pith. sign in

arxiv: 2604.15304 · v2 · pith:TICXFLRUnew · submitted 2026-04-16 · 🌌 astro-ph.EP

A Validated Low-to-Intermediate Mass Planetary Interior Structure Model and New Mass-Radius Relations

Bennett Neil Skinner , Ralph E. Pudritz , Ryan Cloutier This is my paper

Pith reviewed 2026-05-10 09:36 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords planetary interior modelsmass-radius relationsexoplanet structureequations of statemineralogysolar system validationiron-rich planetswater-rich planets
0
0 comments X

The pith

A new planetary interior model reproduces solar system radii to within 1 percent and supplies updated mass-radius curves for exoplanets of different compositions.

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

The paper presents an interior structure model that incorporates recent equations of state, mineralogies in which multiple species can coexist in the same layer, non-adiabatic temperature profiles, and melting. When applied to solar-system bodies it recovers Earth’s radius and moment of inertia to 0.2 percent, Mars and the Moon to 0.5 percent, and Mercury, Venus, and Europa to within 1 percent or 3 sigma. The same model is then used to generate mass-radius relations for hydrogen-helium, water-rich, Earth-like, and iron-rich planets between 0.01 and 100 Earth masses. Piece-wise power-law fits to the relations below 8 Earth masses show that the exponent in M = a R^b rises with both total mass and core-mass fraction. Radii from the new curves are smaller than earlier literature values at low instellation and larger at high instellation, with the difference comparable to present-day observational uncertainties.

Core claim

The authors construct and validate an interior structure code that employs state-of-the-art equations of state, a mineralogy permitting multiple phases within each layer, non-adiabatic temperature profiles, and melting. The code reproduces the radii and moments of inertia of Earth, Mars, the Moon, Mercury, Venus, and Europa at the stated precision levels. Mass-radius tables are computed for four compositional classes across 0.01–100 Earth masses, yielding 32,971 individual models whose publicly released data are fitted by piece-wise power laws below 8 Earth masses; the power-law exponent increases with mass and core fraction, and the resulting radii depart from previous relations in a manner

What carries the argument

The validated interior structure model that combines updated equations of state, multi-species mineralogy, non-adiabatic temperature profiles, and melting to compute planetary radii from mass and composition.

If this is right

  • Mass-radius relations must be recomputed with current equations of state if observational uncertainties continue to shrink.
  • The power-law exponent in M = a R^b increases with both planetary mass and core-mass fraction for planets below 8 Earth masses.
  • Radii at a given mass are smaller than prior literature values for low-instellation planets and larger for high-instellation planets.
  • Public tables of 32,971 model planets allow direct comparison with new observations.
  • State-of-the-art models are required to interpret current and near-future mass-radius data at the precision now available.

Where Pith is reading between the lines

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

  • The model’s ability to handle arbitrary compositions could be tested by applying it to planets with independently measured core fractions from transit-timing or atmospheric data.
  • Differences at high instellation may affect interpretations of the radius valley if stellar irradiation alters interior thermal profiles.
  • Extension to masses above 100 Earth masses would require checking whether the same mineralogies hold at higher central pressures.
  • The public release of the full model grid allows community re-derivation of occurrence rates or formation constraints without re-running the structure code.

Load-bearing premise

Mineralogies and equations of state calibrated on solar-system bodies and laboratory data remain valid when applied to exoplanets that may have different formation histories, pressures, and temperatures.

What would settle it

A high-precision mass and radius measurement of an exoplanet whose bulk composition can be independently constrained (for example by atmospheric spectroscopy or formation context) that lies more than 3 sigma outside the new model’s predicted radius for that composition.

Figures

Figures reproduced from arXiv: 2604.15304 by Bennett Neil Skinner, Ralph E. Pudritz, Ryan Cloutier.

