Planets similar in size are often dissimilar in interior

E. Mamonova; P. Hatalova; S.C. Werner; Y. Shan

REVIEW 3 major objections 4 minor 82 references

Planets similar in size are often dissimilar in interior

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Neighbouring planets similar in size often have very different masses and interiors, so radius is a weak guide to composition.

desk verdict The mass-null result is solid and worth citing; the interior-dissimilarity headline is only as strong as a 41-pair subset mapped onto a two-layer composition grid. read the letter →

arxiv 2506.05089 v1 pith:WNB6GHJM submitted 2025-06-05 astro-ph.EP

E. Mamonova , Y. Shan , P. Hatalova , S.C. Werner This is my paper

classification astro-ph.EP

keywords peasinapodexoplanetinteriorsmass-radiusrelationmulti-planetsystemsbulkdensityintrasystemuniformityinteriordistanceplanetcomposition

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to test whether the 'peas in a pod' pattern — the observed tendency for planets in the same multi-planet system to be similar in radius, mass, and spacing — extends to planet composition and interior structure. Using a large sample of systems in which at least two planets have directly measured masses and radii, it finds a moderate correlation in adjacent-planet radii but only a weak correlation in bulk density and no overall correlation in mass. Among the pairs that are most similar in radius, most sit on different theoretical composition curves, indicating distinct interior structures and volatile contents. The paper concludes that within a system, similarity in radius is not a reliable proxy for similarity in mass, density, composition, or physical nature. This is consequential because radius is the most easily measured exoplanet property and is routinely used to classify planets by type.

What carries the argument

The load-bearing object is the 'interior distance' metric $I$, defined in Eq. (4). For each planet in a pair, the planet is assigned the nearest curve in a fine grid of theoretical mass–density curves for two-layer interiors made of Fe, MgSiO$_3$, and H$_2$O; the closer of the two curves becomes the pair's reference curve, and $I$ is the average of the signed density gaps between each planet and that reference at the planet's own mass. A threshold of $I \geq 0.1$ corresponds, on the grid, to compositions differing by at least about 30% in component content, so the metric converts the qualitative picture of straddling curves into a count of compositionally similar versus dissimilar pairs. Supporting machinery includes the scale-independent parameter gap $g$ of Eq. (3), the construction of a 'high-correlated in radius' subsample by trimming pairs with radius ratios far from unity, and a Monte Carlo 'error-accommodation' routine plus null populations drawn from a non-parametric mass-radius relation to assess whether the observed correlations and dispersions could arise from measurement noise.

What would settle it

Inspect the atmospheres or interiors of the 26 pairs the paper labels compositionally dissimilar ($I \geq 0.1$) using independent diagnostics such as transmission spectroscopy, atmospheric escape, or asteroseismic density constraints; if most of those pairs turn out to share a similar bulk composition, the interior-distance interpretation is refuted.

Watch

Extended reading notes

Core claim

The paper's central discovery is that the intrasystem uniformity known as the 'peas in a pod' trend holds for planet radius but largely evaporates for mass, density, and interior structure. In the main sample of 184 adjacent planet pairs with directly measured masses, the Pearson correlation coefficient for mass is $R = -0.007$, statistically indistinguishable from zero, whereas for radius it is $R = 0.516$ and for bulk density $R = 0.265$. When the analysis is restricted to pairs that are highly similar in radius, the correlations in mass and density remain weak. For planets up to about 32 Earth masses, placing these similar-radius pairs on a grid of theoretical two-layer composition curves (iron, rock, water) shows that most pairs straddle widely separated curves. Quantifying this with an 'interior distance' metric $I$, the paper counts 26 pairs with $I \geq 0.1$, interpreted as compositions differing by at least 30% in the grid, versus 15 pairs with $I < 0.1$. The conclusion is that neighbouring planets with similar radii can belong to different compositional families, such as rocky versus water-rich worlds, so radius similarity does not imply similarity in composition or interior structure.

