note         = {Machine review of arXiv:2504.20450}
}
abstract

Recently, the James Webb Space Telescope has enabled detailed spectroscopic characterization of sub-Neptune atmospheres. With detections of carbon- and oxygen-bearing species such as CO, CO$_2$, CH$_4$, and H$_2$O, a central question is whether the atmospheric C/O ratio, commonly used to trace formation location in giant planets, can serve a similar diagnostic role for sub-Neptunes. We use the global chemical equilibrium framework of Schlichting & Young (2022) to quantify how magma ocean-atmosphere interactions affect the atmospheric C/O ratio. We find that the resulting C/O ratios range from several orders of magnitude below solar to a few times solar. The atmospheric C/O ratio in sub-Neptunes is therefore not inherited from the protoplanetary disk, but instead emerges from chemical equilibrium between the atmosphere and the underlying magma ocean. Planetary mass, atmospheric mass fraction, and thermal state all strongly influence the atmospheric C/O ratio. In addition, carbon partitioning into the metal phase typically reduces the atmospheric C/O ratio substantially, particularly for atmospheric mass fractions less than a few percent. Finally, we couple the deep equilibrium compositions to 1D atmospheric models that self-consistently solve for the pressure-temperature structure and chemical composition, including photochemistry. We find that the C/O ratio varies with altitude under low vertical mixing conditions (K$_\text{zz}=10^4$ cm$^2$s$^{-1}$), but remains constant under strong mixing (K$_\text{zz}=10^7$ cm$^2$s$^{-1}$). Our results imply that observed C/O ratios of sub-Neptunes can be used to probe their interiors. Specifically, C/O ratios much lower than host star values would imply an underlying magma ocean with iron metal having sequestered significant amounts of carbon.

Figures

Figures reproduced from arXiv: 2504.20450 by the authors.

Figure 1
Figure 1. Molar bulk atmospheric C/O ratio as a function of atmospheric mass fraction. Dashed lines show results from the reaction network that includes carbon in the metal phase; dotted lines show results from the network excluding carbon in the metal phase. The horizontal dashed lines indicate the initial C/O ratios of the disk and the core. The core C/O ratio is calculated from the initial conditions for the case with C me… view at source ↗
Figure 2
Figure 2. Molar bulk atmospheric C/O ratio as a function of resulting atmospheric metal mass fraction, Zatm, for all models that include carbon in the metallic phase (from [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Molar bulk atmospheric C/O ratio as a function of species mixing ratios for the 3000K atmosphere–magma ocean interface (AMOI) temperature models with carbon in the metallic phase, from [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: shows the atmospheric structure of a 6 M⊕ planet selected from the 3000 K AMOI temperature case shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Molar bulk atmospheric C/O ratio as a func￾tion of atmospheric mass fraction. A 6 M⊕ planet with an AMOI temperature of 3000 K and an SME temperature of 3500 K is shown. The orange dashed line reproduces the default case from [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Forward citations

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.