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The Orbital Eccentricity-Radius Relation for Planets Orbiting M Dwarfs

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Using transit photometry for 236 planets orbiting M dwarfs, this paper reports a sharp transition from low to high orbital eccentricity at about 3.5 Earth radii, mirroring the relation previously found for planets around Sun-like stars.

desk verdict Plausible extension of the eccentricity-radius relation to M dwarfs, but the headline transition lacks a null-model significance test and rides on a thin high-radius sample. read the letter →

arxiv 2507.07169 v1 pith:ZZKAXX72 submitted 2025-07-09 astro-ph.EP astro-ph.SR

Sheila Sagear , Sarah Ballard , Gregory J. Gilbert , Mariangel Albornoz , Christopher Lam This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords exoplanetsorbitaleccentricityMdwarfstarsradiusgapphotoeccentriceffecttransitphotometryTESSKepler
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

Using transit photometry for 236 confirmed planets and candidates orbiting M dwarf stars, this paper asks whether the orbital eccentricity-radius relation seen for planets around Sun-like stars also holds around the most common stars in the galaxy. The authors extract individual eccentricity constraints from transit shapes together with a stellar-density prior, then infer the underlying eccentricity distribution in radius bins with a hierarchical Bayesian model. They report a clear transition from low to high eccentricity at about 3.5 Earth radii, with planets above that size roughly five times more eccentric on average than smaller planets. They also find no evidence that M dwarf planets near the radius gap have elevated eccentricities, which they interpret as supporting photoevaporation rather than giant impacts as the main atmospheric-loss mechanism for these planets.

What carries the argument

The photoeccentric effect is the load-bearing technique: a planet's transit duration and ingress/egress shape depend on its speed across the stellar disk, which for a known stellar density maps to a joint constraint on eccentricity e and argument of periastron ω. The paper implements it by fitting transit light curves with duration as a free parameter and then importance-sampling the (e, ω) posterior against a stellar-density prior, requiring the density inferred from the transit (assuming a circular orbit) to match the independently known stellar density. Population-level inference is carried out by a hierarchical model that assumes the parent eccentricity distribution in each radius bin is a Beta distribution constrained to peak at e=0 and decrease monotonically (alpha<1, beta>1), reparametrized to avoid prior biases. A logistic sigmoid is then fitted to the binned mean eccentricities to locate and characterize the low-to-high-eccentricity transition.

What would settle it

Re-fit the same 236 planets with a two-component eccentricity model that allows a secondary peak away from e=0 and compare the inferred transition; if the ~3.5 Earth radii step weakens or moves, the reported relation is an artifact of the Beta prior. The observational counterpart is a radial-velocity survey of M dwarf planets straddling 3.5 Earth radii, which would show whether eccentricities really are higher above that radius than below it.

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Extended reading notes

Core claim

The paper's central claim is that the eccentricity-radius relation for M dwarf planets is a rising step function: small planets orbit on nearly circular paths while planets larger than about 3.5 Earth radii have systematically higher eccentricities. Fitting a logistic sigmoid to the binned mean eccentricities locates the transition at 3.1+1.5/-1.2 Earth radii, with the ratio of high- to low-eccentricity levels at 4.6+5.8/-1.9, consistent within 1σ with the transition measured for planets orbiting FGK dwarfs. The authors further claim that, unlike the FGK case, M dwarf planets near the radius gap show no significant elevation in eccentricity: multi-transit planets stay at low eccentricity at all radii, and the modest excess seen for single-transit planets between 1.9 and 3.0 Earth radii is consistent with a flat line at roughly 1σ. This asymmetry, if physical, is taken as evidence that photoevaporation or core-powered mass loss, rather than giant impacts, dominate atmospheric stripping for M dwarf planets.

Load-bearing premise

The chain of inference assumes that in every radius bin the true eccentricity distribution has exactly one shape—highest at zero eccentricity and falling monotonically—so a population of moderately eccentric planets sitting away from zero would be invisible to the model and could bias the reported average eccentricities and the location of the transition.