Load-bearing premise

The conclusion rests on the assumption that the grid of two-layer iron–rock–water compositions used to define 'interior distance' adequately represents the real interiors of planets up to about 32 Earth masses, so that a large interior distance indicates a genuine compositional difference and not, for example, the presence of hydrogen-helium atmospheres or mixed ice-rock material that the grid simply does not include.

Editorial extensions

If this is right

Radius-based planet classification becomes unreliable: two planets of the same size in the same system can be a rocky world and a water world, so demographic cuts by radius alone mix different physical populations.
Part of the scatter in the observed mass-radius relation is intrasystem, not merely an inter-system effect of different formation environments, so population models must explain diversity produced within a single protoplanetary disc.
Formation models that predict strong mass uniformity within a system need to reconcile with the absence of mass correlation in the full sample, while the enhanced uniformity found around cool, old, low-metallicity stars marks the conditions where such models may apply.
Radius by itself cannot indicate a planet's physical nature: same-size neighbours in one system can have dissimilar densities, masses, and implied volatile content, so composition estimates must combine mass and radius.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If radius similarity does not track interior similarity, the 'peas in a pod' pattern measured on radius-dominated samples such as the Kepler sample may overstate the architectural uniformity of the underlying planet population, since the signal rides on the easiest-to-measure quantity.
Recomputing interior distances with interior models that include hydrogen-helium envelopes or mixed ice-rock mixtures would test how many of the paper's 'similar-interior' pairs survive; adding more composition families could push more pairs above the dissimilarity threshold.
The pairs the paper flags as compositionally diverse despite matching radii are natural targets for atmospheric characterisation, because they offer the most information about how different interiors can arise from a single protoplanetary disc.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Hi — I read the Mamonova et al. paper. The result worth remembering is that in a large sample of multi-planet systems with directly measured masses and radii, adjacent-planet masses show no correlation (R≈-0.007) while radii show a moderate correlation (R≈0.52), and the intrasystem dispersion story goes the same way. That is a real, useful update to the peas-in-a-pod literature, and it is likely robust: they cross-validated masses against two databases to exclude theoretical MRR values, ran error-accommodating Monte Carlo draws, checked Kepler-only and Gaia DR3 radii, and built stability-preserving nulls. I would cite the mass-null result.

The HCR exercise is the cleanest part of the paper. Taking the 149 pairs that are highly correlated in radius and showing that their masses and densities are only weakly correlated (R≈0.33 and 0.46) makes the point that size similarity does not imply mass/density similarity without relying on any composition model. That part deserves to be published.

The soft spots are in the interior claim. First, the density correlation is not stable: R=0.265 in the full sample jumps to R=0.654 under the σ≤0.5P cut (n=44). They report this honestly, but it means the headline 'weak density correlation' is sample-dependent. Second, the interior distance I is computed for only 41 of the 149 HCR pairs, and it depends on the Zeng two-layer grid, which omits H/He envelopes, mixed ice-rock interiors, and non-solar Fe/Si ratios. The 26/15 split is therefore a statement about planets that happen to fall near that grid, not about similar-radius neighbours in general. The paper's own Section 4.3 concedes that the volatile-rich population's constituents are only theorized, but the title and abstract do not carry that caveat. Third, Eq. 4 as written takes the absolute value of the sum of signed gaps, so a pair straddling the reference curve can look similar by cancellation; that needs a fix or at least a clarification. The moving-window stellar-property results are exploratory but not load-bearing.

This is a revise-and-resubmit, not a reject. The mass-null and HCR mass/density results are solid; the interior interpretation needs to be restructured around the 41-pair subsample, with the grid limitation and the metric definition fixed, and the title softened or justified. I would send it to a serious referee. Good reading-group material.

