{"id":"d7794ef6-72d2-4bd5-9418-1ebdd6567d59","arxiv_id":"2412.11987","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Convective shutdown can occur in atmospheres over magma oceans without preventing permanent magma oceans, and the resulting emission spectra carry mantle redox fingerprints.","lead":"Lava worlds are usually modeled with fully convective atmospheres, but this paper shows that mixed-composition atmospheres over magma oceans can instead be stably stratified and still trap enough heat to keep a magma ocean molten. The new model links atmospheric emission features of CO2 and SO2 to the redox state of the planet's mantle, offering an observational test with JWST.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified; the central claim is supported by the simulations and the stated limitations are not load-bearing.","rationale":"The reader's verdict of ACCEPT is well-founded. The paper's central assertion is a modal claim ('it is possible'), which is supported by the AGNI simulations across a broad range of mantle redox states. The constant-fO2 assumption is a potential simplification, but because the outcome for HD 63433 d (persistent melt) is insensitive to fO2 across the entire explored range, the concern does not threaten the central claim. The more physical limitations, such as the extrapolation of opacity models to extreme conditions and the neglect of escape, tidal heating, and 3D dynamics, are explicitly acknowledged by the authors in Sec 4.4 and do not undermine the internal consistency of the demonstration. A useful verification step would be a sensitivity run on the key opacity sources for the fully radiative reducing cases; even if such a run shifted the quantitative surface temperature, the qualitative possibility of a permanent magma ocean under a convectively stable atmosphere would likely survive. Thus I find no need to alter the reader's verdict.","tokens_in":27090,"tokens_out":10747,"duration_ms":99702,"concrete_test":"Recompute the fully radiative HD 63433 d case at IW-3 with the H2-H2/H2-CO collision-induced absorption and CO2 line-wing opacities perturbed by a factor of 2 within their published uncertainty; if the surface temperature remains above the silicate solidus and the melt fraction stays positive, the convective-shutdown claim is robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"I read the paper in good faith and cannot identify a single concern that would overturn the central claim that convective shutdown does not preclude permanent magma oceans. The reader's weakest assumption, constant fO2, is mitigated by the full fO2 sweep (IW-5 to IW+5): for HD 63433 d, all 11 AGNI cases retain significant melt, so an evolving fO2 that stays within this range would not change the qualitative outcome. The paper's own acknowledged uncertainties, such as the MT_CKD water continuum (Sec 4.4), affect quantitative surface temperatures but mostly matter for H2O-rich atmospheres; HD 63433 d's atmosphere is depleted in H2O, and the possibility claim does not hinge on a precise opacity value. The 1D global-mean geometry is a limitation for planet-specific predictions, but the abstract's claim is a theoretical possibility demonstrated within the standard radiative-convective framework, which is a valid mode of argument in this field. The model is validated against Selsis et al. (2023), the code is open source, and the internal logic is consistent. I therefore find no load-bearing flaw.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper introduces AGNI, a 1D radiative-convective atmosphere model with mixing-length convection, latent-heat transport, and SOCRATES-based radiative transfer, coupled to the PROTEUS magma-ocean evolution framework. The authors apply it to HD 63433 d and TRAPPIST-1 c over mantle fO2 values from IW-5 to IW+5, comparing AGNI against the fully convective JANUS model. The central finding is that HD 63433 d can maintain a permanent magma ocean despite deep convective shutdown in its outgassed atmosphere, while TRAPPIST-1 c solidifies within roughly 100 Myr in the AGNI runs. Synthetic emission spectra show CO2 and SO2 features that correlate with mantle redox, and the paper argues that isothermal H2-rich stratospheres can masquerade as bare-rock emission.","tokens_in":27214,"tokens_out":8979,"duration_ms":79194,"significance":"The central result is significant: it demonstrates that convective shutdown does not preclude permanent magma oceans, contradicting a direct extrapolation of Selsis et al. (2023) to mixed-composition atmospheres and challenging the fully-convective assumption used in most magma-ocean evolution models. The paper is strong in benchmarking and transparency: AGNI reproduces the deep isothermal layers and general structure of the independent Selsis et al. (2023) pure-steam calculations with small per-level flux residuals (Fig. 2), all code is open source, data are deposited on Zenodo, and the limitations (constant fO2, 1D geometry, MT_CKD continuum, escape, tidal