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arxiv: 2606.20249 · v1 · pith:SEVBNG2Gnew · submitted 2026-06-18 · 🌌 astro-ph.EP · physics.geo-ph

Geophysical and atmospheric implications of fO₂-dependent melting on rocky exoplanets

Mariana Sastre , Tim Lichtenberg , Laurent Soucasse , Dan J. Bower , Harrison Nicholls , Inga Kamp This is my paper

Pith reviewed 2026-06-26 15:44 UTC · model grok-4.3

classification 🌌 astro-ph.EP physics.geo-ph
keywords rocky exoplanetsmagma oceansoxygen fugacityvolatile inventoryatmospheric compositionsuper-Earthredox statethermal evolution
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The pith

Volatile inventory and surface oxygen fugacity primarily regulate rocky exoplanet thermal states, with fO2-dependent melting as secondary modulation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper quantifies how experimentally derived oxygen-fugacity-dependent melting curves affect magma ocean evolution inside a coupled interior-atmosphere model applied to the super-Earth GJ 1132 b. In volatile-poor cases, reduced melting curves cause earlier deep-mantle crystallization and favor late surface magma oceans with H2-CO-rich atmospheres, whereas oxidized curves sustain higher melt fractions and extended magma oceans with thinner H2O-CO2 envelopes. Volatile-rich systems reach radiative equilibrium at high melt fractions regardless of the melting curve, producing a steady global magma ocean. This establishes a hierarchy in which volatile content and surface redox state dominate over melting thermodynamics. The resulting regimes imply distinct atmospheric compositions and formation timescales.

Core claim

The geochemical evolution of long-lived magma oceans is strongly regulated by volatile exchange between the molten mantle and the atmosphere. Implementing fO2-dependent melting curves within the PROTEUS framework produces strongly non-linear thermal responses. In volatile-poor systems reduced curves promote earlier deep-mantle crystallisation and late-stage surface magma oceans sustained by greenhouse warming, while oxidized curves maintain higher melt fractions and vertically extended magma oceans; reduced mantles yield massive H2-CO-rich atmospheres and oxidized mantles yield thinner H2O-CO2 envelopes. Volatile-rich systems reach radiative equilibrium at high melt fractions, sustaining a s

What carries the argument

fO2-dependent melting curves implemented inside the coupled interior-atmosphere PROTEUS framework, which control melt fraction, rheological evolution, and volatile release as functions of redox state.

If this is right

  • Reduced mantles produce massive H2-CO-rich atmospheres while oxidized mantles produce thinner H2O-CO2 envelopes in volatile-poor systems.
  • Volatile-poor reduced cases develop late-stage surface magma oceans sustained by greenhouse warming.
  • Oxidized melting curves maintain higher melt fractions and vertically extended magma oceans.
  • Volatile-rich systems reach radiative equilibrium at high melt fractions with solidification timing insensitive to melting-curve choice.
  • The two regimes generate distinct atmospheric compositions and formation timescales.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • JWST transmission spectra of short-period rocky planets could distinguish the predicted H2-CO versus H2O-CO2 envelopes.
  • Surface redox state may set long-term atmospheric chemistry even after magma-ocean solidification completes.
  • Applying the same hierarchy to planets with intermediate volatile inventories could map the transition between the two regimes.
  • If high-pressure melting relations deviate from the extrapolated curves, the secondary role of redox melting would become more prominent.

Load-bearing premise

Experimentally derived fO2-dependent melting curves remain valid when extrapolated to the pressure-temperature-composition conditions of super-Earth mantles.

What would settle it

Atmospheric spectra of a volatile-poor close-in rocky exoplanet showing neither dominant H2-CO nor H2O-CO2 signatures, or identical solidification timescales across redox states in a volatile-rich case.

Figures

Figures reproduced from arXiv: 2606.20249 by Dan J. Bower, Harrison Nicholls, Inga Kamp, Laurent Soucasse, Mariana Sastre, Tim Lichtenberg.

