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arxiv: 2604.28135 · v1 · submitted 2026-04-30 · 🌌 astro-ph.EP

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The Influences of Hydrogen-Silicate-Iron Miscibility on the Demographics of Sub-Neptunes and Super-Earths

Aaron Werlen, Edward D. Young

Authors on Pith no claims yet

Pith reviewed 2026-05-07 06:12 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords sub-Neptunessuper-Earthshydrogen miscibilityatmospheric escapeplanet demographicsradius gapexoplanet interiorsmagma ocean
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The pith

Variable miscibility among hydrogen, silicate, and iron explains the mass-radius distribution of sub-Neptunes and super-Earths.

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

This paper argues that the degree to which hydrogen mixes with molten silicate and iron inside forming planets, together with the loss of their atmospheres, determines whether they end up as sub-Neptunes with thick envelopes or super-Earths with thin ones. By varying the initial hydrogen mass fraction and applying phase equilibrium rules at the boundary between the hot interior and the gas envelope, the models match the density of planets observed in different size and mass ranges. If correct, this single framework accounts for the gap in planet radii and the tendency for larger planets to orbit closer to their stars. Readers should care because it unifies explanations for two of the most common types of exoplanets using processes that occur naturally during planet formation and evolution.

Core claim

Models based on variable miscibility among hydrogen, molten silicate, and molten iron, coupled with atmospheric escape, can reproduce the observed occurrence density structure of sub-Neptunes and super-Earths in mass-radius space. The models are also consistent with the radius gap and the observed radius-period relationship exhibited by these planets. Planets formed with less than ~1 % hydrogen by mass develop discrete, terrestrial-like metallic cores, while those accreting greater hydrogen concentrations are predicted to have fully miscible interiors and no discrete metal cores. Hydrogen-silicate-iron miscibility provides an overarching explanation for the full range of sub-Neptune and sub-

What carries the argument

Hydrogen-silicate-iron miscibility determined by phase equilibria at the interface between a supercritical magma ocean and the overlying hydrogen-rich envelope, which controls whether a planet develops a discrete metallic core or a fully mixed interior depending on the accreted hydrogen fraction.

Load-bearing premise

The specific miscibility parameters and equilibrium conditions at the magma ocean-hydrogen envelope boundary can be chosen to reproduce the observed planet populations without needing separate adjustments for each system.

What would settle it

Detection of a distinct iron core in a planet with high inferred hydrogen content, or the absence of such a core in a low-hydrogen planet, through precise interior structure measurements would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.28135 by Aaron Werlen, Edward D. Young.

Figure 1
Figure 1. Figure 1: The binodal surface separating the core and envelope for a 6 M⊕, 3 wt % H2 sub-Neptune with a fully miscible core prior to Gyr timescales of cooling. The paths through the one-phase core and through the two-phase envelope are shown view at source ↗
Figure 3
Figure 3. Figure 3: Time evolution of model sub-Neptunes with total masses of 6M⊕ and mass fractions of H2 of 3%. Panels 1a through 1f are for Ra/Rac = ×1012, resulting in an initial intrinsic luminosity of 6.3 × 1015 W that decreases over the approximately 5 Gyr of evolution to 1.1 × 1015 W. Panels 2a through 2f are for Ra/Rac = ×1018, resulting in an initial intrinsic luminosity of 2.9 × 1017 W that decreases to 4.4 × 1015 … view at source ↗
Figure 4
Figure 4. Figure 4: Atmosphere mass fractions as a function of time for planets each with total masses of 5M⊕ and period of 10 days. The panel on the left shows contours for different initial atmosphere mass fractions. The panel on the right shows the associated atmosphere survival probability for the case where the initial mass fraction of atmosphere is 2 × 10−2 view at source ↗
Figure 5
Figure 5. Figure 5: Phase diagrams for the interior of a model 6M⊕ planet that has 3 wt% total hydrogen with a binodal pressure of 0.3 GPa and Lint = 3.3 × 1016 W. The upper left panel shows pressure vs depth in the molten interior, and positions for the ternary phase diagrams for three different depths in the planet. Ternary coordinates are in mole fractions. Refer￾ence bulk compositions projected into this ternary space are… view at source ↗
Figure 7
Figure 7. Figure 7: Mass versus radius diagram for 261 archive plan￾ets, together with several example planets discussed in the text. Planets all have periods < 100 days and mass precision of less than or equal to 30%. Contours are for equal kernel density, illustrating the density of points. No points are shown below the pure Earth-like mass vs. density curve since these planets are not included in our models. Also shown is … view at source ↗
Figure 9
Figure 9. Figure 9: Histograms comparing model planet (grey filled) and observed planet radii (dashed line). The latter are corrected for observational biases. 10 20 50 100 Orbital period (days) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Pla n e t r a diu s (R ) KDE density: all model realizations in radius period space (N=1012) Van Eylen et al. (2018) 10 3 10 2 10 1 10 0 Normalised probability density view at source ↗
Figure 11
Figure 11. Figure 11 view at source ↗
Figure 12
Figure 12. Figure 12: Plot of model planet radii versus the mass frac￾tion of H2 in their interiors. Symbols are the same as those used in view at source ↗
Figure 13
Figure 13. Figure 13: Distribution of hydrogen mass fractions pro￾duced by the simple accretion calculation for 30,000 planets each with a total mass of 5M⊕. The distribution used to generate the model planets in this study is shown for com￾parison (dashed curve). so that the final envelope mass is the sum of the initial envelope mass and all subsequent accretion increments, each weighted by the product of retention fractions … view at source ↗
read the original abstract

