Pith. sign in

REVIEW 4 major objections 4 minor 5 references

The Orbital Eccentricity--Radius Distribution for Warm, Single Planets in TESS

T0 review · 4 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Warm single planets split into two eccentricity families, with the excited share rising steeply above about ten Earth radii.

desk verdict A genuinely useful new TESS-wide eccentricity–radius analysis, but the headline high-e Jovian fraction depends on a modeling choice the paper doesn't defend. read the letter →

arxiv 2602.20015 v2 pith:WV6Q4HIP submitted 2026-02-23 astro-ph.EP

Tyler R. Fairnington , Jiayin Dong , Chelsea X. Huang , Emma Nabbie , George Zhou , Duncan Wright , Karen A. Collins , David Ciardi
show 35 more authors
Jon M. Jenkins David W. Latham George Ricker Samuel N. Quinn Sara Seager Avi Shporer Roland Vanderspek Joshua N. Winn Khalid Barkaoui Allyson Bieryla Lars Buchhave Dmitry Cheryasov Jessie Christiansen Courtney Dressing Akihiko Fukui Alexey Garmash Steven Giacalone Eric G. Hintz Steve B. Howell Keisuke Isogai Jerome de Leon Jorge Lillo-Box Felipe Murgas Norio Narita Louise D. Nielsen Enric Palle Markus Rabus Benjamin V. Rackham Richard P. Schwarz Gregor Srdoc Denise C. Stephens Gavin Wang Noriharu Watanabe Francis P. Wilkin Joe Williams
This is my paper · ORCID
classification astro-ph.EP
keywords eccentricitydistributionwarmJupitersphotoeccentriceffecthierarchicalBayesiananalysisplanetradiusTESSsingle-transitingplanetstransitduration
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 argues that the eccentric orbits of warm (8–200 day) single-transiting planets are not drawn from one smooth population. Instead, a hierarchical analysis of 347 TESS planets finds two components: a dominant near-circular mode and a separate dynamically excited mode with mean eccentricity above 0.6. The fraction of planets in the excited mode rises steeply with planet radius, crossing over at a break radius of about 9.8 Earth radii. Below that size, sub-Neptunes and sub-Saturns mostly stay on the low-eccentricity track; above it, warm Jovians are frequently eccentric, with roughly 59% assigned to the high-e mode. This matters because eccentricity encodes whether a planet formed quietly in a disk or was later scattered or perturbed.

What carries the argument

The central object is the photoeccentric effect: the ratio of the stellar density derived from the transit light curve under a circular-orbit assumption (the pseudo-density) to the true stellar density from SED/isochrone fitting yields, via g(e,ω) = (1+e sinω)/sqrt(1−e^2), a joint constraint on eccentricity e and argument of periastron ω. The population-level engine is a three-stage hierarchical Bayesian model: a two-component Beta mixture for eccentricity, with the mixture weight set by a logistic sigmoid function of planet radius, so the transition radius Rbr and the low-e/high-e component means are inferred simultaneously while propagating radius uncertainties.

What would settle it

Re-run the hierarchical mixture including the 47 excluded grazing-transit candidates with an explicit high-impact-parameter model; if their inclusion pulls the Jovian high-e fraction down toward the sub-Saturn level or moves the break radius above 12 Earth radii, the two-component/transition claim fails. Alternatively, measure eccentricities for a sample of 30–50 of these warm Jovians by radial velocity; if the RV eccentricities are predominantly below 0.3, the photoeccentric high-e mode is an artifact.

Watch

Extended reading notes

Core claim

On the paper's own terms: using the photoeccentric effect—where a transiting planet's light-curve duration betrays its orbital speed and hence its eccentricity—the authors infer the population-level eccentricity distribution of 347 warm single-planet systems observed by TESS. A two-component Beta mixture, with membership governed by a logistic sigmoid of radius, cleanly separates the population into a low-eccentricity component (mean e ~ 0.07) and a high-eccentricity component (mean e ~ 0.62). The high-e fraction grows from about 15% for 1–4 Earth-radii planets to about 59% for 8–16 Earth-radii Jovians, with a transition at Rbr = 9.8+1.4−1.1 Earth radii. The authors interpret this as evidenc

Load-bearing premise

The central result relies on removing 47 planets whose transits are almost grazing (impact parameter at least 0.9), because such transits can look like eccentric orbits; if those planets are actually eccentric, the measured high-eccentricity fraction and break radius would be off, and the paper does not test this.