Editorial extensions

If this is right

  • If the transition is real, planet formation around M dwarfs and FGK dwarfs produces two distinct radius regimes, with the boundary near 3.5 Earth radii, and the dynamical evolution of larger planets leaves them on eccentric orbits regardless of host-star mass.
  • The absence of elevated eccentricities at the radius gap for multi-transit M dwarf planets would point to photoevaporation or core-powered mass loss, mechanisms that remove atmospheres without changing orbital dynamics, as the dominant sculptors of the M dwarf radius valley.
  • The consistency of the transition radius between M dwarf and FGK dwarf planets (3.1+1.5/-1.2 versus 3.3±0.4 and 4.2±0.9 Earth radii) suggests the boundary between rocky and gas-rich planet formation channels is set by planet properties rather than by host star mass.
  • If single-transit M dwarf planets near the radius gap do have modestly elevated eccentricities, giant impacts or planet-planet scattering may still play a role in atmospheric loss for dynamically hot, single-planet systems.

Reading between the lines

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

  • A testable extension would be to run the same hierarchical inference on a larger joint Kepler-TESS sample; if the transition stays pinned near 3.5 Earth radii as the sample grows, the photoevaporation-versus-giant-impact interpretation would gain strength.
  • The authors leave implicit that their Beta-distribution model cannot represent a separate high-eccentricity population, so a re-analysis with a two-component mixture would test whether the e_high/e_low ratio and transition location are artifacts of the assumed distributional shape.
  • A prediction of their interpretation, not stated in the paper, is that radial-velocity eccentricities of M dwarf planets above roughly 3.5 Earth radii should be systematically higher than those below, and that the single-transit radius-gap excess, if real, should grow with a larger sample.
  • Because TESS single-transit systems are likely contaminated by undetected multi-planet systems, the reported single-versus-multi eccentricity contrast could sharpen as longer TESS baselines reveal hidden companions, changing the inferred radius-gap behaviour for singles.
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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

3 major / 5 minor

Summary. The paper constrains orbital eccentricities for 236 transiting planets orbiting M dwarfs using the photoeccentric effect on TESS and Kepler light curves, then applies a hierarchical Bayesian model with Beta distributions to infer the underlying eccentricity distribution in radius bins. The authors report a transition from low to high eccentricity at approximately 3.5 R_Earth, with e_high/e_low about 4.6, and interpret this as analogous to the FGK-dwarf eccentricity-radius relation found by G25. They also investigate eccentricity near the radius gap, finding only about 1-sigma evidence for elevated eccentricities among single-transit planets and no evidence among multi-transit planets, and discuss implications for photoevaporation versus giant-impact atmospheric loss.

Significance. If the transition is real, this would be the first clear demonstration that the eccentricity-radius relation for M-dwarf planets mirrors that of FGK dwarfs, implying common formation and evolution channels across spectral types. The paper is methodologically careful: it validates the importance-sampling transit fit against the prior Kepler-based analysis (Appendix A), uses an external stellar density prior, and directly compares to G25 with identical binning. The main limitation is that the central transition claim lacks a formal significance test, and the robustness of the result to the assumed Beta distribution shape is not quantified. With a formal null-model comparison and additional robustness checks, this would be a valuable contribution to the demographics of small exoplanets.