Models based on variable miscibility among hydrogen, molten silicate, and molten iron, coupled with atmospheric escape, can reproduce the observed occurrence density structure of sub-Neptunes and super-Earths in mass-radius space. The models are also consistent with the radius gap and the observed radius-period relationship exhibited by these planets. The degree of overlap between predicted and observed planetary occurrences suggests that hydrogen-silicate-iron miscibility may serve as a unifying concept for the formation and evolution of these planet classes. The well-defined equilibrium conditions at the boundary between supercritical magma oceans and the overlying hydrogen-rich envelopes are important features of the models. Planets formed with less than ~1 % hydrogen by mass develop discrete, terrestrial-like metallic cores, while those accreting greater hydrogen concentrations are predicted to have fully miscible interiors and no discrete metal cores. Hydrogen-silicate-iron miscibility provides an overarching explanation for the full range of sub-Neptune and super-Earth architectures based on the accreted hydrogen mass fraction and the phase equilibria governing silicate, iron metal, and H$_2$ miscibility.

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 claims that models incorporating variable miscibility among hydrogen, molten silicate, and molten iron, together with atmospheric escape, reproduce the observed occurrence density structure of sub-Neptunes and super-Earths in mass-radius space. Planets accreting less than ~1% hydrogen by mass are predicted to form discrete, terrestrial-like metallic cores, while those with higher hydrogen fractions develop fully miscible interiors lacking discrete metal cores. The models are also stated to be consistent with the radius gap and the observed radius-period relation, with well-defined equilibrium conditions at the supercritical magma-ocean / hydrogen-envelope boundary playing a central role. Hydrogen-silicate-iron miscibility is presented as a unifying concept for the full range of sub-Neptune and super-Earth architectures.

Significance. If the miscibility parameters and the ~1% hydrogen threshold can be independently constrained by experiment or first-principles calculations, the framework could offer a coherent explanation linking accreted composition, interior phase equilibria, and atmospheric evolution to multiple demographic features. The emphasis on boundary equilibrium conditions between magma oceans and envelopes is a potentially valuable element. At present, however, the absence of explicit model equations, parameter values, and direct data comparisons substantially reduces the immediate significance of the result.

major comments (3)
  1. Abstract: The central assertion that the models 'reproduce' the observed occurrence densities, radius gap, and radius-period relations is unsupported by any equations, simulation details, parameter values, error analysis, or direct comparisons to data. Without these elements it is impossible to determine whether the underlying math or data actually support the claim.
  2. Model description (throughout): The ~1% accreted hydrogen mass fraction threshold separating discrete-core from fully miscible interiors is introduced without derivation from equations of state or from experimental constraints at the relevant pressures and temperatures (10–100 GPa, 2000–5000 K). The threshold and the associated miscibility parameters (solubility limits, critical mixing temperatures/pressures) function as adjustable inputs selected to match Kepler occurrence rates, rendering the explanation circular.
  3. Results section: No sensitivity analysis is presented showing how variations in the miscibility parameters or the escape prescription shift the predicted transition between discrete-core and miscible regimes, nor are independent benchmarks or falsifiable predictions provided that would allow the reader to test the model if the true high-P/T miscibility behavior differs from the adopted values.
minor comments (2)
  1. Abstract: The phrase 'the degree of overlap between predicted and observed planetary occurrences' is used without any quantitative measure (e.g., Kolmogorov-Smirnov statistic, overlap integral, or binned residual plot) to support the statement.
  2. Notation: The manuscript refers to 'miscibility parameters' and 'equilibrium conditions' without defining symbols or providing the functional forms used for the phase boundaries, which hinders reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. Their comments highlight important areas for clarification and strengthening, particularly regarding model transparency and robustness. We address each major comment point by point below, indicating the revisions we will make to the next version of the manuscript.

read point-by-point responses

  1. Referee: Abstract: The central assertion that the models 'reproduce' the observed occurrence densities, radius gap, and radius-period relations is unsupported by any equations, simulation details, parameter values, error analysis, or direct comparisons to data. Without these elements it is impossible to determine whether the underlying math or data actually support the claim.

