{"id":"b2239901-0685-4115-b5a6-835dff7ddcd1","arxiv_id":"2509.13610","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A coupled atmosphere-interior model shows that magma ocean oxygen fugacity controls the spectral appearance of hot rocky exoplanets, with SO2 and H2O/CO2 band ratios as the key diagnostics.","lead":"This paper simulates the atmospheres of hot rocky exoplanets in equilibrium with their magma oceans, varying oxygen fugacity, volatile mass, and metallic composition to compute their emission and transmission spectra. It identifies sulfur dioxide and the relative strengths of water and carbon dioxide bands as the most promising spectral probes of a planet's interior state, and applies the model to the JWST observations of 55 Cancri e.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The SO2 fO2-tracer claim rests on an unvalidated 1200 K extrapolation of the S2 solubility law.","rationale":"After reading the paper, the central claim is that fO2 controls spectral shape and SO2 is a robust tracer. This rests on the computed pSO2 as a function of fO2. The dominant control on pSO2 at the MAI is the sulfur solubility law. The law is extrapolated by ~1200 K beyond its calibration range, which the authors acknowledge. While the reader flagged the general equilibrium assumption, that assumption is at least motivated by short reaction timescales at high T; the solubility law is a quantitative empirical parameterization with known limited T range. The paper's application to 55 Cnc e hinges on the SO2 feature strength. If the peak shifts, the inferred fO2 range and the exclusion of VIBSE-like planets could change. This is a falsifiable, model-level concern; the proposed test using an alternative solubility model would settle it. The paper is otherwise careful and transparent, so I recommend keeping the conditional verdict.","tokens_in":36855,"tokens_out":12752,"duration_ms":139887,"concrete_test":"Re-run the Atmodeller grid of Fig. 2 at T_MAI=3000 K replacing the Boulliung & Wood (2022) S2 solubility with the sulfide-capacity model of O'Neill & Mavrogenes (2002) (or another T-dependent parameterization that extends beyond 1800 K). If the fO2 at which pSO2 peaks shifts by >1 log unit from ΔIW+3, or if the ΔIW+3±3 range no longer brackets the maximum, the central 'SO2 as robust fO2 tracer' claim is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central diagnostic claim—that the 8–9 µm SO2 feature is the most robust fO2 tracer, peaking near ΔIW+3—is set by the model's sulfur partitioning at the magma–atmosphere interface. That partitioning uses the S2 solubility law of Boulliung & Wood (2022, 2023), which is calibrated over 1473–1773 K for basaltic/andesitic melts (Table A.1). 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), so the law is extrapolated ~1200 K beyond its calibration. The authors explicitly caution in Sec. 4.3 that 'experimental constraints are typically half that temperature' and that S2 solubility is sensitive to melt FeO content. If the true S2 solubility at 3000 K differs from the Henry/Sieverts extrapolation, the location and strength of the pSO2 maximum as a function of fO2 could shift, undermining the claim that SO2 is a robust fO2 tracer in the ΔIW+3±3 range (except z≈0). Because the MIRI constraint on 55 Cnc e (Sec. 4.2.1) uses the absence of a strong SO2 feature to exclude oxidised VIBSE scenarios, a quantitative error in the sulfur solubility directly affects the paper's key observational conclusion. This is a more specific, correctable flaw than the general equilibrium assumption, which the paper justifies with timescale arguments.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":37198,"tokens_out":4047,"duration_ms":52657,"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":[{"comment":"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","section":"Sec 3.3.1 / Sec 4.3(2) / Table A.1"},{"comment":"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.","section":"Sec 4.3(1) / Table C.1"},{"comment":"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.","section":"Sec 4.2.1 / Fig. 10"}],"minor_comments":[{"comment":"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.","section":"Sec 4.3(1)"},{"comment":"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.","section":"Fig. 2"},{"comment":"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.","section":"Eq. (12)"},{"comment":"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.","section":"Sec 4.1"},{"comment":"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.","section":"Code and Data availability"},{"comment":"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.","section":"Sec 3.3.1"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid forward-modeling contribution with clear observational relevance, and the authors are honest about many limitations. The main issue is that the quantitative 55 Cnc e exclusion and the 'most robust fO2 tracer' claim depend on an unvalidated 1200 K extrapolation of the S2 solubility law; this is fixable with a sensitivity analysis or a more cautious wording. I see no circularity or fabrication concerns. The manuscript fits A&A's scope. If the S2 issue is addressed, the paper would likely be acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nThe 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.","headline":"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.","tokens_in":37764,"tokens_out":1519,"would_cite":true,"duration_ms":21074,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["hot rocky exoplanets","magma ocean","oxygen fugacity","SO2","emission spectra","transmission spectra","55 Cancri e","atmosphere-interior coupling"],"falsifier":"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.","tokens_in":36704,"feed_emoji":"🔭","tokens_out":2893,"duration_ms":33876,"temperature":0.7,"pith_summary":"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.","feed_headline":"SO2 marks the redox state of magma-ocean worlds","feed_subtitle":"The 8–9 µm SO2 feature is the most robust spectral tracer of magma-ocean oxygen fugacity.","key_machinery":"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.","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Magma ocean redox drives hot exoplanet spectral shape","SO2 absorption reveals magma-ocean oxygen fugacity","Oxygen fugacity, not volatile mass, controls hot rocky spectra","8–9 µm SO2 feature traces magma ocean oxidation state","Magma ocean fO2 sets spectral fingerprints of hot exoplanets"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Magma ocean redox drives hot exoplanet spectral shape","SO2 absorption reveals magma-ocean oxygen fugacity","Oxygen fugacity, not volatile mass, controls hot rocky spectra","8–9 µm SO2 feature traces magma ocean oxidation state","Magma ocean fO2 sets spectral fingerprints of hot exoplanets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001016,"raw_usage":{"total_tokens":4231,"prompt_tokens":957,"completion_tokens":3274,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":701,"completion_tokens_details":{"reasoning_tokens":3188}},"tokens_in":701,"tokens_out":3274,"duration_ms":23928,"temperature":1.0,"reasoning_tokens":3188,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T16:28:51.884211+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}