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Planets larger than Neptune have elevated eccentricities

T0 review · 2 major / 8 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper establishes that the mean orbital eccentricity of close-in planets rises from about 0.05 to 0.20 at a radius near 3.5 Earth radii, matching breaks in occurrence rate and host-star metallicity and pointing to distinct formation…

desk verdict A careful, large-sample photoeccentric eccentricity measurement that suggests a real size-eccentricity step, but the missing flat-truth injection test leaves a nagging systematic worry. read the letter →

arxiv 2507.07840 v1 pith:2IUFU2AY submitted 2025-07-10 astro-ph.EP

Gregory J. Gilbert , Erik A. Petigura , Paige M. Entrican This is my paper · ORCID
classification astro-ph.EP
keywords exoplanetsorbitaleccentricityphotoeccentriceffectKeplermissionhierarchicalBayesianinferenceradiusvalleyplanetformationtransittimingvariations
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

This paper makes the case that the average orbital eccentricity of close-in planets changes sharply with planet size: the population mean rises from $\langle e \rangle = 0.05 \pm 0.01$ for planets below about 3.5 Earth radii to $\langle e \rangle = 0.20 \pm 0.03$ for larger planets. The evidence comes from eccentricity constraints for 1646 Kepler planets, 92% of them smaller than Neptune, derived by comparing transit light-curve shapes with Gaia-based stellar densities. The authors point out that this same size threshold marks abrupt changes in planet occurrence rate and host-star metallicity, which together suggest separate formation channels for small and large close-in planets. They also find that the eccentricity distribution peaks at zero for every planet size and report a tentative peak in eccentricity among radius-valley planets at $2.1\sigma$ significance.

What carries the argument

The paper uses the photoeccentric effect: a planet's transit duration relative to a circular, center-crossing transit depends on eccentricity $e$ and argument of pericenter $\omega$ through the factor $(1 + e \sin\omega)/\sqrt{1-e^2}$, so a duration anomaly can be converted into a per-planet eccentricity constraint once the stellar density is known. It couples full light-curve fitting, including Gaussian-process detrending and iterative transit-timing-variation correction, to an importance-sampling scheme that combines transit posteriors with Gaia stellar-density priors, producing joint posterior samples of $\{e,\omega\}$ for each planet. A hierarchical Bayesian model with a flexible, regularized histogram and an empirical template then turns these noisy per-planet constraints into intrinsic population eccentricity distributions while accounting for geometric detection biases.

What would settle it

Re-measure eccentricities for a sample spanning the 3-4 Earth-radius transition using an independent technique, such as radial velocities or asteroseismic stellar densities, and compare the inferred $\langle e \rangle$ values; if the jump disappears or shifts to another radius, the photoeccentric result would be an artifact of the transit-duration or stellar-density assumptions.

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Extended reading notes

Core claim

The central discovery is a size-dependent population eccentricity: small planets below roughly 3.5 Earth radii orbit on nearly circular paths with $\langle e \rangle \approx 0.05$, while larger planets have $\langle e \rangle \approx 0.20$. The transition appears in both single- and multi-transiting systems, with singles uniformly about 2.4 times more eccentric than multis. Because the same radius threshold also separates a common, metal-insensitive population of small planets from a rare, metal-rich population of large planets, the paper interprets the eccentricity jump as evidence that the two size groups formed through distinct dynamical pathways. The eccentricity distribution is self-similar in shape across size classes, peaking at $e = 0$ and declining monotonically, so the size effect is primarily a change in the spread of the distribution rather than its functional form.

Load-bearing premise

The load-bearing premise is that, after Gaussian-process detrending and transit-timing-variation correction, the measured transit durations are unbiased and the Gaia-based stellar densities are accurate, so any leftover duration anomaly is a real eccentricity signal rather than a size-dependent systematic error.

