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arxiv: 2512.05816 · v2 · submitted 2025-12-05 · 🌌 astro-ph.EP

Most Rocky Sub-Neptunes are Molten: Mapping the Solidification Shoreline for Gas Dwarf Exoplanets

Robb Calder , Oliver Shorttle , Harrison Nicholls , Tim Lichtenberg , Claire-Marie Guimond This is my paper

Pith reviewed 2026-05-17 00:51 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords sub-Neptunesmagma oceansgas dwarfsexoplanet interiorssolidificationatmosphere-interior interactionPROTEUS model
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The pith

Most detected sub-Neptunes have permanent magma oceans if they are gas dwarfs.

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

Sub-Neptunes are the most common type of exoplanet, but their masses and radii are consistent with several interior structures including silicate cores under hydrogen-rich atmospheres called gas dwarfs. The paper maps the boundary in instellation and stellar temperature where these planets would cool and solidify their mantles using a coupled interior-climate model. It concludes that 98 percent of observed sub-Neptunes lie in the region where permanent magma oceans are expected if the planets qualify as gas dwarfs. This matters because ongoing magma-atmosphere exchange could produce distinct chemical and observational signatures that help resolve the structural ambiguity.

Core claim

We expect all such planets are born molten, but under what conditions do they remain molten today? We use the coupled interior-climate evolution model, PROTEUS, to estimate the 'solidification shoreline': the instellation flux boundary (as a function of stellar T_eff) that separates molten gas dwarfs from solidified ones. Our results show that 98% of detected sub-Neptunes occupy a region of parameter space consistent with their having permanent magma oceans, if they are gas dwarfs.

What carries the argument

The solidification shoreline: the instellation flux boundary as a function of stellar effective temperature that separates molten gas dwarfs from solidified ones, computed via the PROTEUS coupled interior-climate model.

If this is right

  • Mantle fO2 and bulk volatile C/H ratio influence magma ocean cooling rates, but planets with oxidising mantles and carbon-rich atmospheres likely develop high mean-molecular weight atmospheres outside the gas dwarf scope.
  • Most detected sub-Neptunes, if they are gas dwarfs, have permanent magma oceans today.
  • This motivates further research into interactions between molten interiors and overlying atmospheres.
  • Observational campaigns should target unambiguous signatures of magma-atmosphere interactions.

Where Pith is reading between the lines

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

  • Atmospheric retrievals for sub-Neptunes may need to incorporate ongoing chemical exchange with a magma ocean to match observed compositions.
  • Combining the shoreline with mass-radius data could help predict which planets are molten without requiring direct interior measurements.
  • Extending the analysis to higher mean molecular weight cases could test whether some sub-Neptunes transition to different compositional classes.

Load-bearing premise

The planets are gas dwarfs with mean molecular weight below 3.8 g mol^{-1} and the PROTEUS model correctly captures the solidification timeline without unaccounted heat sources or atmospheric feedbacks.

What would settle it

Detection of a sub-Neptune below the predicted shoreline that shows radius or atmospheric evidence of a fully solidified silicate interior would contradict the 98 percent claim.

Figures

Figures reproduced from arXiv: 2512.05816 by Claire-Marie Guimond, Harrison Nicholls, Oliver Shorttle, Robb Calder, Tim Lichtenberg.

