Volatile-bearing mineral atmospheres of hot rocky exoplanets as probes of interior state and composition

Brice-Olivier Demory; Dan J. Bower; Fabian L. Seidler; Paolo A. Sossi

REVIEW 3 major objections 6 minor 122 references

Volatile-bearing mineral atmospheres of hot rocky exoplanets as probes of interior state and composition

T0 review · 3 major / 6 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A magma ocean's oxygen fugacity, not its volatile budget, is the major control on the spectra of hot rocky exoplanets, with the SO2 8–9 µm feature as the most robust tracer of redox state.

desk verdict A genuinely self-consistent coupled magma-ocean/atmosphere model that makes a strong qualitative case for fO2 as the main spectral knob, but the quantitative 55 Cnc e exclusion of oxidized VIBSE rests on an unvalidated ~1200 K extrapolation of the S2 solubility law. read the letter →

arxiv 2509.13610 v2 pith:BWA4AYSF submitted 2025-09-17 astro-ph.EP

Fabian L. Seidler , Paolo A. Sossi , Dan J. Bower , Brice-Olivier Demory This is my paper

classification astro-ph.EP

keywords hotrockyexoplanetsmagmaoceanoxygenfugacitySO2emissionspectratransmission55Cancrieatmosphere-interiorcoupling

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 redox state of a hot rocky exoplanet's magma ocean—measured as oxygen fugacity (fO2)—shapes the planet's atmospheric spectrum far more than its total volatile abundance or elemental composition. The authors build a coupled atmosphere-interior model that lets a molten silicate surface equilibrate with an overlying gas mixture, then computes emission and transmission spectra across a wide grid of fO2, volatile mass fraction, and metallicity. They find that the SO2 feature near 8–9 µm is the most sensitive spectral marker of fO2, and that the relative strengths of H2O and CO2 features can distinguish outgassed from accreted atmospheres. Applying the model to existing observations of 55 Cancri e, they conclude that neither a scaled-up Earth-like oxidised atmosphere nor a captured hydrogen-rich primordial atmosphere fits the MIRI data; future observations beyond 8 µm are key to breaking the remaining degeneracies.

What carries the argument

The key machinery is a coupled atmosphere-interior equilibrium model that imposes chemical equilibrium between a fully molten magma ocean and the gas at their interface. The oxygen fugacity of the melt, expressed relative to the iron-wüstite buffer (ΔIW), is treated as an independent variable that sets the fugacities of mineral gases (SiO, Mg, Fe) and, together with solubility laws, controls the partitioning of volatiles (H, C, N, S) between melt and atmosphere. The resulting gas composition feeds a 1D radiative-transfer model that computes the pressure–temperature structure and synthetic emission and transmission spectra, including wavelength-dependent planetary radius.

What would settle it

Measure the 8–9 µm emission spectrum of a hot rocky exoplanet whose bulk density and irradiation independently require an oxidised magma ocean near ΔIW+3; if the SO2 absorption feature is absent, the claimed fO2 tracer is not robust.

Watch

Extended reading notes

Core claim

The central claim is that the oxygen fugacity of the magma ocean, not the volatile mass fraction or metallicity, is the dominant variable controlling the shape of emission and transmission spectra of hot rocky exoplanets. In particular, the SO2 absorption feature at 8–9 µm appears most prominently near ΔIW+3 and weakens at both higher and lower fO2, making it a robust but non-monotonic tracer of redox state. The model also shows that high-fO2, carbon- and sulfur-rich atmospheres produce strong CO2 and SO2 absorption, while low-fO2, mineral-rich atmospheres generate SiO-driven thermal inversions and emission features. For 55 Cancri e, the MIRI spectrum disfavours oxidised Earth-like and reduc

Load-bearing premise

The atmosphere's gas composition is set by chemical equilibrium with the magma ocean at their interface; if escape, photochemistry, or a solid crust prevents this equilibrium, the spectrum no longer reflects the interior's redox state.

Editorial extensions

If this is right

Observers can use the SO2 8–9 µm feature to infer the redox state of a magma ocean, with the strongest signal near ΔIW+3.
The relative intensities of H2O and CO2 features can distinguish atmospheres outgassed from the interior from those accreted from a nebula.
Mass–radius measurements alone are degenerate in fO2, volatile mass, and metallicity; spectra are required to break this degeneracy.
Existing MIRI data for 55 Cancri e rule out both an oxidised Earth-like atmosphere and a reduced primordial (solar-composition) atmosphere.
Future MIRI medium-resolution observations at wavelengths beyond 8 µm can distinguish the remaining candidate scenarios for 55 Cancri e.