Referee Report

3 major / 4 minor

Summary. The manuscript re-examines 'peas in a pod' correlations in multi-planet systems using a catalogue-based sample of systems with at least two directly measured masses and radii. It reports a moderate intrasystem radius correlation (R=0.516), a weak density correlation (R=0.265), and no overall mass correlation (R=-0.007) in the main sample, with system-wide dispersion consistently smaller in radius than in mass or density. The authors construct high-correlated-in-radius (HCR) subsamples and, using a new interior-distance metric I based on the Zeng et al. (2016) two-layer composition grid, find 26 of 41 HCR pairs with I>=0.1, concluding that similar-size neighbouring planets often have dissimilar interiors. The analysis is accompanied by multiple robustness checks, including Monte Carlo error accommodation, bootstrap tests, Kepler-only subsamples, Gaia DR3 stellar radii, and stability-constrained null populations from the non-parametric Ning et al. (2018) mass-radius relation.

Significance. If the result holds, the paper is an important counterweight to the common interpretation that intrasystem radius uniformity implies density and compositional uniformity: it would show that radius similarity within a system is not a reliable proxy for interior similarity, and it would pose a direct constraint on formation models that produce uniform compositions within a system. The paper is valuable for its large assembled sample, its transparent multiple robustness checks, and its public code and data availability. However, the headline interior claim rests on a selected subset of the HCR sample and on a grid-based metric whose definition and coverage need to be clarified, so the significance is conditional on resolving the issues described below.

major comments (3)

[Section 3.2, Eq. (4)] The definition of the interior distance I is inconsistent with its verbal description. The text states that I is the mean of the two gap distances, but Eq. (4) gives I=|I_p1+I_p2|/2 with I_pi defined as signed density gaps relative to the reference curve. Opposite-sign gaps can cancel in this formula, yielding a small I for a genuinely dissimilar pair, and the formula is not the mean of the two distances unless the individual gaps are taken in absolute value. Please clarify the sign convention and, if the intended quantity is the mean absolute gap, use I=(|I_p1|+|I_p2|)/2 and re-check the 26/15 classification under the corrected definition.
[Section 3.2, Table 3] The headline interior claim is based on only 41 of the 149 HCR pairs. The sample is further restricted to planets with M_pl <= 32 M_Earth and to pairs in which at least one planet lies near the Zeng et al. (2016) Fe-MgSiO3-H2O two-layer grid; pairs whose planets are far from all grid curves are excluded by construction. Because inclusion therefore depends on the same composition model used to define I, the 26/15 split cannot be read as evidence about small neighbouring planets with similar radii in general. The paper should report the selection fractions explicitly, test how the split changes when the excluded HCR pairs are assigned conservative or model-independent I values, and qualify the abstract and Section 5 statements accordingly.
[Section 3.1.1, Table 1] The abstract's claim of a 'weak correlation in densities' is not robust to the precision cut used in the same table: the subsample with sigma_P <= 0.5 P gives R=0.654 (n=44, p=1.4e-6), more than double the main-sample value R=0.265. The text mentions this result but the abstract and conclusions present the weak-density finding without this caveat. The authors should either present the precision-restricted result as the better estimate, or provide a quantitative selection-bias or sample-size argument for discounting it; as written, the density conclusion is sample-dependent.

minor comments (4)

[Section 3.2] The sentence excluding 'pairs where both planets have I_pi <= 0.1' contradicts its explanatory clause about planets being 'farther than 0.1 from any MRR curve'; the inequality direction and the definition of I_pi (distance to the nearest curve versus signed distance to the reference curve) should be corrected.
[Section 3.2, Eq. (3)] With the chosen indicator f(x,y)=(1/2(x^2+y^2))^{1/2}, the denominator in g should be ((x^2+y^2)/2)^{1/2}, not (x^2+y^2)^{1/2}; the printed formula is missing a factor of sqrt(2).
[Figure 3] The caption refers to 'dashed black lines' connecting HCR pairs, while the text in Section 3.2 describes 'dotted lines'; these should be made consistent.
[Section 3.1.1] The phrase 'see e.q. Wang (2017); Otegi et al. (2022)' should read 'e.g.'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are direct empirical measurements against external catalogs and external interior-structure grids; the only self-citation is not load-bearing.