Editorial extensions

If this is right

  • If the claim holds, warm Jupiters are not uniformly circularized; a majority have eccentricities around 0.6, so high-eccentricity migration or scattering must be common for giant planets at 8–200 day periods.
  • Sub-Saturns (4–8 R⊕) behaving like sub-Neptunes argues against the idea that most sub-Saturns are simply failed gas giants with giant-planet-like dynamics; their dynamical history resembles smaller planets.
  • The existence of a ~15% eccentric sub-Neptune tail implies a population of small planets excited by unseen companions, predicting detectable outer companions or transit-timing variations around those systems.
  • The break radius near 10 R⊕ provides a target for formation models: whatever process pumps eccentricity must switch on sharply between 4 and 16 Earth radii.
  • The observed distribution is transit-selected; accounting for detection completeness will shift the intrinsic distribution, but the qualitative rise of eccentricity with radius should persist.

Reading between the lines

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

  • If the 47 removed grazing-transit systems were included, the high-eccentricity fraction could shrink: grazing transits shorten durations and mimic eccentric orbits, so the reported 59% Jovian high-e share and the 9.8 Earth-radii break may be upper bounds rather than intrinsic values.
  • A natural next test is to apply the same sigmoid mixture to warm multi-planet systems, which should show a much smaller high-e fraction; that would confirm that the high-e mode is tied to single-planet architectures, as the paper expects.
  • The radius-continuous model predicts a specific, testable conditional distribution: for any newly discovered warm single planet with a measured radius, the probability it belongs to the high-e mode is a smooth function of radius; future TESS samples can check whether the predicted logistic curve reproduces out-of-sample eccentricities.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper infers the eccentricity distribution of warm, single transiting planets in TESS using the photoeccentric effect within a hierarchical Bayesian framework. It first analyzes discrete radius bins (sub-Neptunes, sub-Saturns, Jovians) and then introduces a radius-continuous three-stage mixture model in which the low-eccentricity fraction varies with planet radius through a logistic sigmoid. The central claims are that the warm-single population is best described by two eccentricity components, that the high-eccentricity fraction increases strongly with radius with a break radius near 9.8 R⊕, and that warm Jovians are frequently eccentric (59% high-e fraction). A non-negligible tail of high-eccentricity sub-Neptunes is also claimed.

Significance. If the results hold, this would be an important homogeneous, all-sky characterization of the radius–eccentricity relation for warm single planets, unifying previously segmented TESS and Kepler studies. The analysis pipeline is state-of-the-art: it uses photoeccentric likelihoods with hierarchical Bayesian modeling, validates a Gaussian-approximation shortcut against full posterior chains, performs a 30% random-dropping robustness test, and checks individual photoeccentric constraints against published radial-velocity eccentricities. These are real strengths. However, the central quantitative claims are conditional on a parameterization that is not formally model-selected and is not tested against equally plausible alternatives; the current manuscript overstates the strength of evidence for bimodality.