Reading between the lines

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

If fO2 is the master variable, then spectral classification of hot rocky exoplanets should be organized by redox state rather than by presumed bulk composition; planets with similar spectra could have very different volatile histories.
Because the SO2 feature is non-monotonic in fO2, a single-band detection may be ambiguous; combining it with SO and OH features in the UVIS could break the degeneracy.
The model's equilibrium assumption implies that the proposed tracer fails if a solid crust, photochemical escape, or atmospheric dynamics decouples the gas from the magma ocean—time-variable spectral observations could test this directly.

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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

The thing to know about this paper is that it does the coupling right: volatile partitioning between a fully molten magma ocean and the atmosphere is solved together with mineral-gas evaporation and full radiative transfer, on a systematic fO2–volatile mass–metallicity grid. That is a real step beyond earlier work that injected pre-formed silicate vapour into a volatile background. The central qualitative result, that oxygen fugacity is the main control on emission and transmission spectral shape and that SO2 near 8–9 µm is the best single fO2 tracer, is well supported by the internal logic of the model and is consistent with prior work. The paper is also honest: it lists the ideal-gas breakdown, incomplete opacity tables, solubility-law extrapolation, and missing clouds in Sec. 4.3, and it ships the grid as figures even where the conclusions are load-bearing.

The soft spots are real but mostly correctable. The stress-test concern about the S2 solubility law is on target: Boulliung & Wood is calibrated at 1473–1773 K and the model runs at T_MAI ~3000 K, a ~1200 K extrapolation. The paper acknowledges this, but it does not quantify how the location and strength of the pSO2 maximum would shift under a different solubility law, even though the MIRI-based exclusion of oxidised VIBSE scenarios for 55 Cnc e depends on the absence of a strong SO2 feature. So I would call the qualitative ranking robust and the specific quantitative exclusion conditional. Second, the NIRCam fits use a per-visit vertical offset as a free parameter, which the paper itself notes loses baseline information; the visits also conflict with each other and with the MIRI/radius constraints. That is a fair summary, not a hidden flaw. Third, the code and data are promised on github/zenodo only upon acceptance. Given that the whole point is a reproducible forward model, that is a reasonable reviewer request.

The biggest unresolved question is whether the ideal-gas and opacity-table extrapolations bias the absolute flux levels enough to change which grid points fit 55 Cnc e. The model’s internal consistency and the explicit caveats mean this is a paper for a serious referee, but I would want the authors to add a sensitivity test on the sulfur solubility law before publication. As an editor, I would send it out. As a colleague, I’d cite it for the coupled framework and the fO2 diagnostic concept, while being careful not to over-read the 55 Cnc e constraints until the solubility issue is quantified.

Referee Report

3 major / 6 minor

Summary. The manuscript presents a coupled magma-ocean/atmosphere model for hot rocky exoplanets (HREs) with fully molten mantles. The atmosphere-interior equilibrium code Atmodeller computes gas speciation at the magma-ocean-atmosphere interface from the system Si-Mg-Fe-O-C-H-S-N-He, combining mineral vapor fugacities with volatile solubility laws; the radiative transfer pipeline phaethon (HELIOS + FastChem COND + petitRADTRANS) then computes self-consistent P-T structures and emission/transmission spectra. The model is applied to a fiducial 8 Earth-mass, 55 Cnc e-like planet across a grid spanning oxygen fugacity (ΔIW from -6 to +6), volatile mass fraction (log fVMF from -1 to 1 relative to Earth), and metallicity mixing between solar and VIBSE compositions (z=0 to 1). The central result is that oxygen fugacity is the dominant control on spectral shape, with the SO2 8–9 μm absorption feature identified as the most robust tracer of fO2, peaking near ΔIW+3; CO2 and H2O are ubiquitous and less diagnostic. Applying the grid to JWST MIRI observations of 55 Cnc e, the authors argue that oxidized VIBSE-like and reduced primordial (SOLAR) atmospheres are disfavored, while intermediate or low-z/reduced scenarios remain viable. NIRCam data are found to be internally inconsistent and inconclusive. The paper also uses mass-radius relations to argue that most HREs require modest atmospheres of mixed heritage, with TOI-1408 c as a rare inflated case.