full rationale

The paper's load-bearing claims are empirical comparisons, not derivations from fitted inputs. The HCR subsample is selected purely on radius correlation (R~0.95) and is then used to measure mass, density, and interior-distance distributions; nothing in that construction forces the subsequent finding that masses and interiors are often dissimilar. The null comparisons use the external Ning et al. (2018) non-parametric mass-radius model, and the interior classification uses the external Zeng et al. (2016) two-layer composition grid, with the threshold I>=0.1 calibrated to the grid's 10% composition steps. The paper benchmarks its interior-distance classification against external results (Rodríguez Martínez et al. 2023) for HD 260655 and LTT 1445A. The single self-citation (Hatalova et al. 2023, Section 4.3) is used only to motivate a speculation about incompleteness of simulated systems and does not carry any of the statistical or interior conclusions. The grid coverage limitation (41 of 149 HCR pairs) and the omission of H/He envelopes are legitimate scope/robustness concerns but are not circularity: the interior claim is conditional on the external grid, not equivalent to the paper's own input by construction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No continuous parameters are fitted to produce the central claim; the conclusions instead rest on a series of manually chosen thresholds and model grids. The most consequential choices are the uncertainty cut, the HCR trimming target, and the I=0.1 interior-distance boundary. The Zeng grid and Ning MRR are external models used as benchmarks, so they appear under axioms rather than invented entities.

free parameters (5)

Uncertainty cut sigma_P_sum <= 2P = 2P
Main results are reported for this sample-defining threshold. Stricter cuts alter the density result (R=0.654 at sigma<=0.5P), so the 'weak density correlation' headline depends on this choice.
HCR target Pearson R = 0.95
Pairs are sequentially removed until the adjacent-pair radius correlation reaches R about 0.95; the sizes of the HCR subsample and the subsequent interior-distance analysis depend on this manually chosen target.
Interior distance threshold I = 0.1 = 0.1
Used to separate planet pairs into similar and dissimilar interior structures; the threshold is justified by the 10% composition-grid spacing, but it is an ad hoc classification boundary.
Moving window size for stellar-property test = 40 pairs
Stellar Teff, metallicity, and age ranges are identified by a 40-pair moving window; the ranges found depend on the window width.
Mass and radius subsample cuts = M_p < 100 M_Earth, R_p < 10 R_Earth
Adopted from prior literature; correlations change substantially in this restricted subsample (R_mass=0.35, R_density=0.16), so the presence of gas giants strongly influences the main-sample null result for mass.

assumptions (5)

domain assumption The sample of multi-planet systems with directly measured masses and radii is sufficiently representative of the intrinsic multi-planet population for the inferred correlations to be meaningful.
Invoked in Section 2.1 when constructing the main sample; the authors acknowledge incompleteness and biases in Section 4.3 but do not correct for them.
domain assumption Radii and mass uncertainties are independent and the reported error intervals can be modelled as uniform distributions for the Monte Carlo error-accommodation.
Used throughout Section 2.2 and in Tables 1-3 via the 10^5 random uniform draws; real error distributions are typically not uniform and may be correlated.
standard math The Pearson correlation coefficient is an appropriate statistic for these planet-parameter comparisons.
Used as the primary test in Section 2.2 with caveats about non-normality and outlier sensitivity that the authors themselves note.
ad hoc to paper The Zeng et al. (2016) two-layer interior model grid (Fe, MgSiO3, H2O) is an adequate representation of exoplanet compositions for M_pl <= 32 M_Earth.
The interior-distance I in Section 3.2 (Eq. 4) assigns each planet to its nearest grid curve; if the true composition space includes other materials, the metric mischaracterizes interiors.
ad hoc to paper The non-parametric mass-radius relation of Ning et al. (2018) provides a valid null model for generating mock mass and density populations.
Used in Section 2.2 and 3.1 to build 10^5 test populations and expected distributions D_sim and I_sim; results are compared against this model rather than against a fully detection-bias-aware forward model.