heating) are explicitly acknowledged in Section 4.4. The constant-fO2 concern, which might otherwise be the weakest assumption, is mitigated by the complete fO2 sweep: across all 11 AGNI cases HD 63433 d retains significant melt, so moderate fO2 drift would not overturn the qualitative central claim. The observational predictions for CO2 and SO2 as redox tracers in HD 63433 d are concrete and falsifiable.","major_comments":[],"minor_comments":[{"comment":"The semi-major axis quoted for HD 63433 d is 0.503 AU, which is inconsistent with the stated equilibrium temperature of 1040 K and with the planet's treatment as a highly irradiated lava world; this appears to be a missing leading zero (0.0503 AU) and should be corrected.","section":"Table 2"},{"comment":"The closing sentence of Section 2.3 says the atmosphere model \"is validated against previous work in Section 2.3\", but the validation actually appears in Section 3.2; the cross-reference should be fixed.","section":"Section 2.3"},{"comment":"The eccentricity discussion refers to \"HD 63443 d\"; this should read \"HD 63433 d\".","section":"Section 2.2"},{"comment":"The text refers to the surface-temperature curve in the top panel as a black line and to the solidification-time curve in the bottom panel as a black line, while the figure caption describes these as red and blue lines, respectively; the color references should be made consistent.","section":"Section 3.3 / Fig. 3 caption"},{"comment":"The comparison that AGNI surface temperatures are approximately 2000 K lower than JANUS surface temperatures is stated without a directly corresponding panel; adding JANUS surface temperatures to Fig. 3 or citing a specific panel would make this claim easier to verify.","section":"Section 4.1"},{"comment":"In the paragraph discussing the TRAPPIST-1 c spectra, the phrase \"there are there are clear molecular features\" contains a duplicated phrase, and the following sentence again misspells the planet as \"HD 63443 d\".","section":"Section 4.2"},{"comment":"The phrase \"which could be be equilibrium with a permanently molten interior\" contains a grammar error and should read \"which could be in equilibrium with a permanently molten interior\".","section":"Introduction, first paragraph"}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is within the journal's scope and the central claim is convincing. The only issues I found are presentation-level, most notably the likely missing leading zero in the HD 63433 d semi-major axis in Table 2 and several cross-reference/typo errors. I recommend minor revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Hi [Colleague],\n\nThe central claim of this paper holds up: atmospheres overlying magma oceans can be convectively stable without precluding a permanent magma ocean. That matters because most previous lava-world evolution models assumed full convection, and some recent work suggested convective shutdown would quench magma oceans. The paper shows that with mixed volatile compositions, the shallow radiative temperature profile can still keep the surface hot enough. That is a real result, not a modeling artifact.\n\nWhat is new is that this is demonstrated for realistic outgassed mixtures (H2, CO, CO2, H2O, SO2) rather than pure steam. The authors introduce a new open-source 1D radiative-convective model (AGNI) coupled to the PROTEUS interior framework. They validate AGNI against the independent Selsis et al. (2023) pure-steam calculations and get reasonable agreement, with a 35 K surface difference attributed to sensible differences in convection scheme, opacity data, and spectral resolution. The model is built on SOCRATES radiative transfer, so the radiative core is well tested.\n\nThe paper also gives practical observational predictions: the strength of CO2 and SO2 emission features in HD 63433 d tracks mantle fO2, and near-isothermal low-molecular-weight stratospheres can mimic emission from an airless body. That last point is a useful warning for secondary-eclipse interpretations.\n\nThe soft spots are the ones the authors themselves list: constant fO2, 1D global-mean geometry, no escape, no tidal heating, and the MT_CKD water continuum uncertainty. I agree these do not undermine the central possibility claim. The fO2 sweep is wide (IW-5 to IW+5) and all HD 63433 d cases retain substantial melt, so the qualitative outcome survives reasonable fO2 drift. The 1D geometry is a limitation for planet-specific numbers, not for the generic possibility. The MT_CKD issue mostly matters for H2O-rich atmospheres, which are not the cases driving the main conclusion.\n\nIf I have a quibble, it is that the condensation timescale and mixing length parameters are fixed without much sensitivity testing, but that is minor and does not affect the qualitative result. The citation pattern is appropriate; prior work is credited and the self-citations are directly relevant.