Significance. If the central claim holds, the paper provides a practical roadmap for using mid-infrared spectra to infer the redox state of magma oceans on hot rocky exoplanets, thereby linking an observable (emission/transmission spectra) to an inaccessible interior property (fO2). This would be a valuable contribution to the interpretation of current and upcoming JWST observations. The model's strengths include its self-consistent treatment of mineral-vapor fugacities and volatile partitioning (avoiding the a posteriori closure criticized in earlier work), the use of external thermodynamic and opacity data rather than circular retrieval inputs, explicit listing of caveats (ideal-gas breakdown, incomplete line lists, solubility-law extrapolation, no clouds), and concrete, falsifiable predictions for MIRI MRS observations. The code and data products are promised on GitHub/Zenodo upon acceptance, which will aid reproducibility. The main risk to the quantitative conclusions is the large extrapolation of the S2 solubility law to 3000 K, which directly affects the predicted strength and location of the SO2 fO2-tracer feature and hence the 55 Cnc e interpretation.

major comments (3)

[Sec 3.3.1 / Sec 4.3(2) / Table A.1] The central diagnostic claim—that the 8–9 μm SO2 feature is the most robust fO2 tracer and that its maximum near ΔIW+3 constrains the 55 Cnc e MIRI data—rests on the S2 solubility law of Boulliung & Wood (2022, 2023), calibrated over 1473–1773 K for basaltic/andesitic melts. The model grid is evaluated at T_MAI = 3000 K (Fig. 2) and the fiducial 55 Cnc e model reaches T_MAI ≈ 3000 K (Sec. 3.1). This is a ~1200 K extrapolation, acknowledged in Sec. 4.3 point 2 but not quantified. If the true solubility of S2 at 3000 K differs from the Henry/Sieverts extrapolation (e.g., due to temperature-dependent sulfide capacity or FeO content), the pSO2 peak could shift in both amplitude and ΔIW, directly changing the exclusion of oxidized VIBSE scenarios in Sec. 4.2.1. I request a sensitivity test (e.g., varying the solubility parameters within plausible bounds, or comparing with an alternative sulfi
[Sec 4.3(1) / Table C.1] The opacity tables for SO2 (ExoAmes) extend only to 1900 K, while the bottom-of-atmosphere temperatures in many models exceed this (up to ~3000 K). The authors note in Sec. 4.3 that 'SO2 ... only extends up to 1900 K' but do not state the impact on the 8–9 μm feature if part of the line-forming region lies above 1900 K. Even if the photosphere is generally cooler, high-T layers could contribute to the feature wings, and the correlated-k tables are truncated. A brief analysis of where the SO2 feature forms (contribution-function peak temperature) would clarify whether this is a quantitative or only a minor limitation.
[Sec 4.2.1 / Fig. 10] The conclusion that the MIRI observation 'preclude[s] oxidised VIBSE-scenarios' is based on a ~2σ discrepancy between the predicted and observed flux in the SO2 band segment. Given the discrete model grid, the unknown vertical offset in the NIRCam data, and the S2 solubility extrapolation discussed above, the significance of this exclusion is uncertain. I recommend presenting the χ2 differences with a more explicit treatment of model uncertainty (e.g., including the effect of the S2 solubility uncertainty on the predicted spectra) and softening 'preclude' to 'disfavour' unless robustness is demonstrated.

minor comments (6)

[Sec 4.3(1)] The text states that H2O opacity extends only up to 2900 K, but Table C.1 lists H2O (POKAZATEL) valid up to 8900 K. Please reconcile this inconsistency.
[Fig. 2] The partial-pressure curves in Fig. 2 are not individually labeled in the figure; the caption refers to 'gas species' but the reader cannot distinguish e.g. SO2 from H2O without reference to the text. Adding a legend or labels would improve readability.
[Eq. (12)] The scaled density ρs is defined using ρ'_Earth(Mp), but it is not immediately clear whether this is the uncompressed or compressed Earth density at the same mass. Please state the reference density model explicitly in the text.
[Sec 4.1] There is an apparent typo in the age range '3.800.66-0.79 Gyr' for HD 213885 b; the formatting is broken. Please fix.
[Code and Data availability] The statement 'Repo available upon acceptance' and 'Upload to zenodo upon acceptance' means the reproducibility artifacts are not currently accessible to the referee. Please provide a permanent DOI or at least a preprint-accessible repository link in the final version.
[Sec 3.3.1] The statement that 'distinguishing between redox states based on the SO2 feature alone may be challenging because a ΔIW+6 atmosphere is ostensibly similar in the SO2-bands to one formed at ΔIW+1.5' is useful but seems to weaken the 'most robust tracer' claim. Consider rephrasing to clarify that the tracer is robust for distinguishing reducing from oxidizing states, not for finely resolving ΔIW within +1.5 to +6.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: forward model from external thermodynamics; SO2 fO2 tracer is a model output, not a fitted input.