Editorial extensions

If this is right

  • Large and small close-in planets must be explained by separate formation channels, one that preserves low eccentricities for sub-Neptune-sized bodies and one that excites eccentricities for larger planets.
  • Models of planet occurrence must reproduce a coordinated break at roughly 3.5 Earth radii in eccentricity, occurrence rate, and host-star metallicity simultaneously.
  • If the radius-valley eccentricity excess is real, gap planets likely formed through collisions or atmospheric stripping, a prediction testable with radial-velocity follow-up or JWST secondary-eclipse measurements.
  • Single- and multi-transiting planets share one parent population, with singles representing the high-eccentricity, high-inclination tail, which bears on explanations of the Kepler dichotomy.
  • For planets above 4 Earth radii, the positive eccentricity-metallicity and eccentricity-period correlations constrain when and how giant planet eccentricities are excited relative to disk dispersal.

Reading between the lines

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

  • A natural extension is to test whether the 3.5 Earth-radius threshold shifts with stellar mass or orbital period, which would sharpen the formation-channel interpretation by separating intrinsic size effects from environmental ones.
  • The same hierarchical photoeccentric machinery could be applied to TESS light curves, where shorter baselines and higher noise may require combining many systems to recover the same size-eccentricity signal.
  • The paper's eccentricity-dilution argument implies that any small planet found with a confidently high eccentricity may be a marker for an unseen outer giant companion, a prediction that radial-velocity surveys could directly test.
  • If the radius-valley eccentricity peak is confirmed, it would motivate targeted searches for collision remnants or stripped cores in that radius range using atmospheric and density measurements.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 8 minor

Summary. This paper measures eccentricities for 1646 Kepler planets with periods 1–100 days and radii 0.5–16 R⊕, using the photoeccentric effect: transit durations from the ALDERAAN pipeline are compared to duration predictions from Gaia stellar densities via importance sampling, producing per-planet posterior samples in (e, ω). The authors then infer population eccentricity distributions with an approximate hierarchical Bayesian model using a non-parametric regularized histogram, later compressed into a two-parameter empirical template. The central claim is that mean population eccentricity rises from ⟨e⟩ = 0.05 ± 0.01 for planets smaller than about 3.5 R⊕ to ⟨e⟩ = 0.20 ± 0.03 for larger planets, and that this transition aligns with breaks in occurrence rate and host-star metallicity, implying distinct formation channels. Additional findings include a tentative (2.1σ) elevation of eccentricity for planets in the radius valley, and a single-to-multi eccentricity ratio of about 2.5 with similar ⟨e⟩–R_p curves for both populations.

Significance. If the size–eccentricity step is real, it is an important demographic signature that connects planet occurrence, composition, and dynamical history, and it sharpens the evidence for distinct formation channels around 3.5 R⊕. The paper's strengths are substantial: the analysis pipeline is open source; the authors run a large injection/recovery campaign; they check robustness across distributional choices (empirical, beta, half-Gaussian), binning schemes, selection cuts, and detection-bias corrections; they forward-model duration ratios; and they honestly report the weak 2.1σ radius-valley signal. The per-planet eccentricity constraints are weak (σ(e) ≈ 0.3), so the population claims rest on the ensemble analysis being unbiased as a function of planet radius. The main weakness is that the injection/recovery tests validate recovery of a step-like ground truth but do not test the null hypothesis of a size-independent eccentricity distribution; this missing test is directly relevant to the central claim.