Figure 1
Figure 1. Figure 1: Schematic overview of the PROTEUS framework and its time-integration workflow. The interior, surface volatile exchange, and radiative– convective atmosphere are solved as independent modules that iteratively exchange boundary conditions at each timestep. In the time-flowchart, each timestep proceeds by iterating the coupled modules until the surface fluxes, volatile inventories, and atmospheric structure c… view at source ↗
Figure 2
Figure 2. Figure 2: Solidus (solid lines) and liquidus (dashed lines) for mantle re￾dox states relative to the iron–wüstite buffer (IW-4.0, IW-2.0, IW+0, IW+2.0, IW+4.0). Colours indicate increasing oxidation from dark blue (IW-4.0) to pink (IW+4.0). The reference melting curves correspond to IW+2.0, representing an oxidized, broadly Earth-like mantle state consistent with experimental constraints (Andrault et al. 2011; Haman… view at source ↗
Figure 3
Figure 3. Figure 3: T–P profiles for two simulations of a 3 M⊕ planet showing the coupled interior–atmosphere evolution from an initially global magma ocean to radiative equilibrium (partial pressures in bar). Left: Baseline melting curves from Andrault et al. (2011); Hamano et al. (2013). The mantle remains partially molten for an extended period and solidifies through fractional crystallisation, reaching steady state after … view at source ↗
Figure 4
Figure 4. Figure 4: Smoothed distributions of simulation outcomes across the parameter grid. Rows show variations in the driving parameters (C/H ratio, surface oxidation state f O surf 2 relative to the iron–wüstite buffer, orbital separation, volatile inventory in H-ocean mass, planetary mass, and deep￾mantle oxidation state f O melt 2 ), while columns show interior outcomes (time to radiative equilibrium, bulk melt fraction… view at source ↗
Figure 5
Figure 5. Figure 5: Smoothed density distributions of atmospheric outcomes across the parameter grid. Rows show variations in the driving parameters (C/H ratio, surface oxidation state f O surf 2 relative to the iron–wüstite buffer, orbital separation, volatile inventory in H-ocean mass, planetary mass, and deep-mantle oxidation state f O melt 2 ), while columns show interior outcomes (time to radiative equilibrium, bulk melt… view at source ↗
Figure 6
Figure 6. Figure 6: Volume mixing ratio of outgassed volatiles as a function of the deep-mantle oxidation state f O melt 2 for simulations with initial water inventories of 3, 10, and 100 Hoceans. Numbers within the bars indicate the number of simulations contributing to each median value and numbers on top of each bar represent the median surface pressure Psurf in bar. Colours denote the relative contributions of major atmos… view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of the mantle melt fraction with time for three ini￾tial water inventories (Hoceans = 3, 10, 100; top to bottom) and different redox-dependent melting scenarios (f O melt 2 : IW–4.0 to IW+4.0). Curves show the median across simulations at each time, with shaded regions indicating the full range. Each curve is truncated at the median time for equilibrium. tion state f O melt 2 and initial volatile… view at source ↗
Figure 8
Figure 8. Figure 8: Atmosphere-interior partitioning of major volatile species as a function of deep-mantle oxidation state f O melt 2 and initial volatile inventory. Each panel corresponds to a different initial H inventory (3, 10, and 100 Hoceans). Colours indicate the median logarithmic ratio of atmospheric to interior volatile mass, log Matm/Mint, for each species and oxidation state offset along the melting curve (f O me… view at source ↗
read the original abstract

The geochemical evolution of long-lived magma oceans is strongly regulated by volatile exchange between the molten mantle and the atmosphere. For planets inside the runaway-greenhouse limit, this coupled evolution can persist for billions of years. However, most existing studies assume Earth-like (oxidized) conditions and neglect the influence of redox state on melt thermodynamics and volatile release. We quantified how experimentally derived, oxygen-fugacity-dependent melting curves implemented within the coupled interior-atmosphere framework PROTEUS propagate into the thermal structure, melt fraction, and rheological evolution of rocky exoplanet interiors, applying this to the short-period super-Earth GJ 1132 b. We found strongly non-linear thermal responses to variations in melting curves. In volatile-poor systems, reduced melting curves promote earlier deep-mantle crystallisation relative to oxidised and Earth-like cases, favouring late-stage surface magma oceans sustained by greenhouse warming, while oxidized melting curves maintain higher melt fractions and a vertically extended magma ocean. Reduced mantles produce massive H$_2$-CO-rich atmospheres; oxidized mantles favour thinner H$_2$O-CO$_2$ envelopes. In volatile-rich systems, the interior reaches radiative equilibrium at high melt fractions, sustaining a steady-state global magma ocean in which melting curve variations do not significantly influence solidification timing. This indicates a hierarchical control: volatile inventory and surface oxygen fugacity act as the primary regulators of thermal state, while oxygen-fugacity-dependent melting relations provide a secondary modulation. These contrasting regimes produce distinct atmospheric compositions and formation timescales, offering testable spectral predictions for close-in rocky exoplanets evaluable with forthcoming JWST observations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses the PROTEUS coupled interior-atmosphere model to simulate fO2-dependent melting on the super-Earth GJ 1132 b. It reports strongly non-linear thermal and rheological responses, concluding that volatile inventory and surface oxygen fugacity are the primary controls on thermal state and magma-ocean lifetime while fO2-dependent solidus/liquidus relations provide only secondary modulation. This produces two regimes: volatile-poor cases with distinct crystallization paths and atmospheres (H2-CO for reduced, H2O-CO2 for oxidized) versus volatile-rich cases that sustain global magma oceans independent of melting-curve choice. Testable spectral predictions for JWST are offered.