full rationale

The paper's derivation chain is a forward modeling pipeline: Atmodeller computes equilibrium gas speciation from imposed fO2, volatile mass fraction, metallicity, and external thermodynamic data (solubility laws from Boulliung & Wood 2022/2023, Sossi et al. 2023, etc.); phaethon/HELIOS/petitRADTRANS then compute P-T structure and spectra from these compositions and external opacity tables. The central claim that fO2 controls spectral shape, and that the SO2 8-um feature is a robust fO2 tracer, is a model output rather than an input: the grid varies fO2 and records spectral changes, and the SO2 feature location/strength is not used to define fO2 or to fit any parameter. The only fitted quantities are nuisance offsets in the NIRCam light curves (Sec. 4.2.2), explicitly treated as free parameters for shape fitting, not as predictions. Citations to the authors' own codes (Atmodeller, phaethon) and prior fugacity relations (Seidler et al. 2024 Eq. 8) are references to public, independently usable tools and standard thermodynamic identities; they do not smuggle in the result. The manuscript's acknowledged limitations—extrapolation of S2 solubility laws to ~3000 K and SO2 opacity to 1900 K (Sec. 4.3)—are validity/correctness concerns about external input data, not circularity, because the model does not redefine those inputs in terms of the spectral features it predicts. No fitted parameter is renamed as a prediction, and no self-citation chain forces the conclusion.

Assumptions & free parameters 5 free parameters · 8 assumptions · 0 invented entities

The central result is a forward model with three varied physical parameters (fO2, z, fVMF) and a grid of temperatures; none of these are derived from the target observable. The model leans on experimentally calibrated solubility laws and opacity tables, which are external benchmarks, but several are extrapolated beyond their calibration range. No new physical entities are postulated.

free parameters (5)

Delta IW (oxygen fugacity relative to iron-wustite buffer) = -6 (best fit for 55 Cnc e MIRI; grid -6 to +6)
Independent variable controlling redox equilibrium; varied across grid and fitted to observations.
z (metallicity mixing fraction between SOLAR and VIBSE) = 0.5 (best fit for 55 Cnc e MIRI; grid 0 to 1)
Mixes volatile element ratios; set by assumed accretion heritage.
log fVMF (log10 volatile mass fraction relative to Earth) = 0 (best fit for 55 Cnc e MIRI; grid -1 to 1)
Determines total volatile inventory and atmospheric mass.
T_irr (irradiation temperature) = 2500 K for 55 Cnc e; grid 1000-2500 K
Sets energy input and day-side temperature of atmosphere.
NIRCam vertical offset Phi (average eclipse depth) = Fitted per visit (e.g., 116 ppm, 31 ppm)
Free nuisance parameter in chi-square fits because white-light curves are autocorrelated.

assumptions (8)

domain assumption Melt and gas are in chemical equilibrium at the magma ocean-atmosphere interface
Sec 2.1.1 states this as the fundamental assumption; if false, the atmospheric composition is not tied to magma fO2.
domain assumption Mantle is fully molten (x_melt=1) and of bulk silicate Earth composition
Sec 2.1.1 fixes BSE melt composition and x_melt=1; different mantle compositions change mineral gas fugacities.
domain assumption Ideal gas equation of state for all gas species
Sec 2.1.1 and 4.3.3; violated in atmospheres above ~1000 bar, which appear in high-fVMF models.
domain assumption Solubility laws calibrated at lower temperatures and basaltic compositions apply at magma ocean conditions
Sec 4.3.2; only H2O measured up to ~2173 K, most others below 1800 K, while T_MAI can approach 3000 K.
domain assumption Elemental abundances are constant with altitude (infinitely well mixed)
Sec 2.1.2 step 4; ignores diffusive separation, which could alter upper atmosphere composition.
domain assumption Opacity tables for key absorbers are valid at the temperatures and pressures modeled
Sec 4.3.1: SO2 opacity only up to 1900 K and H2O up to 2900 K, both below 3000 K MAI; C2H2 omitted due to missing UV line lists.
domain assumption Mantle acts as an infinite reservoir of oxygen, fixing fO2; O2 and mineral gas masses are not conserved
Sec 2.1.1 imposes fO2 as independent variable; valid only while melt reservoir is much larger than atmosphere.
domain assumption No internal heat sources, zero bond albedo, and heat redistribution factor f=2/3
Sec 2.1.2; albedo and f affect day-side energy budget, though the paper argues f does not change observable quantities.