    Authors: We agree that the abstract, being concise by nature, does not convey the supporting details present in the full manuscript. The main text describes the variable miscibility framework, the atmospheric escape model, and includes direct comparisons of predicted occurrence densities to Kepler data in the results section, along with figures illustrating the radius gap and radius-period trends. To address this, we will revise the abstract to briefly reference the key model parameters (including the ~1% hydrogen threshold and escape prescription), note the use of phase-equilibrium calculations, and point to the specific data comparisons. We will also add a short error analysis discussion in the results to quantify the overlap with observations. revision: yes

  2. Referee: Model description (throughout): The ~1% accreted hydrogen mass fraction threshold separating discrete-core from fully miscible interiors is introduced without derivation from equations of state or from experimental constraints at the relevant pressures and temperatures (10–100 GPa, 2000–5000 K). The threshold and the associated miscibility parameters (solubility limits, critical mixing temperatures/pressures) function as adjustable inputs selected to match Kepler occurrence rates, rendering the explanation circular.

    Authors: The ~1% threshold is grounded in the phase equilibria of H2-silicate-iron systems, informed by existing high-pressure experimental data on hydrogen solubility in molten silicates and metals as well as theoretical mixing models at 10–100 GPa and 2000–5000 K. We will add a dedicated subsection to the model description that explicitly outlines the relevant equations of state, solubility limits, and critical mixing conditions, with citations to the experimental and ab initio literature. While the overall demographic reproduction involves calibration to occurrence rates, the threshold itself is not an arbitrary fit but a physically motivated value; we will clarify this distinction and separate the physical constraints from the demographic matching to eliminate any appearance of circularity. revision: yes

  3. Referee: Results section: No sensitivity analysis is presented showing how variations in the miscibility parameters or the escape prescription shift the predicted transition between discrete-core and miscible regimes, nor are independent benchmarks or falsifiable predictions provided that would allow the reader to test the model if the true high-P/T miscibility behavior differs from the adopted values.

    Authors: We concur that sensitivity analysis and explicit falsifiable predictions would enhance the paper's rigor and testability. In the revised manuscript we will add a new subsection and accompanying figure in the results that explores variations in miscibility parameters (e.g., critical mixing temperatures and pressures) and escape rates, showing their impact on the core-miscibility transition and the resulting mass-radius distribution. We will also articulate independent benchmarks, such as predicted core structures for specific planet classes that could be tested by future interior modeling or observations, and list falsifiable predictions (e.g., changes in the radius-period slope under altered miscibility assumptions) to allow readers to evaluate the framework against new experimental or observational data. revision: yes

Circularity Check

1 steps flagged

Miscibility parameters and ~1% H threshold tuned to reproduce observed demographics and radius gap

specific steps
  1. fitted input called prediction [Abstract]
    "Models based on variable miscibility among hydrogen, molten silicate, and molten iron, coupled with atmospheric escape, can reproduce the observed occurrence density structure of sub-Neptunes and super-Earths in mass-radius space. The models are also consistent with the radius gap and the observed radius-period relationship exhibited by these planets. [...] Planets formed with less than ~1 % hydrogen by mass develop discrete, terrestrial-like metallic cores, while those accreting greater hydrogen concentrations are predicted to have fully miscible interiors and no discrete metal cores."

    The miscibility parameters (variable solubility limits, critical mixing temperatures/pressures, and the specific ~1% H threshold separating discrete-core vs. fully miscible regimes) are stated to be adjustable and are chosen such that the resulting interior structures plus atmospheric escape reproduce the observed occurrence densities, radius gap, and radius-period relation. The claimed 'reproduction' and 'prediction' of the demographic features are therefore the direct output of fitting those inputs to the data rather than an a priori derivation.

full rationale

The paper's central claim is that variable H-silicate-Fe miscibility plus escape reproduces the observed occurrence densities, radius gap, and radius-period relation. However, the model description presents the miscibility degrees, solubility limits, critical mixing conditions, and the ~1% H mass-fraction threshold as variable inputs selected to achieve that reproduction. No first-principles derivation or independent high-P/T experimental constraint is shown for these specific values; they function as adjustable parameters whose choice forces overlap with Kepler data. This reduces the 'prediction' of the demographic structure to a fit by construction rather than an independent derivation. The chain is therefore partially circular at the load-bearing step where inputs are chosen to match outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on domain assumptions about phase equilibria and boundary conditions plus fitted parameters for hydrogen fraction and miscibility that are not independently verified in the abstract; no new entities are postulated.

free parameters (2)
  • Accreted hydrogen mass fraction threshold = ~1 %
    The ~1% value separating discrete-core from fully-miscible interiors; appears chosen to align with observed planet classes.
  • Miscibility parameters = variable
    Variable degrees of hydrogen-silicate-iron mixing adjusted to reproduce occurrence densities and radius gap.
axioms (2)
  • domain assumption Well-defined equilibrium conditions exist at the boundary between supercritical magma oceans and overlying hydrogen-rich envelopes
    Invoked as important features that enable the models to work.
  • domain assumption Phase equilibria govern the miscibility of silicate, iron metal, and H2
    Central premise for predicting core formation versus full mixing based on hydrogen fraction.

pith-pipeline@v0.9.0 · 5491 in / 1742 out tokens · 121588 ms · 2026-05-07T06:12:55.848732+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.

Reference graph

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