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Cite this review

Pith. "Pith review of Planets similar in size are often dissimilar in interior." pith.science (2026). https://pith.science/paper/WNB6GHJM

@misc{pith2026250605089,
  author       = {Pith},
  title        = {Pith review of: Planets similar in size are often dissimilar in interior},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WNB6GHJM}},
  note         = {Machine review of arXiv:2506.05089}
}

read the original abstract

Recent works have found evidence of significant intrasystem uniformity in planet properties such as radius, mass, and orbital spacing, collectively termed 'peas in a pod' trends. In particular, correlations in radius and mass have been interpreted as implying uniformity in planet bulk density and composition within a system. However, the samples used to assess trends in mass tend to be small and biased. In this paper, we re-evaluate correlations in planet properties in a large sample of systems with at least two planets for which mass and radius have been directly measured, and therefore bulk density can be calculated. Our sample was assembled using the most up-to-date exoplanet catalogue data, and we compute the relevant statistics while using a procedure to 'weight' the data points according to measurement precision. We find a moderate correlation in radius and a weak correlation in the densities of adjacent planets. However, masses of neighbouring planets show no overall correlation in our main sample and a weak correlation among pairs of planets similar in size or pairs restricted to Mp<100 M_Earth, Rp<10 R_Earth. Similarly, we show that the intrasystem dispersion in radius is typically less than that in mass and density. We identify ranges in stellar host properties that correlate with stronger uniformity in pairs of adjacent planets: low Teff for planet masses, and low metallicity and old age for planet densities. Furthermore, we explore whether peas in a pod trends extend into planet compositions or interior structures. For small neighbouring planets with similar radii, we show that their masses and interior structures are often disparate, indicating that even within the same system, similarity in radii is not necessarily a good proxy for similarity in composition or the physical nature of the planets.

Figures

Figures reproduced from arXiv: 2506.05089 by the authors.

**Figure 1.** Masses, radii, densities, and period ratios of adjacent planets. The scatter graph for mass (top left), radius (top right), and density (bottom left) of a planet against the same parameter of the next planet farther from the star is plotted with observational errors indicated by the grey lines. The bottom right panel shows the period ratio between the middle and inner planet against that between the outer and middle… view at source ↗

**Figure 2.** Intrasystem dispersion in mass, radius, and density. The x-axis shows dispersion in mass for systems in the main sample, the y-axis represents dispersion in radii, and the colour of the dots corresponds to dispersion in density. The red colours indicate similarity in density, and the blue colours indicate dissimilarity. The black dashed line is 1:1. sample, D in mass is typically larger than 0.5, whereas our calcul… view at source ↗

**Figure 3.** The sample on the mass–density diagram. The black spheres represent the sample’s planets and the red spheres are the Solar System planets, plotted for comparison. Dashed black lines connect a pair of adjacent planets in the "high correlated in radius" subsample. The coloured interior curves (from red to light blue) are taken from Zeng et al. (2016) and correspond to different calculated MRR for several potential 2-l… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: ECDF of the parameter gap g in mass, radius, and density in the HCR subsample. The x-axis shows g in a certain parameter, the yaxis represents the proportion of the gaps in pairs that reached a certain value. in the HCR subsample. ECDF represents the proportion of ob…

**Figure 6.** Figure 6: HCR sample on the mass–density diagram. The dots, connected by black dashed lines, are planet pairs that belong to this sample. The coloured dots represent those planets, for which we calculated interior distance I. The red colours indicate a pair of planets at a short…

**Figure 7.** Figure 7: Interior distance in HCR sample systems. Observed I in the xaxis is plotted against expected I from non-parametric MRR (Ning et al. 2018) at the y-axis. The colours of the dots indicate stellar Teff of the system’s host star. The black dashed line is unity [PITH_FULL…

**Figure 8.** Figure 8: P-value dynamics for subsets of data points. Coloured lines indicate P-value changes during the moving window test for density depending on host star age (green) or metallicity (grey) and for masses depending on host star Teff (blue). The light-coloured shades under …

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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