major comments (2)
  1. [SI, Injection-and-recovery tests (Table 4, Figs. 15–20)] The validation simulations inject a step-like ground truth: small planets (Rp < 4 R⊕) drawn from a half-normal with σ = 0.03 (⟨e⟩ ≈ 0.023) and large planets drawn from a beta distribution with mean ≈ 0.23. The authors then show that the recovered ⟨e⟩ values are consistent with these injected values. This demonstrates that the pipeline can recover an injected step, but it does not test whether the pipeline could create a spurious step from a population whose eccentricity distribution is the same at all sizes. Because individual eccentricity posteriors have σ(e) ≈ 0.3, the reported rise from 0.05 to 0.20 is an ensemble-level statement; a size-dependent bias in measured T14 from, e.g., unaccounted TTV smearing, long-cadence smearing, or GP detrending could in principle produce the observed trend even if the intrinsic population is flat in planet size. The authors should inject a population with a single global f(e) (or size-independent template parameters) for all radii and show that the recovered ⟨e⟩–R_p relation is flat; analogous tests with a mild intrinsic slope would also constrain the pipeline response. This null test is the most important missing validation for the central claim.
  2. [Methods, Eq. (5); SI, Eq. (22)] The detection-bias correction in the hierarchical likelihood uses only the geometric transit probability, (1−e²)/(1+e sinω). However, Kepler's detection probability also depends on transit duration and depth, which are correlated with e and ω through the same photoeccentric relation. The injection/recovery tests do not simulate the full planet detection process: they inject synthetic transits into existing Kepler light curves and then fit them, so the recovered posteriors are conditioned on the transit being present and fitted, not on the original detection selection. The claim that Eq. (5) yields the intrinsic (rather than observed) eccentricity distribution is therefore not fully validated by the presented tests. This could affect the absolute scale of ⟨e⟩, and possibly the size-dependent trend if duration- and depth-dependent detectability vary with planet radius. I ask the authors to either add a duration-dependent detection term to Eq. (5) or demonstrate through a forward-modeled survey simulation (including the detection step) that the geometric correction alone is sufficient for the claimed precision.
minor comments (8)
  1. [Methods, first paragraph] The sentence "We first select a sample of 1209 single Sun-like stars hosing 1646 planets" contains a typo: "hosing" should be "hosting".
  2. [Introduction, paragraph 2] The phrase "has be remarkably successful at at explaining" contains duplicated words; please correct to "has been remarkably successful at explaining".
  3. [Conclusions, item 3] The phrase "Planets in the the radius valley" has a duplicated "the".
  4. [SI, Fig. 11 caption] The caption reads "for each of our five plannet size classes"; "plannet" should be "planet".
  5. [Abstract] The clause "a narrow band of low occurrence rate density which separates rocky ``super-Earths'' (1.0–1.5 Earth-radii) from gas-rich ``sub-Neptunes'' (2.0–3.0 Earth-radii" is missing a closing parenthesis after "Earth-radii".
  6. [SI, after Eq. (26)] The regularization term added to the log-likelihood, ln L = −(ν−h)², is ad hoc and not derived from the data; please justify its form and strength, or show that results are unchanged when this term is omitted (Figure 14 partially addresses this via alternative parametric models, but not for the template fit itself).
  7. [Methods, Table 1] The paper does not report the number of planets per size bin; given that the largest bins (R0 ≈ 14.6 R⊕) contain very few planets, the sigmoid fit parameters and their uncertainties would be more interpretable with effective sample sizes listed.
  8. [SI, Estimating the significance of the eccentricity peak in the radius valley] The combination of tail probabilities P(A_singles ≤ 0) and P(A_multis ≤ 0) treats the two measurements as independent, but they share the same empirical template and are drawn from the same parent population according to the paper's own conclusion; please discuss the sensitivity of the 2.1σ figure to this independence assumption.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the eccentricity measurements are inferred from external Kepler and Gaia data, and the size-eccentricity trend is not equivalent to any fitted input.