major comments (4)
  1. [§4.2, Eq. (5), Table 3] The radius-continuous model fixes the component means µ_low and µ_high as global constants. Table 2's independent discrete Beta-mixture fits show that the low-e component mean rises from 0.028 for sub-Neptunes to 0.111 for sub-Saturns to 0.225 for Jovians. Under the continuous model with µ_low = 0.070, moderately eccentric Jovians (e ~ 0.2–0.3) that the discrete fit places in the low-e component are reassigned to the high-e component. This explains the difference between the Jovian high-e fraction of 0.59 in Table 3 and w2 = 0.37 in Table 2. Because the model can express radial change only through π_low(Rp), a radial drift in the location of the low-e component is absorbed as an apparent increase in high-e membership. The paper does not test a model with radius-dependent µ_low. This is load-bearing for the headline 59% high-e fraction and for Rbr. Please rerun with a flexible µ_low(Rp) (
  2. [§5.1 and Abstract] The abstract states that the population is 'best described by two components' and that bimodality is detected at '>4σ', but §5.1 explicitly says 'we do not compute Bayesian evidences for the hierarchical models considered here.' No model comparison between the single-Beta and Beta-mixture models is performed. A credible interval excluding w2 = 0 at 4σ is evidence for a non-zero second component, not for bimodality or for the mixture being the best description. The language in the abstract and conclusions should be softened unless formal model selection (e.g., PSIS-LOO, WAIC, or cross-validated predictive comparison) is added. As it stands, the central 'two-component' claim is not formally supported.
  3. [§3.2, §4.1, and both abstracts] The manuscript contains inconsistent sample definitions. §3.2 says '374 planets are therefore used in our final eccentricity distribution,' while §4.1 and the full-text abstract use N = 347. The initial abstract block reports N = 219, P = 8–50 days, Rbr = 9.2 R⊕, and a 65% Jovian high-e fraction, whereas the full-text abstract and body report N = 347, P = 8–200 days, Rbr = 9.8 R⊕, and a 59% high-e fraction. These are incompatible sets of numbers. The reader cannot tell which sample and which results are the definitive ones. This must be reconciled in any revised version.
  4. [§3.2] The removal of 47 targets with >50% of posterior samples at b ≥ 0.9 is not tested for sensitivity. Grazing/high-impact-parameter transits show shortened durations that can mimic the photoeccentric signature of high eccentricity; if the removed systems are preferentially eccentric, the inferred high-e fraction and break radius would be biased. Unlike the 13 unconstrained-eccentricity systems, which were explicitly re-tested, this larger and arguably more dangerous cut has no robustness test. Please report the sensitivity of the §4.2 results to this cut, or provide a quantitative argument that the bias direction and magnitude are negligible.
minor comments (4)
  1. [Title/Abstracts] The title in the LaTeX source has spacing errors ('W arm', 'inTESS'), and the first abstract block differs from the full-text abstract. This appears to be a version-control issue, but as submitted it is confusing.
  2. [§4.1] There is a duplicated word: 'find our results are consistent consistent to well within 1σ.'
  3. [§5.1] The phrase 'a 4σ credible interval of w2 > 0' is unclear; credible intervals are two-sided, and a one-sided exclusion of zero is not reported in standard form. Please state the actual posterior probability or interval.
  4. [Table 4] The table caption uses 'Rp < 6 R⊕' while the text mentions 'Rp < 6 R⊕' and 'Rp < 4 R⊕' in different places; please make the selection criterion consistent and explicit.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the eccentricity–radius trend is an empirical HBM fit with external photoeccentric calibration, not a derivation whose output is equivalent to its input.

full rationale

The paper's central results (two-component Beta mixture, sigmoid π_low(Rp), R_br, high-e fractions) are obtained by fitting a hierarchical Bayesian model to the TESS photoeccentric data, not by deriving a prediction from first principles. Equations (5)–(7) define the model: π_low(Rp) is a logistic sigmoid and the reported mean-eccentricity trend is E[e|Rp] = π_low µ_low + (1−π_low) µ_high. Thus the 'increase of high-e fraction with radius' and the 'break radius' are re-expressions of fitted parameters, but the paper transparently frames them as inferences and does not claim an a priori prediction. The photoeccentric relation (Eqs. 1–2) is calibrated externally (Dawson et al. 2012; Kipping 2010), and the authors validate individual eccentricities against published RV solutions (Figure 3). Self-citations to Dong et al. (2021a) and Fairnington et al. (2025) supply methodology only; the models are re-fit on a new 347-planet TESS sample. The paper also states it does not compute Bayesian model evidence (§5.1), so the two-component description is not advertised as a formally selected model. The grazing-transit cut and the fixed global µ_low in the continuous model are model-sensitivity concerns, not circular reductions: the data could in principle have yielded a flat or opposite sigmoid, and the discrete binned analysis provides a less parametric cross-check. No load-bearing step reduces, by the paper's equations or by self-citation, to its own inputs.

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

The central model is a heavily parameterized empirical fit: 8 hyperparameters (plus 15 discrete-bin Betas) are fitted to 347 systems. The only physical input is the photoeccentric effect; no new physics is postulated. The free parameters are the actual content of the result, so the 'discovery' is a compressed description of the data, not a theory-derived prediction.