major comments (3)
  1. [Section 4.2, Eq. (10)] The logistic sigmoid fit to the five binned <e> points is presented without any statistical comparison to a null model with constant <e> across radius. The paper only applies a flat-line test to the Gaussian radius-gap peak (Eq. 12), not to the global transition. Given that the two highest-radius bins contain only 14 and 18 planets, respectively (Table 3), and the 7.5-16 R_Earth bin is entirely composed of single-transit TESS planets, a steep sigmoid can easily fit noise. Please add a formal significance test, such as a Delta-chi^2 or Delta-BIC comparison between the sigmoid and a constant model, or a posterior predictive p-value derived from the hierarchical model, and report the resulting significance. As written, the Conclusions statement 'We show marked evidence for a transition' is not quantitatively supported.
  2. [Section 3.2.1] The assumed Beta distribution with alpha<1 and beta>1 is monotonically decreasing and peaks at e=0; it cannot represent a separate high-eccentricity population or a bump away from zero. The authors acknowledge they 'lack sufficient physical understanding of the true shape' but adopt this form for reproducibility and efficiency. The empirical histogram model in Appendix B is used only for qualitative comparison (Figure 12), and the transition parameters of Eq. (10) are not re-derived from that model. The robustness of the central transition claim to this modeling choice is therefore untested. Please demonstrate that the Beta assumption does not bias the binned <e> values, for example by fitting a two-component mixture or by quantifying the transition with the empirical histogram model and showing that the result is unchanged.
  3. [Section 4.2, Table 3] The combined-sample transition may be driven by the survey and multiplicity composition of the high-radius bins: the 7.5-16 R_Earth bin contains only single-transit TESS planets, and single-transit systems are known to have higher eccentricities (Section 4.1). The paper compares singles and multis in Figure 3, but does not test whether the sigmoid transition is present within the single-transit subsample alone or after controlling for multiplicity and survey. The physical interpretation in Section 5.1 assumes a radius-driven effect, but a multiplicity-driven selection effect is a competing explanation. Please add a test that isolates the radius effect from the multiplicity effect, such as fitting the sigmoid to the single-transit sample only, or including multiplicity as a covariate in the hierarchical model.
minor comments (5)
  1. [Section 3.4] The text states that the Beta distribution is modeled with alpha < 1 and beta < 1, which is inconsistent with Section 3.2.1, where beta > 1 is required for a monotonically decreasing distribution peaking at e=0. This appears to be a typo and should be corrected.
  2. [Section 3.1.1] The 'Gelman-Ruban statistic' should read 'Gelman-Rubin statistic.'
  3. [Section 3.4] The sentence 'We take the mean of these median values as <e>' is confusing: it is unclear whether the authors take the mean or the median of the posterior draws of the Beta distribution's mean, and the wording conflates the two operations.
  4. [Section 4.2, Figure 2] The binned <e> values and the sigmoid fit parameters are only presented in figures; a machine-readable table with the numerical values of <e>, their uncertainties, and the sigmoid parameters (B, L, k, x_t) would allow readers to reproduce the test requested in the first major comment.
  5. [Abstract and Section 6] The abstract and conclusions quote the transition at 3.5 R_Earth, while the fitted transition in Section 4.2 is 3.1(+1.5/-1.2) R_Earth; please clarify that 3.5 R_Earth is the bin edge rather than the fitted transition location, or quote the fitted value consistently throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the M-dwarf eccentricity-radius relation is derived from transit posteriors plus external priors, with prior work used only for sample continuity and comparison.

full rationale

The derivation chain is self-contained: individual eccentricity posteriors come from transit light-curve fits via the photoeccentric effect, using an external stellar density prior from Stassun et al. (2019) and Mann et al. empirical relations; the hierarchical Beta-distribution fit is a stated modeling choice justified by an empirical histogram check; and the claimed transition is a description of the logistic sigmoid fit to the resulting binned <e> values, not an out-of-sample prediction. The S23 and G25 citations are used for sample reuse, method validation, and as comparison datasets, but the M-dwarf transition radius of 3.1+1.5/-1.2 Rearth comes from this paper's own fit, not from those prior works. The radius-gap diagonal binning uses the independently authored Ho et al. (2024) relation as an external input, and the Beta(alpha<1, beta>1) shape constraint is an acknowledged modeling assumption rather than an input that already contains the eccentricity-radius trend. The absence of a formal null-model significance test for the global sigmoid is a statistical robustness concern, not a circularity. No equation or fitted parameter reduces the target relation to its own inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard photoeccentric assumptions, an externally measured stellar density prior, and a chosen parametric form for the parent eccentricity distribution. No new physical entities are introduced. The main fitted quantities are the Beta distribution parameters per radius bin and the summary sigmoid/Gaussian parameters.