full rationale

The paper's central claim, that mean eccentricity rises from about 0.05 for small planets to about 0.20 for planets larger than roughly 3.5 Earth-radii, is derived from photoeccentric inversion of transit durations against Gaia-based stellar densities. The inference chain is self-contained: transit shapes are fit to Kepler photometry, eccentricity posteriors are obtained by importance sampling that compares the implied stellar density to the Gaia prior, and the hierarchical model fits population-level eccentricity distributions to those posteriors. The method relies on the authors' prior papers (refs 40 and 44), but that reliance is methodological rather than circular: the cited importance-sampling equivalence is a stated mathematical procedure, and the present paper validates the same pipeline with injection-and-recovery tests against external synthetic data. Those injections do simulate a step-like eccentricity ground truth, so they do not by themselves rule out a flat-truth systematic, but that is a validation limitation, not a circular reduction. The alignment with occurrence-rate and metallicity breaks is supported by independent catalog results (refs 57-59), and the radius-valley peak is tested with null injections that depopulate the gap. No equation in the paper reduces the size-eccentricity trend to a fitted parameter or to a self-referential definition.

Assumptions & free parameters 6 free parameters · 6 assumptions · 1 invented entities

The central claim depends on the photoeccentric effect (standard geometry), the accuracy of Gaia stellar densities, the modeling choices in the hierarchical Bayesian analysis (uniform e/omega prior, self-similar template, GP smoothness), and the completeness of the selection function correction. No new physical entities are required beyond an inferred population of radius-gap planets.

free parameters (6)
  • Template tail weight nu per size class = Jovians 0.68+0.31/-0.14; sub-Saturns 0.80+0.25/-0.16; sub-Neptunes 1.01+0.09/-0.06; super-Earths 1.60+0.34/-0.25…
    Fitted in Eq. 6 to each sub-population's eccentricity posteriors; controls the tail of f(e) and directly affects inferred <e>.
  • Template width scale h = Jovians 0.55+0.27/-0.21; sub-Saturns 0.60+0.29/-0.20; sub-Neptunes 1.21+0.29/-0.23; super-Earths 1.02+0.28/-0.21…
    Fitted alongside nu; scales the horizontal width of the eccentricity distribution.
  • Sigmoid transition radius x_t = Rp = 3.3 +/- 0.4 R_Earth (singles), 4.2 +/- 0.9 R_Earth (multis)
    Location of the low-to-high eccentricity transition in Eq. 10; the paper's ~3.5 R_Earth threshold is this fitted quantity.
  • Gaussian peak amplitude A in radius valley = A > 0 in 73% (singles) and 89% (multis) of posterior samples
    Amplitude of the tentative eccentricity excess in Eq. 30; the 2.1-sigma significance is computed from A.
  • GP smoothness hyperparameters ln(s), ln(l) = ln(s) ~ N(3,1), ln(l) ~ N(0,1) hyperpriors
    Hyperparameters of the Gaussian process prior on histogram bin heights; they regularize the nonparametric f(e) fit.
  • Outlier correction epsilon = 1e-6
    Ad hoc addition to parametric distributions to robustify against high-e outliers; results insensitive between 1e-9 and 1e-3.
assumptions (6)
  • standard math The transit duration formula T14 (Eq. 15) accurately describes the relation between observed duration and P, Rp/R*, b, e, omega, and rho*.
    Keplerian geometry; used throughout the importance sampling inversion.
  • domain assumption Gaia-derived stellar densities rho* are accurate to their quoted uncertainties and serve as the external calibration for eccentricity.
    Any systematic error in stellar density directly biases the inferred eccentricity distribution; see importance sampling in Methods.
  • domain assumption A uniform interim prior on e and omega (p0(e)=1) during importance sampling is appropriate.
    The hierarchical likelihood in Eq. 5 divides by p0; this prior choice is standard but is an assumption.
  • ad hoc to paper All planet size classes share the same functional form of f(e) up to the scaling parameters nu and h (Eq. 6).
    This self-similarity assumption is introduced in this paper and is load-bearing for the <e>-Rp summary; it is tested with a flexible histogram but that model also enforces smoothness.
  • standard math The geometric transit probability p = (1 + e sin(omega)) / (1 - e^2) fully corrects the sample selection bias for eccentric orbits.
    Used in Eq. 5; does not correct for Kepler pipeline detection completeness as a function of depth and duration.
  • ad hoc to paper The GP smoothness prior and the manual monotonicity enforcement on the histogram do not distort the inferred distribution shape.
    Described in SI: 'we imposed monotonicity on the PDF by extending a shallowly sloped tangent line past the first local minimum'; a subjective step.
invented entities (1)
  • Radius-valley 'gap planets' population independent evidence
    purpose: Explains the tentative 2.1-sigma eccentricity excess in the radius gap; hypothesized to be products of giant impacts or atmospheric stripping.
    The paper gives falsifiable predictions: elevated eccentricities testable by radial velocity, and tenuous atmospheres testable by JWST secondary eclipses. The existence of such a population is not established, but it is a concrete astrophysical hypothesis rather than a new fundamental entity.