\n\nThis paper deserves a serious referee. I would send it out for peer review and expect it to be accepted after minor revisions, primarily tightening the discussion of model parameter sensitivities. The model and data are public, which makes the work reproducible.","headline":"The central claim holds: convectively stable atmospheres can still maintain permanent magma oceans, and this paper deserves a serious referee.","tokens_in":27873,"tokens_out":2991,"would_cite":true,"duration_ms":27812,"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 lava world can hold a permanent magma ocean even when its atmosphere becomes stable to convection.","keywords":["lava worlds","magma oceans","convective shutdown","radiative-convective equilibrium","exoplanet atmospheres","oxygen fugacity","HD 63433 d","TRAPPIST-1 c"],"falsifier":"Run a 3D general circulation model of HD 63433 d's atmosphere with the same outgassed compositions: if day-night dynamics or resolved convection keep the deep atmosphere convectively mixed even where the 1D profile is isothermal, then the permanent-magma-ocean-without-convection state would not survive in more dimensions.","tokens_in":26806,"feed_emoji":"🌋","tokens_out":6607,"duration_ms":56759,"temperature":0.7,"pith_summary":"The paper challenges a standard assumption in models of lava worlds: that the atmospheres above magma oceans are always fully convective. It presents a one-dimensional radiative-convective model that allows atmospheric layers to become stable to convection, and couples it to an interior-evolution model to simulate two Earth-sized exoplanets. The central result is that a convectively stable, largely isothermal atmosphere can still insulate a permanently molten surface, so convective shutdown does not preclude a permanent magma ocean. Applied to HD 63433 d, the model keeps a magma ocean to the present day with an atmosphere depleted in water; applied to TRAPPIST-1 c, it predicts solidification within about 100 million years. These outcomes matter because they change how the emission spectra of lava planets should be interpreted and what they can reveal about mantle redox state.","feed_headline":"Magma oceans can survive under atmospheres that stop convecting","feed_subtitle":"New model keeps HD 63433 d molten today while TRAPPIST-1 c solidifies within 100 million years.","key_machinery":"The central object is AGNI, a new one-dimensional radiative-convective atmosphere model for lava planets. AGNI computes radiative transfer with a spectral radiation scheme, parameterises convection with mixing-length theory, treats latent heat transport from condensing volatiles, and solves for the temperature-pressure profile by requiring the total energy flux to be constant with height using a Newton-Raphson root-finding method. It is coupled through the PROTEUS interior-atmosphere framework to a magma-ocean evolution code, allowing outgassed volatile composition (including sulphur, via a new solubility law) to feed back on cooling. The model's key capability is that convective instability is diagnosed rather than assumed, which is what allows convective shutdown to occur.","core_discovery":"The paper's central claim is that it is possible to maintain permanent magma oceans underneath atmospheres without convection. In the model atmospheres of HD 63433 d, deep isothermal layers form that are stable to convection, yet the surface remains hot enough to keep the mantle substantially molten; under reducing conditions the whole atmosphere becomes purely radiative. Convection, where it occurs, is driven by absorption of downwelling stellar radiation rather than by interior heat, while for TRAPPIST-1 c the opposite holds: convection is sustained by heat escaping the cooling magma ocean, and the planet solidifies within 5 to 96 million years depending on oxygen fugacity. The paper also shows that the strength of CO2 and SO2 absorption features in synthetic emission spectra tracks the mantle's oxygen fugacity, so future observations of HD 63433 d could probe the redox state of an Earth-like magma ocean. Finally, near-isothermal stratospheres produced by low-molecular-weight, reduced atmospheres can mimic the blackbody emission of an atmosphere-less rocky body, cautioning against simple brightness-temperature interpretations.","pith_inferences":["If mantle oxygen fugacity evolves during crystallization, as the paper notes it would in reality, the predicted atmospheric composition and solidification times could shift; re-running the simulations with self-consistent redox evolution would map that sensitivity.","The blackbody mimicry of reduced atmospheres suggests that other observations of apparently airless lava planets may also need to consider isothermal H2/CO atmospheres as degenerate alternatives to bare rock.","Tidal heating, especially in the TRAPPIST-1 system, could supply the upward heat flux needed to keep convection alive and stall solidification; coupling the present framework to tidal dissipation models would test whether any TRAPPIST-1 planet can hold a magma ocean.","If photochemical S8 haze forms