Figure 1
Figure 1. Figure 1: The species and phases of those species in our mantle. Solid lines represent changes in chemical composition, dashed lines represent solely changes in phase of a species. Colours are arbitrary but are consistent across panels. Equil. is an abbreviation for equilibrium. + indicates the coexistence of multiple species. Note that many phase and chemical transitions take place in the region labelled HeFESTo Eq… view at source ↗
Figure 2
Figure 2. Figure 2: The phase diagram of iron employed in our model. Solid lines indicate phase transitions while dashed lines represent transitions between using different EOS for the same phase. EOS labels indicate the isothermal portion only, see text and [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A diagram showing the variables 𝑟 (light red lines) and 𝑧 (dark red line) in relation to 𝑠 (purple line), the length along which 𝜏 = 2 3 . The darkest circle represents the solid surface of the planet, the lighter circle the transit radius of the planet, and the lightest circle the outermost layer of the atmosphere, defined here to be where 𝑃 = 100 Pa. 2.8 Transit Radii We report our final planetary radii … view at source ↗
Figure 4
Figure 4. Figure 4: The internal r-𝜌 profile of Earth as determined by the model in this work as compared to REM1D, a reference model for the Earth derived from seismology and other constraints. The box in the upper left of panel a is shown in more detail in panel b. Horizontal lines indicate the observed locations of phase transitions in Earth’s interior (although note that the association of 𝐷′′ with the Pv->Ppv transition … view at source ↗
Figure 5
Figure 5. Figure 5: The internal r-𝜌 profile of the Mars as determined by the model in this work compared to the inversion of InSight seismic data from Khan et al. (2023). Khan et al. (2023) provide 1000 models consistent with Martian observations, all of which are plotted with some transparency such that darker shades of blue represent regions where more models agree. We plot four Mars models with each possible combination o… view at source ↗
Figure 6
Figure 6. Figure 6: The internal r-𝜌 profile of the Moon as determined by the model in this work and found in various models of the lunar interior informed by seismology. Dotted lines indicate errors where applicable. Horizontal lines correspond to lunar core radii from other considerations (Viswanathan et al. (2019): the oblateness of the lunar core, Briaud et al. (2023): lunar tidal deformation). The format of boundaries be… view at source ↗
Figure 7
Figure 7. Figure 7: The internal r-𝜌 profile of Mercury as determined by the model in this work compared to the plausible locations of Mercury’s mantle/core and inner/outer core transitions from Genova et al. (2019), indicated by horizontal shaded regions. The format of boundaries between layers is lower pressure layer/higher pressure layer. The inner/outer core transition boundary is 0.4-0.7 times the core radius following G… view at source ↗
Figure 8
Figure 8. Figure 8: The isocomposition curves in mass-radius space for several planetary compositions. Multiple H/He-rich compositions are present, higher transparency curves have higher H/He fractions and the H/He fraction by mass is labelled on the left of each curve. See text for further elaboration on compositions. The shaded region corresponds to planets with gravities at their transit radius outside the bounds of the an… view at source ↗
Figure 9
Figure 9. Figure 9: The same as [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The same as [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The same as [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: The relative difference between our calculated planetary radii for an Earth-like composition and the 𝑀 = 0.994𝑅 3.701 power law that best fits it for masses between 0.93 and 2.58 Earth masses (see [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: The mass-radius relations for planets with a 100% core mass fraction in our model, both composed of pure iron and an Earth-like chemical inventory, compared to the findings of Zeng et al. (2016) for pure iron. Scatterpoints are the same as in [PITH_FULL_IMAGE:figures/full_fig_p030_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The radii of planets in our model as calculated for a transit radius (see section 2.8) as compared to the radii of planets in our model at a specific outer boundary pressure. We compare to outer boundary pressures of 100 Pa and 2000 Pa, both of which are common in the literature. lar work in the literature to ours, including mantle Gibbs free energy minimization, a correction for transit radii, an irradia… view at source ↗
read the original abstract