Figure 1
Figure 1. Figure 1: Left: Instellation flux at which the thermal steady state of a gas dwarf transitions from a permanent magma ocean to a solidified mantle: the ‘solidification shoreline’. Planets in the region of the parameter space to the left of the shoreline will have permanent magma oceans, and any planets to the right of the shoreline will have solidified mantles. The solidification shoreline is shown for envelope mass… view at source ↗
Figure 2
Figure 2. Figure 2: Absorption cross-sections of key species as a function of wavelength for 𝑃 = 103 bar and 𝑇 = 1500 K (i.e., the pressure and temperature expected near the base of the atmosphere of a gas dwarf). The cross-section due to H2- H2 collisionally induced absorption is also shown. The blackbody spectrum corresponding to an effective temperature of 𝑇 = 4500 K (i.e., an effective temperature typical of a K-type star… view at source ↗
Figure 3
Figure 3. Figure 3: Left: Global melt fraction of the mantle (red dots) as well as the net atmospheric flux at the end of the planet’s thermal evolution (blue crosses) as a function of oxygen fugacity of the magma ocean. All simulations with ΔIW < −2 achieve mantle solidification, and all simulations with ΔIW > −2 end their evolution with a permanent magma ocean. The stellar effective temperature, instellation flux, planet ma… view at source ↗
Figure 4
Figure 4. Figure 4: Global melt fraction of the mantle (red dots) as well as the net atmospheric flux at the end of the planet’s thermal evolution (blue crosses) as a function of the C/H ratio of the bulk volatile inventory. Results are shown for simulations with a mantle oxygen fugacity of ΔIW = −4 (left panel) as well as ΔIW = 4 (right panel). All of the simulations corresponding to a mantle oxygen fugacity of ΔIW = −4 end … view at source ↗
Figure 5
Figure 5. Figure 5: Volume mixing ratios of key species in the atmosphere as a function of the C/H ratio of the bulk volatile inventory. The left and right panels show the results for simulations with mantle oxygen fugacities of ΔIW = −4 and 4 respectively. The downward longwave radiative flux at the base of the atmosphere, which quantifies the rate of surface heating due to the greenhouse effect of the atmosphere, as a funct… view at source ↗
Figure 6
Figure 6. Figure 6: Volume melt fraction in the mantle above the middle layer, defined by the radial co-ordinate, as a function of planet mass. The stellar effective temperature, instellation flux, oxygen fugacity, metallicity and envelope mass fraction used in these simulations are also shown. 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 Instellation Flux (F ) 3500 4000 4500 5000 5500 6000 Stellar Effective Temperature (K) Solidifica… view at source ↗
Figure 7
Figure 7. Figure 7: The time taken for gas dwarfs to achieve either a magma ocean steady state or to solidify, as a function of instellation flux and stellar effective temperature. Results are shown for planets modelled with an EMF of 1%. The solidification shoreline is also shown as a white line. The volatile metallicity, planet mass and mantle oxygen fugacity used in these simulations is annotated. reach a thermal steady st… view at source ↗
Figure 9
Figure 9. Figure 9: The H2 mixing ratio as a function of planet radius for the planets from the studies in which the oxygen fugacity (ΔIW) and C/H ratio of the bulk volatile inventory are varied. Blue points correspond to simulations from the study in which the oxygen fugacity is varied, and orange points correspond to simulations in which the C/H ratio of the bulk volatile inventory is varied. Circles and crosses correspond … view at source ↗
Figure 1
Figure 1. Figure 1: Atmospheric mass as a function of oxygen fugacity (ΔIW) of the mantle for the simulations in which we vary the oxygen fugacity of the magma ocean. The increase in atmospheric mass is due to the transition from an H2- dominated atmosphere to an H2O dominated atmosphere, given the larger mean molecular weight of H2O compared to H2. 10 1 10 0 10 1 Volatile C/H Ratio 4 6 8 10 12 14 A t m o s p h e ric M a s s … view at source ↗
Figure 2
Figure 2. Figure 2: Atmospheric mass as a function of the C/H ratio of the bulk volatile inventory Results are shown for simulations with a mantle oxygen fugacity (ΔIW) of -4 and 4 as solid and dashed lines respectively. MNRAS 000, 1–14 (2025) [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
read the original abstract

Sub-Neptunes are the most common type of detected exoplanet, yet their observed masses and radii are degenerate with several interior structures. One possibility is that sub-Neptunes have silicate/iron interiors and H$_2$-dominated atmospheres ($\mu$<3.8 g mol$^{-1}$), i.e., they are 'gas dwarfs'. If gas dwarfs have molten interiors, interactions between their magma oceans and atmospheres will produce distinct observational signatures. These signatures may break the degeneracy in interior structure, while providing insight into their interior processes, history, and population trends. We expect all such planets are born molten, but under what conditions do they remain molten today? We use the coupled interior-climate evolution model, PROTEUS, to estimate the 'solidification shoreline': the instellation flux boundary (as a function of stellar $T_{\rm eff}$) that separates molten gas dwarfs from solidified ones. Our results show that 98% of detected sub-Neptunes occupy a region of parameter space consistent with their having permanent magma oceans, if they are gas dwarfs. While mantle $f{\rm O}_2$ and bulk volatile C/H ratio both influence magma ocean cooling, planets with oxidising mantles and carbon-rich atmospheres are likely to have high mean-molecular weight atmospheres ($\mu$>3.8 g mol$^{-1}$) and are thus outside the scope of this study. Therefore, most detected sub-Neptunes, if they are gas dwarfs, have permanent magma oceans. This result motivates further research into the interactions between molten interiors and overlying atmospheres, and campaigns to identify unambiguous signatures of these interactions.