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Cite this review

Pith. "Pith review of Volatile-bearing mineral atmospheres of hot rocky exoplanets as probes of interior state and composition." pith.science (2026). https://pith.science/paper/BWA4AYSF

@misc{pith2026250913610,
  author       = {Pith},
  title        = {Pith review of: Volatile-bearing mineral atmospheres of hot rocky exoplanets as probes of interior state and composition},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BWA4AYSF}},
  note         = {Machine review of arXiv:2509.13610}
}

abstract

The atmospheres of hot rocky exoplanets (HREs), should they persist, are products of interactions with underlying magma oceans. Spectra collected by the James Webb Space Telescope (JWST) hint at a CO/CO$_2$-rich atmosphere on the HRE 55 Cancri e, indicative of such a process. Here, we aim to identify diagnostic features that can be used to infer the composition and geochemical state of HREs. We construct a coupled atmosphere-interior model that computes the equilibrium gas speciation in the atmosphere in the system Si-Mg-Fe-O-C-H-S-N-He. The model accounts for both the equilibrium vaporisation of mineral gases and the partitioning of volatile species between the magma ocean and atmosphere. Using a fiducial planet with the properties of 55 Cancri e, we explore a parameter space that spans volatile mass fractions from 0.1 to 10 times that of the Earth, solar- to Earth-like metallicities, and 12 orders of magnitude in oxygen fugacity fO$_2$. We find fO$_2$ to be the major control of the shape of emission and transmission features. The presence of species such as SO$_2$ and the relative intensities of H$_2$O and CO$_2$ features allow to distinguish the origin of the gas, accreted or outgassed, while the atmospheric mass is more challenging to constrain. Inflated HREs, whose densities are compatible with a nebular atmosphere are rare, but a viable explanation for the planet TOI-1408 c. The majority of HREs, including 55 Cancri e, are too dense to be dominated by H$_2$-rich nebular gas yet too puffy for an Earth-like volatile budget, implying modest atmospheres of mixed heritage that are degenerate in fO$_2$, volatile mass and composition. The MIRI observation of 55 Cancri e disfavours oxidised Earth-like and reduced primoridal atmospheres alike, while the NIRCam data remain inconclusive. Future observations at wavelengths beyond 8 $\mu$m are key to discerning between potential scenarios.

Figures

Figures reproduced from arXiv: 2509.13610 by the authors.

**Figure 2.** Partial pressures of gas species at the magma ocean [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Detailed atmospheric structures for a selected set of synthetic hot rocky exoplanets (log [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Atmospheric thermal structure for representative scenarios. The PT-profiles for each simulated model is shown in colour, [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Condensation degrees of elements (i.e., number fraction of an element that has condensed relative to its total atmospheric [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: Synthetic emission spectra, generated with our model at various [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 7.** Figure 7: Transmission spectra of the synthetic atmospheres from Fig. [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

**Figure 8.** Figure 8: Mass versus the scaled density for observed (dots) and [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

**Figure 9.** Figure 9: Constraints from the radius in the Kepler/ [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]

**Figure 10.** Figure 10: MIRI observations of 55 Cancri e (black dots, [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

**Figure 11.** Figure 11: Best fitting models from our grid (Sec. 3.3) to the NIRCam observations from Patel et al. (2024). The strong autocorrelation within the white lightcurves prohibit the deduction of absolute values in Fp{Fs , thus they are characterized by their relative strength; the a…

**Figure 12.** Figure 12: Prediction for MIRI MRS MEDIUM channel observa [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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