The increasing precision of planetary mass and radius observations is bringing major questions about the structure and formation of planets--such as the nature of the radius valley and origin of super-Mercuries--within reach, demanding the development of interior structure models with more physics to more accurately determine planetary radii for a given composition. Here, we present a new model that includes state-of-the-art equations of state following the latest experimental and computational results, a physically-motivated mineralogy allowing multiple species to coexist within planetary layers, a non-adiabatic temperature profile, melting, and other features. This model replicates Earth's radius and moment of inertia coefficient to within $0.2\%$, Mars and the Moon's to within $0.5\%$, and Mercury, Venus, and Europa's to within $1\%$ or 3$\sigma$. We use this model to calculate mass-radius relationships for H/He-enveloped, water-rich, Earth-like, and iron-rich bodies with masses between $0.01$--$100\, M_\oplus$. We calculate mass-radius tables and fit piece-wise power-laws to them for ${<}8M_\oplus$ planets, finding that the exponent in $M=bR^a$ increases with mass and core mass fraction. We find radii generally smaller than in literature mass-radius relations at low instellations and larger at high instellations, with our improvement on the literature comparable to observational uncertainties. State-of-the-art interior structure models are thus required to interpret observational data. Our mass-radius curves comprising 32,975 model planets are publicly available.

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

0 major / 3 minor

Summary. The manuscript presents a new planetary interior structure model incorporating updated equations of state based on recent experimental and computational results, a multi-species mineralogy allowing coexistence within layers, non-adiabatic temperature profiles, melting, and related features. The model is validated against solar-system bodies, reproducing Earth's radius and moment of inertia coefficient to within 0.2%, Mars and the Moon to within 0.5%, and Mercury, Venus, and Europa to within 1% or 3σ. The authors then compute mass-radius relations for H/He-enveloped, water-rich, Earth-like, and iron-rich compositions across 0.01–100 M⊕, derive piecewise power-law fits (M = a R^b) for planets below 8 M⊕, and publicly release a dataset of 32,971 model planets. They report that the new relations differ from literature values at a level comparable to observational uncertainties, with generally smaller radii at low instellations and larger radii at high instellations.

Significance. If the central results hold, the work provides a meaningfully more physics-rich interior model whose validation precision on multiple independent solar-system constraints (Earth radius+MOI, Mars, Moon, etc.) and public release of the full model grid directly support improved interpretation of exoplanet mass-radius data, including questions such as the radius valley and super-Mercury origins. The explicit quantification of differences from prior relations at the scale of current observational uncertainties, together with the reproducible dataset, strengthens the practical utility of the findings.

minor comments (3)
  1. [Abstract] The abstract states that radii are 'generally smaller than in literature mass-radius relations at low instellations and larger at high instellations'; the main text should explicitly identify the section or figure where this comparison is quantified and clarify how instellation enters the interior model (e.g., via the surface temperature boundary condition).
  2. The piecewise power-law fits for <8 M⊕ planets are central to the new relations; the manuscript should include a table or appendix listing the fitted coefficients a and b, the break points, and the mass ranges for each composition to allow direct use and reproduction.
  3. Acronyms such as EOS (equations of state) and MOI (moment of inertia) should be defined at first use in the main text, even if defined in the abstract.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. We appreciate the recognition of the model's validation precision against multiple solar-system bodies and the value of the publicly released 32,971-planet dataset. No specific major comments were listed in the report, so we have no individual points requiring detailed response at this stage. We will prepare the revised version incorporating any minor editorial changes as needed.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper builds its interior model from external experimental and computational EOS data plus a physically motivated multi-species mineralogy, then validates it against independent solar-system observations (Earth radius/MOI to 0.2%, Mars/Moon to 0.5%, etc.) without defining parameters to force those matches. Mass-radius curves for H/He, water, Earth-like and iron-rich compositions are computed directly from the model and piecewise power-laws are fitted to those computed outputs; neither step reduces to the input data by construction. No load-bearing self-citations, self-definitional steps, or fitted-input-as-prediction patterns appear in the presented chain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on standard planetary structure equations (hydrostatic equilibrium, mass continuity) plus domain-specific assumptions about mineral behavior and heat transport. No new particles or forces are introduced. Free parameters appear limited to composition choices and layer boundaries that are varied systematically rather than fitted to the target exoplanet data.

axioms (2)
  • standard math Hydrostatic equilibrium and mass continuity hold throughout the planet.
    Implicit in any 1D interior structure integration.
  • domain assumption Equations of state from recent experiments and computations accurately describe material behavior at planetary pressures and temperatures.
    Central to the claim of state-of-the-art physics.

pith-pipeline@v0.9.0 · 5594 in / 1481 out tokens · 35404 ms · 2026-05-10T09:36:24.557521+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.