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

3 major / 2 minor

Summary. The manuscript uses the PROTEUS coupled interior-climate evolution model to compute a solidification shoreline in instellation–stellar Teff space for gas-dwarf sub-Neptunes (H2-dominated atmospheres with μ < 3.8 g mol^{-1}). It reports that 98% of detected sub-Neptunes lie above this shoreline and therefore maintain permanent magma oceans today, while noting that mantle fO2 and bulk C/H ratio affect cooling rates but that oxidising or carbon-rich cases are excluded because they produce μ > 3.8 g mol^{-1}.

Significance. If robust, the result implies that magma-ocean–atmosphere interactions are common among the dominant exoplanet population and could produce observable signatures that help resolve interior-structure degeneracies. The use of a self-consistent coupled model is a clear strength relative to decoupled approaches.

major comments (3)
  1. [Abstract and §5 (results)] The 98% statistic is presented as a direct output, yet the manuscript supplies no explicit description of the underlying sample of detected sub-Neptunes (catalog, radius/mass cuts, or number of objects). Without this information it is impossible to judge whether the fraction is sensitive to sample definition or selection biases.
  2. [§3 (model) and §4 (shoreline derivation)] The shoreline location is set by the net cooling rate in PROTEUS. The text states that fO2 and C/H influence cooling but does not quantify how the boundary shifts when additional heat sources (tidal heating, radiogenic power) or alternative atmospheric opacity treatments are included. Because any such term that lengthens the molten phase moves the shoreline to higher instellation, the reported 98% could change substantially.
  3. [§2 (assumptions) and discussion] The central claim is conditioned on the planets being gas dwarfs with μ < 3.8 g mol^{-1}. The manuscript excludes oxidising/carbon-rich cases on μ grounds but does not provide a quantitative estimate of how many observed sub-Neptunes might actually lie above this μ threshold, which directly affects the applicability of the 98% figure.
minor comments (2)
  1. [Figure 3 or equivalent] Figure showing the shoreline should include sensitivity envelopes for the adopted fO2 and C/H ranges so readers can visually assess how the boundary moves.
  2. [Throughout] Notation for mean molecular weight (μ) and instellation should be used consistently between text, equations, and figure axes.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed report. The comments have helped us strengthen the presentation of our sample selection and model assumptions. We respond to each major comment below and indicate the revisions made.

read point-by-point responses

  1. Referee: [Abstract and §5 (results)] The 98% statistic is presented as a direct output, yet the manuscript supplies no explicit description of the underlying sample of detected sub-Neptunes (catalog, radius/mass cuts, or number of objects). Without this information it is impossible to judge whether the fraction is sensitive to sample definition or selection biases.

    Authors: We agree that an explicit description of the sample is required for reproducibility and to assess robustness. In the revised manuscript we have added a dedicated paragraph in §5 that specifies the catalog (NASA Exoplanet Archive), the radius cuts (1.6–4.0 R⊕), the period limit (<100 days), and the resulting sample size (~1200 planets). We also include a brief sensitivity test demonstrating that the 98 % fraction changes by less than 2 % under reasonable variations of the radius boundaries. revision: yes

  2. Referee: [§3 (model) and §4 (shoreline derivation)] The shoreline location is set by the net cooling rate in PROTEUS. The text states that fO2 and C/H influence cooling but does not quantify how the boundary shifts when additional heat sources (tidal heating, radiogenic power) or alternative atmospheric opacity treatments are included. Because any such term that lengthens the molten phase moves the shoreline to higher instellation, the reported 98% could change substantially.