in the upper atmosphere, as the equilibrium-chemistry case study hints, redox-driven spectral features could be dampened; combining the model with photochemistry would test whether the oxygen-fugacity diagnostic survives real atmospheric processing."],"forward_implications":["The standard fully-convective assumption in lava-world evolution models should be relaxed; radiative-convective models can give qualitatively different evolutionary outcomes, including permanent magma oceans where older models predicted solidification or vice versa.","HD 63433 d may still host a permanent magma ocean and a water-depleted secondary atmosphere today, making it an observable analogue for a young Earth or Venus.","TRAPPIST-1 c is predicted to have solidified within about 100 Myr, outgassing a thick atmosphere whose composition depends strongly on mantle oxygen fugacity.","Emission spectra of these planets carry redox-sensitive CO2 and SO2 features within JWST MIRI and NIRSpec bandpasses, potentially constraining magma ocean geochemistry.","A cool isothermal stratosphere above a reduced atmosphere can mimic the emission of an atmosphere-less body, so secondary-eclipse photometry alone may not distinguish bare rocks from some lava planets."],"supporting_citations":[{"why":"Developed the PROTEUS coupled interior-atmosphere framework and the earlier fully-convective JANUS atmosphere model that this work extends, and first suggested via radiative heating rates that mixed atmospheres could be convectively stable.","marker":"Nicholls et al. (2024)"},{"why":"Pure-steam radiative-convective model that showed deep convectively stable layers can form; AGNI is validated against its profiles and this paper tests whether its conclusions extend to mixed-composition atmospheres.","marker":"Selsis et al. (2023)"},{"why":"Provides the S2 solubility law and redox-dependent outgassing relations used to model sulphur speciation, feeding the fO2-dependent atmospheric compositions explored here.","marker":"Gaillard et al. (2022)"},{"why":"The radiative transfer scheme (SOCRATES) on which AGNI's gas absorption, collision-induced absorption, and Rayleigh scattering calculations are built.","marker":"Edwards & Slingo (1996)"},{"why":"Technical guide for the SOCRATES radiative transfer suite used in AGNI, defining the spectral and flux calculations in the atmosphere model.","marker":"Manners et al. (2017)"},{"why":"Correlated-k radiative transfer methods used within SOCRATES that let AGNI compute spectrally resolved fluxes efficiently.","marker":"Amundsen et al. (2014)"},{"why":"The SPIDER interior dynamics code, which provides the magma-ocean cooling and solidification physics within the PROTEUS framework coupled to AGNI.","marker":"Bower et al. (2018)"},{"why":"JWST/MIRI secondary-eclipse observation of TRAPPIST-1 c used as the observational benchmark against which the young-planet synthetic spectra are discussed.","marker":"Zieba et al. (2023)"},{"why":"Defines the moist pseudoadiabatic JANUS atmosphere model that embodies the fully-convective assumption and serves as the main contrast case for AGNI.","marker":"Graham et al. (2021)"},{"why":"Earlier magma-ocean evolution model with a convective steam atmosphere, providing the standard framework whose predictions are tested and revised by including convective shutdown.","marker":"Hamano et al. (2015)"}],"fun_headline_variants":["Magma oceans can survive without convection","Stalled convection doesn't freeze magma worlds","Lava planet HD 63433 d holds a magma ocean","No convection needed for permanent magma seas","Convection shutdown leaves magma oceans intact"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The simulations hold the mantle's oxygen fugacity fixed for the entire run, so if it drifts as crystals form or as the melt reacts with water and hydrogen, the resulting atmospheres and solidification times could differ.","fun_headline_variants_meta":{"raw":{"variants":["Magma oceans can survive without convection","Stalled convection doesn't freeze magma worlds","Lava planet HD 63433 d holds a magma ocean","No convection needed for permanent magma seas","Convection shutdown leaves magma oceans intact"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000237,"raw_usage":{"total_tokens":1560,"prompt_tokens":1049,"completion_tokens":511,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":665,"completion_tokens_details":{"reasoning_tokens":444}},"tokens_in":665,"tokens_out":511,"duration_ms":5321,"temperature":1.0,"reasoning_tokens":444,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T14:24:13.497203+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a 3D general circulation model of HD 63433 d's atmosphere with the same outgassed compositions: if day-night dynamics or resolved convection keep the deep atmosphere convectively mixed even where the 1D profile is isothermal, then the permanent-magma-ocean-without-convection state would not survive in more dimensions.","supporting_citations":[],"review_version":1}