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Cite this review

Pith. "Pith review of Planets larger than Neptune have elevated eccentricities." pith.science (2026). https://pith.science/paper/2IUFU2AY

@misc{pith2026250707840,
  author       = {Pith},
  title        = {Pith review of: Planets larger than Neptune have elevated eccentricities},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2IUFU2AY}},
  note         = {Machine review of arXiv:2507.07840}
}
abstract

NASA's Kepler mission identified over 4000 extrasolar planets that transit (cross in front of) their host stars. This sample has revealed detailed features in the demographics of planet sizes and orbital spacings. However, knowledge of their orbital shapes - a key tracer of planetary formation and evolution - remains far more limited. We present measurements of eccentricities for 1646 Kepler planets, 92% of which are smaller than Neptune. For all planet sizes, the eccentricity distribution peaks at e=0 and falls monotonically toward zero at e=1. As planet size increases, mean population eccentricity rises from $\langle e \rangle = 0.05 \pm 0.01$ for small planets to $\langle e \rangle = 0.20 \pm 0.03$ for planets larger than $\sim$ 3.5 Earth-radii. The overall planet occurrence rate and planet-metallicity correlation also change abruptly at this size. Taken together, these patterns indicate distinct formation channels for planets above and below $\sim$ 3.5 Earth-radii. We also find size dependent associations between eccentricity, host star metallicity, and orbital period. While smaller planets generally have low eccentricities, there are hints of a noteworthy exception: eccentricities are slightly elevated in the ``radius valley,'' a narrow band of low occurrence rate density which separates rocky ``super-Earths'' (1.0-1.5 Earth-radii) from gas-rich ``sub-Neptunes'' (2.0-3.0 Earth-radii. We detect this feature at $2.1\sigma$ significance. Planets in single- and multi-transiting systems exhibit the same size-eccentricity relationship, suggesting they are drawn from the same parent population.

Figures

Figures reproduced from arXiv: 2507.07840 by the authors.