free parameters (4)
  • R_br (break radius) = 9.8+1.4-1.1 R⊕
    Midpoint of the logistic sigmoid describing the low-e fraction as a function of planet radius; fitted directly to the hierarchical model (Equation 5-6, Table 3).
  • lambda (transition steepness) = 15+7-10
    Steepness of the radius-dependent sigmoid; fitted (Table 3).
  • pi_low_small, pi_low_large = 0.852+0.065-0.051, 0.24+0.11-0.16
    Asymptotic low-e membership fractions for small and large radii; fitted (Table 3).
  • mu_low, kappa_low, mu_high, kappa_high = 0.070, 14, 0.616, 12.2 (medians)
    Beta-distribution means/concentrations for the two eccentricity components; fitted (Table 3).
assumptions (5)
  • domain assumption Photoeccentric effect relation g(e,ω) = (1+e sinω)/sqrt(1-e^2), and the pseudo-density comparison ρ̃/ρ* = g^3
    Equations (1)-(2); the entire eccentricity inference rests on this standard relation from transit geometry.
  • domain assumption Geometric transit-probability weighting p(obs) ∝ (R*/a)(1+e sinω)/(1-e^2)
    Equation (3); conditions the population likelihood on the systems being transiting, but does not correct for survey detection efficiency (acknowledged in §5.6).
  • standard math Beta distribution is flexible enough to describe the eccentricity distribution; two-component Beta mixture can represent bimodality
    Used throughout; the paper does not formally model-select Beta vs mixture (§5.1).
  • domain assumption Stellar densities from astroARIADNE SED/isochrone fits (and empirical relations for cool stars) are accurate; unresolved binaries/biases are negligible
    Section 3.1 and §5.6; the photoeccentric comparison requires an independent, unbiased stellar density.
  • domain assumption Gaussian approximation of ρ̃ and ρ* posteriors, variances added in quadrature
    Section 4.1; the authors state previous literature finds consistency and they validated with full chains, but it is an approximation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Orbital Eccentricity--Radius Distribution for Warm, Single Planets in TESS." pith.science (2026). https://pith.science/paper/WV6Q4HIP

@misc{pith2026260220015,
  author       = {Pith},
  title        = {Pith review of: The Orbital Eccentricity--Radius Distribution for Warm, Single Planets in TESS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WV6Q4HIP}},
  note         = {Machine review of arXiv:2602.20015}
}
read the original abstract

We characterize the radius-dependent eccentricity distribution of 219 warm (P = 8--50 days) systems with only one transiting planetary candidate identified during Sectors 1-69 of the TESS mission. Using the ``photoeccentric effect'' in a hierarchical Bayesian framework, we first model the population using discrete planetary size bins (sub-Neptunes, sub-Saturns, and Jovians). We then develop a continuous mixture model with weights governed by a logistic sigmoid function of radius. We find that the warm-single population is best described by two components: a dominant low-eccentricity mode ( <e_low> = 0.039-0.038+0.018) and a secondary dynamically excited mode (<e_high> = 0.466-0.068+0.067). The fraction of planets belonging to this high-eccentricity component increases strongly with planet radius, characterized by a transition at a break radius of R_br = 9.2-1.1+1.9 R_e. This trend places warm sub-Saturns predominantly on the same low-eccentricity track as sub-Neptunes. In contrast, warm Jovians (8--16 R_e) are frequently eccentric, with 65-12+13% of the population in the high eccentricity mode. Under the assumption of a two-component model, we see tentative evidence for a bimodal Jovian distribution at ~2.7 sigma. Finally, we identify a non-negligible tail of highly eccentric sub-Neptunes (1--4 R_e), which comprise 16.2-6.4+5.2% of the population, consistent with excitation by non-transiting external companions.

Figures

Figures reproduced from arXiv: 2602.20015 by the authors.