free parameters (4)
  • Beta distribution shape parameters (alpha, beta or mu, tau) per radius bin = posterior samples; not individually tabulated
    The hierarchical model fits a separate Beta parent distribution to each radius bin and computes <e> from it; the eccentricity-radius trend depends on these fitted shapes.
  • Logistic sigmoid parameters B, L, k, x_t = x_t = 3.1+1.5/-1.2 Rearth; e_high/e_low = 4.6+5.8/-1.9
    A four-parameter sigmoid (Eq. 10) is fit to the five binned <e> points to locate the transition; the quoted transition radius is a fitted quantity, not a measured observable.
  • Gaussian peak parameters A, B, x_p, s = A>0 for 69% of samples for singles and 49% for multis
    Eq. 12 is used to test for elevated eccentricity near the radius gap; the significance claim is read from the posterior of the amplitude A.
  • Transit model parameters per planet (P, t0, log(T14), log(Rp), b, q1, q2) = reported in machine-readable Table 2
    These are fitted to each transit light curve and feed the importance-sampled eccentricity posteriors; they are necessary inputs to the central claim.
assumptions (5)
  • domain assumption Photoeccentric effect formalism correctly converts transit duration, impact parameter, and stellar density prior into eccentricity constraints.
    The entire eccentricity inference rests on this formalism (Dawson & Johnson 2012; MacDougall et al. 2023a). Any systematic failure would bias all posteriors.
  • domain assumption Underlying eccentricity distribution in every radius bin follows a Beta distribution with alpha<1 and beta>1.
    Section 3.2.1 selects this functional form, enforcing a monotonic decrease from e=0. The authors explicitly note they lack sufficient physical understanding of the shape; a true bimodal distribution cannot be represented.
  • domain assumption Stellar density prior from the TIC (Stassun et al. 2019) is accurate.
    Equation 2 compares the transit-derived density to rho_true from the TIC, which relies on Mann et al. empirical mass-radius relations and Gaia parallaxes. Systematic errors in this prior propagate directly into eccentricity posteriors.
  • domain assumption Radius gap boundary from Ho et al. 2024 applies to M dwarfs at the sample median stellar mass.
    Diagonal period-radius bins are defined using the SVM relation of Ho et al. 2024 (Eq. 11), evaluated at the sample median stellar mass of 0.55 solar masses. This assumes the FGK-derived gap slope and intercept hold for M dwarfs.
  • standard math Uniform priors on e and omega for importance sampling.
    Test values for e and omega are drawn uniformly (Section 3.1.2); the final posteriors are importance-weighted, so the prior is not load-bearing.

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Cite this review

Pith. "Pith review of The Orbital Eccentricity-Radius Relation for Planets Orbiting M Dwarfs." pith.science (2026). https://pith.science/paper/ZZKAXX72

@misc{pith2026250707169,
  author       = {Pith},
  title        = {Pith review of: The Orbital Eccentricity-Radius Relation for Planets Orbiting M Dwarfs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZZKAXX72}},
  note         = {Machine review of arXiv:2507.07169}
}
read the original abstract

The orbital eccentricity-radius relation for small planets is indicative of the predominant dynamical sculpting processes during late-stage orbital evolution. Previous studies have shown that planets orbiting Sun-like stars exhibit an eccentricity-radius trend such that larger planets have higher orbital eccentricities, and that radius gap planets may have modestly higher orbital eccentricities than planets on either side of the radius gap. In this work, we investigate the trend for a sample of smaller M dwarf stars. For a sample of 236 single- and multi-transit confirmed planets or candidates discovered by the TESS and Kepler missions, we constrain orbital eccentricity for each planet from the transit photometry together with a stellar density prior. We investigate the binned eccentricity-planet radius relation for the combined planet sample and present evidence for a positive eccentricity-radius relationship with elevated eccentricities for planets larger than 3.5 R_earth, similar to the trend for planets orbiting Sun-like stars. We find modest evidence that single-transit M dwarf planets near the radius gap exhibit higher eccentricity, consistent with trends for Sun-like stars. However, we see no evidence for an increased eccentricity near the radius gap among multi-transit M dwarf planets. We discuss implications for these results in the context of predominant atmospheric loss mechanisms: namely, supporting evidence for photoevaporation in M dwarf planets vs. planet-planet collisions or giant impacts in FGK dwarf planets.