Figure 1
Figure 1. ). Kepler gathered some 40,000 photometric measure￾ments of each star over its four-year mission. Each transit may be described with five transit shape parameters. We derive these parameters with particular care to preserve covariances and uncertainties, thereby compressing the high-dimensional photometric dataset into a low-dimensional catalog of tran￾sit shape measurements. Next, we combine transit shape and stell… view at source ↗
Figure 2
Figure 2. Schematic description of our methods. (a) We began with 1646 photometric lightcurves observed by Kepler. We fit each lightcurve using a five-parameter transit model to produce posterior samples of period P , transit epoch t0, planet-to-star-radius ratio Rp/R⋆, impact parameter b, and transit duration T. (b) By comparing our transit-derived T to the value predicted for a circular, center-crossing transit T0 and apply… view at source ↗
Figure 3
Figure 3. Mean eccentricity ⟨e⟩ as a function of planet radius Rp for single-transiting systems (top) and multi-transiting systems (bottom). Singles and multis exhibit a similar ⟨e⟩-Rp relationship, with planets larger than Neptune having about three times the eccentricity of smaller planets. Singles are 2.4 ± 0.9 times more eccentric than multis across the full range of planet sizes. Analysis & Results Figures 3, 4, and 5 su… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: Mean eccentricity ⟨e⟩ as a function of adjusted planet radius near the radius gap for single-transiting systems (top) and multi-transiting systems (bottom). The “adjusted radius” is calculated following 29 and 56 to account for the period depen￾dence of the radius gap.…
Figure 5
Figure 5. Figure 5: Mean eccentricity ⟨e⟩ as a function of (a) host star metallicity [Fe/H] and (b) orbital period P for each planet size class. Planets larger than 4 Earth-radii exhibit elevated eccentricities compared to their smaller counterparts across all values of [Fe/H] and P . Lef…
Figure 7
Figure 7. Figure 7: Constraints on the eccentricities of individual planets grouped according to size class (indicated at top right). Samples of {e, ω} were generated via importance sampling from Kepler data. For this visualization, we randomly selected 50 planets from each planet class a…
Figure 8
Figure 8. Figure 8: Population-level distribution of eccentricity f(e) inferred using a flexible histogram for Kepler single-transiting systems (top) and multi-transiting systems (bottom). Colorful dashed lines display results for each of five planet size classes, and the solid black line…
Figure 10
Figure 10. Figure 10: Distribution of observed transit duration ratios {T /T0}obs (grey histograms) compared to duration ratios predicted by our best-fit empirical model {T /T0}mod (colored lines) for each of five planet size classes. Error bars on each histogram bin are based on the 16,th…
Figure 11
Figure 11. Figure 11: Maximum likelihood posterior inferences of the eccentricity distribution f(e) assuming different parametric models for each of our five plannet size classes. The thick colored line shows our preferred empirical model derived from a flexible histogram. Beta (solid line…
Figure 12
Figure 12. Figure 12: Cumulative distribution functions (CDF) for transit duration ratio T /T0 for each of five planet size classes. Observations from our transit modeling of Kepler photometry are shown as a grey shaded region. Forward-modeled values of T /T0 based on our empirical model a…
Figure 13
Figure 13. Figure 13: Mean eccentricity as a function of adjusted planet radius for planets in single-transiting (top) and multi-transiting (bottom) systems. Smooth blue/orange curves denote the posterior fit and 68% confidence interval for a logistic sigmoid + Gaussian model, which we use…
Figure 14
Figure 14. Figure 14: Relationship between mean eccentricity ⟨e⟩ and planet size Rp derived using our empirical distribution (left) vs a beta distribution (middle) or half-Gaussian distribution (right). Results are qualitatively consistent regardless of which model is adopted. While there …
Figure 15
Figure 15. Figure 15: Results of specific bias tests used to validate our injection-and-recovery experiment. Specific bias is calculated from Equation 31 following (92). Grey histograms show the distribution of specific biases for Rp/R⋆ (left), b (middle), and T14 (right) for the 1302 synt…
Figure 17
Figure 17. Figure 17: Recovered ⟨e⟩ − Rp relationship for ∼ 900 simulated planets between Rp = 1 − 4R⊕ and P = 1 − 100 days. Left: The dashed black line indicates the ground-truth ⟨e⟩=0.023. Right: Due to measurement uncertainty, some “observed” radii (black points) are different than thei…
Figure 18
Figure 18. Figure 18: Recovered ⟨e⟩ − Rp relationship for injection test with a simulated radius gap between Rp = 1.75 − 1.93R⊕. The blue shaded region indicates the region from which all ground truth planets were removed. Left: Difference in inferred ⟨e⟩ for this simulation vs. the “no ga…
Figure 19
Figure 19. Figure 19: Same as [PITH_FULL_IMAGE:figures/full_fig_p024_19.png]
Figure 20
Figure 20. Figure 20: Same as [PITH_FULL_IMAGE:figures/full_fig_p024_20.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.