Significance. If the central hierarchy holds, the work supplies a concrete mechanism linking mantle redox state to observable atmospheric composition and formation timescale on close-in rocky planets. The use of a self-consistent coupled framework that ingests laboratory melting curves is a clear methodological strength, enabling the reported regime distinctions.

major comments (2)
  1. [Abstract; PROTEUS melting-curve implementation] Abstract and the section describing PROTEUS implementation of melting relations: the claimed secondary role of fO2-dependent melting and the resulting regime distinctions (earlier deep crystallization for reduced curves vs extended magma ocean for oxidized) rest on the validity of the laboratory-derived solidus/liquidus offsets at super-Earth core-mantle boundary pressures. No justification, theoretical scaling, or sensitivity test is supplied for extrapolating curves calibrated below ~10 GPa to ~100 GPa conditions where phase stability and compressibility change; this is load-bearing for the hierarchical-control conclusion.
  2. [Results for GJ 1132 b] Results on volatile-poor vs volatile-rich systems: the distinction between primary (volatile inventory, surface fO2) and secondary (melting curves) regulators is asserted without reported error bars on melt fractions or thermal profiles, and without systematic variation of the post-hoc volatile inventories that define the two regimes. This leaves the robustness of the non-linear response and the “do not significantly influence” statement for volatile-rich cases unquantified.
minor comments (2)
  1. [Methods] Notation for oxygen fugacity (fO2) and the specific functional form of the reduced vs oxidized melting curves should be defined explicitly in a methods subsection or table rather than referenced only to external experiments.
  2. A summary table listing the four end-member cases (volatile-poor/reduced, volatile-poor/oxidized, volatile-rich/reduced, volatile-rich/oxidized) with key outputs (solidification time, dominant atmospheric species, final melt fraction) would improve clarity.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thoughtful and constructive review. The comments highlight important aspects of model assumptions and robustness that we address below. We have revised the manuscript accordingly where feasible while maintaining scientific accuracy.

read point-by-point responses

  1. Referee: [Abstract; PROTEUS melting-curve implementation] Abstract and the section describing PROTEUS implementation of melting relations: the claimed secondary role of fO2-dependent melting and the resulting regime distinctions (earlier deep crystallization for reduced curves vs extended magma ocean for oxidized) rest on the validity of the laboratory-derived solidus/liquidus offsets at super-Earth core-mantle boundary pressures. No justification, theoretical scaling, or sensitivity test is supplied for extrapolating curves calibrated below ~10 GPa to ~100 GPa conditions where phase stability and compressibility change; this is load-bearing for the hierarchical-control conclusion.

    Authors: We agree that the pressure extrapolation of the fO2-dependent solidus/liquidus offsets constitutes a key modeling assumption. The laboratory calibrations are limited to lower pressures, and phase stability changes at super-Earth conditions are not directly constrained. In the revised manuscript we have added an explicit discussion in the Methods section justifying the constant-offset assumption on the basis of available high-pressure mineral physics trends for compressibility and melting slope, while noting the absence of direct data above ~10 GPa. A quantitative sensitivity test at 100 GPa is not possible without new experiments; we therefore treat the relative differences between reduced and oxidized curves as indicative rather than absolute. This addition clarifies but does not remove the limitation for the hierarchical-control claim. revision: partial

  2. Referee: [Results for GJ 1132 b] Results on volatile-poor vs volatile-rich systems: the distinction between primary (volatile inventory, surface fO2) and secondary (melting curves) regulators is asserted without reported error bars on melt fractions or thermal profiles, and without systematic variation of the post-hoc volatile inventories that define the two regimes. This leaves the robustness of the non-linear response and the “do not significantly influence” statement for volatile-rich cases unquantified.

    Authors: We have expanded the Results section to include error bars on melt-fraction and temperature profiles, propagated from the documented uncertainties in PROTEUS input parameters. We also performed additional simulations systematically varying the post-hoc volatile inventory over a wider range (0.1–10 Earth-ocean equivalents) to map the transition between regimes. These runs confirm that the non-linear thermal response and the independence of solidification timing from melting-curve choice in volatile-rich cases remain robust across the tested inventories. The revised figures and text now quantify these distinctions, strengthening the primary/secondary regulator hierarchy. revision: yes

standing simulated objections not resolved
  • Full quantitative assessment of melting-curve extrapolation effects at ~100 GPa cannot be performed without new laboratory data at those pressures.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central results emerge from forward simulations in the PROTEUS coupled interior-atmosphere model that take experimentally derived fO2-dependent solidus/liquidus curves as external inputs. The reported non-linear thermal responses, regime distinctions (early deep crystallization vs sustained magma ocean), and atmospheric outcomes (H2-CO vs H2O-CO2) are generated by varying those inputs across volatile-poor and volatile-rich cases; they do not reduce by definition to the curves themselves, nor do any quoted steps rely on self-citation load-bearing arguments, fitted parameters renamed as predictions, or ansatzes smuggled via prior work. The hierarchical-control claim is therefore an independent modeling outcome rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of lab-derived melting curves to exoplanet conditions and the fidelity of the PROTEUS coupling; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Experimentally derived fO2-dependent melting curves can be directly implemented in the PROTEUS interior-atmosphere model without additional scaling for super-Earth pressures.
    Invoked when the paper states it quantified how these curves propagate into thermal structure and melt fraction.
  • domain assumption Volatile inventory and surface oxygen fugacity can be treated as independent inputs that hierarchically dominate over melting-curve variations.
    Stated explicitly as the primary versus secondary control conclusion.

pith-pipeline@v0.9.1-grok · 5842 in / 1355 out tokens · 17912 ms · 2026-06-26T15:44:52.385907+00:00 · methodology

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