Figure 1
Figure 1. Planet radius versus orbital period for the final sample. Points and error bars represent median posterior values and 68% credible intervals. The side panels show the 1-D histograms for radius (right) and period (top). the standard SNR formula using the planet-to-star radius ratio and transit duration from the TOI catalog, as well as the expected number of transits in the dataset by propagating the TOI period and ep… view at source ↗
Figure 2
Figure 2. Orbital eccentricity (in e 2 ) versus semi-major axis for the planet sample with eccentricities constrained to better than 40% for clarity (or if e < 0.1). Colors denote sub-Neptunes (1–4 R⊕, blue), sub-Saturns (4–8 R⊕, purple), and Jovians (8–16 R⊕, orange). Overlaid curves show theoretical formation channels from R. I. Dawson & J. A. Johnson (2018) for a fiducial planet of ∼6 R⊕ and ∼80 M⊕: high-eccentricity migra… view at source ↗
Figure 3
Figure 3. Joint posterior constraints of e–ω from our photoeccentric-effect analysis. Each mini-corner panel shows the marginalized posteriors of ω (top) and e (right), along with their joint distribution (lower-left). The top row displays previously known high-eccentricity systems, while the bottom row shows newly identified candidate high-e planets with Rp ≲ 4, R⊕. For the known systems, the published radial-velocity soluti… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Posterior eccentricity distribution for the full warm-single planet sample (1–16 R⊕) inferred with our hierarchical Bayesian framework. Left: Beta model. Right: Two-component Beta mixture model. The solid blue curve shows the median posterior density as a function of e…
Figure 5
Figure 5. Figure 5: Posterior eccentricity distributions for three planet size classes derived from hierarchical Bayesian inference. Left: Single Beta distribution fits. Right: Two-component Beta mixture model fits. Colors denote sub-Neptunes (1–4 R⊕, blue), sub-Saturns (4–8 R⊕, purple), …
Figure 6
Figure 6. Figure 6: Radius dependence of eccentricity for the warm sample. Gray contours show the density of the individual-planet eccentricity posterior modes from Section §3.3. Open circles with error bars show the radius-binned (“discrete”) analysis, where independent Beta distribution…
Figure 7
Figure 7. Figure 7: Robustness of the inferred ⟨e⟩–Rp trend to sample removal. Blue curves/points reproduce the fiducial results from [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Inferred low-eccentricity mixture fraction πlow(Rp) from the continuous sigmoid mixture model of the final sample (left) and randomly-dropped 30% sample (right). The line and shaded band denote the posterior median and 68% credible interval. Coloured points summarize t…
Figure 9
Figure 9. Figure 9: Eccentricity–radius diagram for the planet sample. Points show the mode eccentricity, with errors drawn from 68% credible intervals. The curves indicate first-order scattering-based characteristic eccentricities, esc = √ Θ, evaluated at fixed (a = 0.2) AU and (M⋆ = 1 M…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

5 extracted references · 2 linked inside Pith

  1. [1]

    2020, AJ, 159, 123, doi: 10.3847/1538-3881/ab4fee Allard, F., Homeier, D., & Freytag, B

    Agol, E., Luger, R., & Foreman-Mackey, D. 2020, AJ, 159, 123, doi: 10.3847/1538-3881/ab4fee Allard, F., Homeier, D., & Freytag, B. 2012, Philosophical Transactions of the Royal Society of London Series A, 370, 2765, doi: 10.1098/rsta.2011.0269 Angelo, I., Naoz, S., Petigura, E., et al. 2022, AJ, 163, 227, doi: 10.3847/1538-3881/ac6094 Astropy Collaboratio...

    arXiv 2020

  2. [2]

    Batygin, K., Bodenheimer, P

    Corner plot of fiducial 3-stage sigmoid model. Batygin, K., Bodenheimer, P. H., & Laughlin, G. P. 2016, ApJ, 829, 114, doi: 10.3847/0004-637X/829/2/114 Bieryla, A., Dong, J., Zhou, G., et al. 2025, The Astronomical Journal, 169, 273, doi: 10.3847/1538-3881/adc441 Bitsch, B., Crida, A., Morbidelli, A., Kley, W., & Dobbs-Dixon, I. 2013, A&A, 549, A124, doi:...

    doi:10.3847/0004-637x/829/2/114 2016

  3. [3]

    Cabezas, A., Corenflos, A., Lao, J., et al

    Same as Figure 6 but including more discrete bin-size analyses: ∆1 .0 Rp, ∆1.5 Rp, and ∆3 .0 Rp. Cabezas, A., Corenflos, A., Lao, J., et al. 2024, BlackJAX: Composable Bayesian inference in JAX, https://arxiv.org/abs/2402.10797 Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A. 2008, ApJ, 686, 580, doi: 10.1086/590227 Christiansen, J. L., McElroy,...

    arXiv 2024

  4. [4]

    Gilbert, G

    Same as Appendix 2 but with the sample of 30% randomly dropped targets. Gilbert, G. J., Petigura, E. A., & Entrican, P. M. 2025, Proceedings of the National Academy of Science, 122, e2405295122, doi: 10.1073/pnas.2405295122 Goldreich, P., Lithwick, Y., & Sari, R. 2004, ARA&A, 42, 549, doi: 10.1146/annurev.astro.42.053102.134004 Goldreich, P., & Tremaine, ...

    arXiv 2025

  5. [5]

    Hoffman, M

    Same as Figure 6 but showing the full sample compared to the GKM-type host targets only, defined here as Teff < 6000 K. Hoffman, M. D., & Gelman, A. 2011, The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo, https://arxiv.org/abs/1111.4246 Høg, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A, 355, L27 Hogg, D. W., Myers, ...

    arXiv 2011

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.