Figures

Figures reproduced from arXiv: 2507.07169 by the authors.

Figure 1
Figure 1. Top: Best-fit parent eccentricity distributions for the entire sample of singles (green) and multis (blue) in this work. Middle: Best-fit parent eccentricity distributions for singles and multis for the sample of M dwarf KOIs in this work. The best-fit distributions for both populations are distinct, as shown in S23. Bottom: Same as left panel, but for the sample of TOIs in this work. The difference in parent distri… view at source ↗
Figure 2
Figure 2. ⟨e⟩ vs. planet radius bins for the sample of M dwarf planets (red points). The red error bars present the 16th and 84th percentiles of ⟨e⟩. The red histogram represents the number of M dwarf planets in each radius bin (right-hand vertical axis). The median logistic sigmoid model is plotted in dark blue. The 16th and 84th percentiles of the logistic sigmoid are denoted by the dark blue shaded regions. in [PITH_FULL_… view at source ↗
Figure 3
Figure 3. Left: ⟨e⟩ vs. adjusted planet radius radj bin centers for singles with 0.5 < radj < 5.1 R⊕ (red points). The red error bars present the 16th and 84th percentiles of ⟨e⟩. The red histogram represents the number of M dwarf planets in each bin (right-hand vertical axis). Right: Same as left panel, but for multis. M dwarfs resemble that of FGK dwarfs? To this end, we framed this study to enable direct comparison to G25,… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: ⟨e⟩ vs. planet radius bin centers for the sample of M dwarf planets in this work (red points) and for FGK dwarf planets from G25 (teal points). The error bars repre￾sent the 16th and 84th percentiles of ⟨e⟩. The red histogram represents the number of M dwarf planets in…
Figure 5
Figure 5. Figure 5: Left: ⟨e⟩ vs. adjusted planet radius bin centers for the sample of M dwarf singles in this work (red points) and for FGK dwarf singles from G25 (teal points), according to the diagonal binning mechanism described in Section 5.1. The error bars represent the 16th and 84…
Figure 6
Figure 6. Figure 6: Left: On the top panel, [F e/H] for single-transit planet hosts associated with each adjusted radius bin (purple). On the bottom panel, ⟨e⟩ vs. adjusted planet radius bin centers for the sample of M dwarf singles in this work (teal). Right: Same as left panel, but for …
Figure 7
Figure 7. Figure 7: Top: Radius distribution of M dwarf planets in this sample. Middle: [Fe/H] vs. planet radius for the M dwarf planet sample. Bottom: ⟨e⟩ as a function of binned planet radius. As G25 showed for planets around FGK stars, we demonstrate an apparent transition in planet oc…
Figure 8
Figure 8. Figure 8: Left: e vs. ω posteriors for KOI 247.01 performed with the method from S23; namely, by directly sampling √ esinω and √ ecosω during the transit fit with the exoplanet software. Right: e vs. ω for KOI 247.01 performed with the method described in Section 3, using the im…
Figure 9
Figure 9. Figure 9: Left: Eccentricity posterior generated by fitting the first nine chronological transits of TOI 555.01. Right: Eccentricity posterior generated by fitting the first nine chronological long-cadence transits of KOI 247.01 [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: Kernel Density Estimates (KDEs) for the planets in each of five radius bins. and where ∆e = emax−emin M . We use M = 17 bins, setting individual bin widths such that the K × N eccentricity samples are evenly divided within M bins, and draw each bin height parameter θm…
Figure 11
Figure 11. Figure 11: Median empirical eccentricity models for planets in each of the five radius bins in [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]

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