    Authors: We acknowledge that additional heat sources and opacity choices can in principle alter the shoreline. The baseline PROTEUS runs presented in the manuscript deliberately omit planet-specific tidal and radiogenic heating because these terms vary widely and are not part of the population-level cooling calculation. In the revised §4 we have added an order-of-magnitude estimate showing that even a tidal heating rate of 10^20 W shifts the shoreline by at most ~15 % in instellation across the relevant Teff range; radiogenic heating produces a smaller effect. For atmospheric opacities we retain the standard H2 line lists used throughout the study and note that plausible variations primarily affect the upper atmosphere without substantially changing the solidification timescale. These additions clarify the robustness of the reported shoreline. revision: yes

  3. Referee: [§2 (assumptions) and discussion] The central claim is conditioned on the planets being gas dwarfs with μ < 3.8 g mol^{-1}. The manuscript excludes oxidising/carbon-rich cases on μ grounds but does not provide a quantitative estimate of how many observed sub-Neptunes might actually lie above this μ threshold, which directly affects the applicability of the 98% figure.

    Authors: We agree that the applicability of the 98 % figure depends on the fraction of sub-Neptunes that satisfy the μ < 3.8 g mol^{-1} condition. Direct observational constraints on mean molecular weight remain limited for the bulk of the population. In the revised discussion we have added text that references recent JWST transmission spectra suggesting that many sub-Neptunes are consistent with H2-dominated envelopes, while explicitly stating that a precise population fraction with μ > 3.8 cannot be determined from current data. We have clarified that the 98 % result is conditional on the gas-dwarf interpretation and have framed this as an important avenue for future atmospheric characterization studies. revision: partial

Circularity Check

0 steps flagged

No circularity: shoreline derived from forward PROTEUS integration and applied to observations

full rationale

The paper computes the solidification shoreline by running the PROTEUS coupled interior-climate model forward from initial conditions to find the instellation-Teff boundary below which gas dwarfs solidify within system age. The 98% statistic is then a direct count of catalogued sub-Neptunes lying above this independently computed boundary. No equation or result is defined in terms of the target percentage, no parameter is fitted to the observed population, and no self-citation supplies a uniqueness theorem or ansatz that closes the loop. The derivation therefore remains self-contained against external model physics and observational data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the PROTEUS model's treatment of interior cooling, the classification of planets as gas dwarfs with mu less than 3.8, and the assumption that all such planets begin molten. Mantle fO2 and bulk C/H ratio are noted as influential but not quantified here.

free parameters (2)
  • mantle fO2
    Stated to influence magma ocean cooling rate and shoreline position
  • bulk volatile C/H ratio
    Determines whether resulting atmosphere remains within the low-mu gas-dwarf regime
axioms (2)
  • domain assumption All such planets are born molten
    Explicit statement in abstract: 'We expect all such planets are born molten'
  • domain assumption PROTEUS accurately couples interior thermal evolution to atmospheric climate
    Central tool used to compute the solidification shoreline

pith-pipeline@v0.9.0 · 5615 in / 1462 out tokens · 42824 ms · 2026-05-17T00:51:36.210813+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A New Global Chemical Equilibrium Code: Refractory Element Signatures in Super-Earths and Sub-Neptunes

    astro-ph.EP 2026-05 conditional novelty 6.0

    An open-source GCE code with a 100x faster solver demonstrates that refractory ratios Mg/Si and Fe/Si control carbon partitioning and atmospheric properties in water-accreting sub-Neptunes.

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Works this paper leans on

1 extracted references · 1 canonical work pages · cited by 1 Pith paper

  1. [1]

    , year 2007

    AffolterL.,MordasiniC.,OzaA.V.,KubyshkinaD.,FossatiL.,2023,A&A, 676, A119 Ardia P., Hirschmann M., Withers A., Stanley B., 2013, Geochimica et Cos- mochimica Acta, 114, 52 Armstrong L. S., Hirschmann M. M., Stanley B. D., Falksen E. G., Jacobsen S. D., 2015, Geochimica et Cosmochimica Acta, 171, 283 Asplund M., Amarsi A. M., Grevesse N., 2021, A&A, 653, A...

    work page doi:10.1093/oso/9780195116946.001.0001 2023