An Analysis of the Radius Gap in a Sample of Kepler, K2 and TESS exoplanets orbiting M Dwarf Stars

Aida Behmard; Carlos Allende Prieto; Diogo Souto; Dmitry Bizyaev; F\'abio Wanderley; Ilaria Pascucci; Katia Cunha; Marc Pinsonneault; Rachael L. Beaton; Simone Daflon

REVIEW 3 major objections 4 minor 159 references

An Analysis of the Radius Gap in a Sample of Kepler, K2 and TESS exoplanets orbiting M Dwarf Stars

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The M-dwarf radius gap is nearly flat in orbital period, with slope +0.01, unlike -0.10 for Sun-like stars.

desk verdict Useful homogeneous M-dwarf planet radii, but the flat gap slope is not secure until the completeness question is actually tested. read the letter →

arxiv 2509.01930 v1 pith:HPLTARCN submitted 2025-09-02 astro-ph.EP astro-ph.SR

Fábio Wanderley , Katia Cunha , Verne V. Smith , Diogo Souto , Ilaria Pascucci , Aida Behmard , Carlos Allende Prieto , Rachael L. Beaton

show 6 more authors

Dmitry Bizyaev Simone Daflon Sten Hasselquist Steve Howell Steven R. Majewski Marc Pinsonneault

This is my paper

classification astro-ph.EPastro-ph.SR

keywords exoplanetsradiusgapMdwarfstarssuper-Earthssub-Neptunespebbleaccretionorbitalmigrationtransitphotometry

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 asks whether the radius gap, the scarcity of planets between about 1.6 and 2.0 Earth radii, behaves around M dwarf stars the same way it does around Sun-like stars. From a homogeneous set of 218 transiting planets around 161 M dwarfs, it finds the gap stays at nearly the same planet radius at all orbital periods: slope +0.01 (+0.03, -0.04) in log period, compared with about -0.10 for FGK stars. Because only pebble-accretion models that include photoevaporation and inward migration predict a near-flat slope, the result shifts the dominant explanation for M-dwarf planet evolution away from photoevaporation and core-powered mass loss alone. The sample also places the M-dwarf sub-Neptune desert at much lower stellar irradiation than for FGK stars, and reveals a density gap near 0.9 Earth densities that separates rocky planets from two distinct sub-Neptune density classes.

What carries the argument

The load-bearing object is the radius-gap line in the log-planet-radius versus log-orbital-period plane: the valley of a two-dimensional kernel-density estimate of the planet distribution, fit as R_gap(P_orb) = 1.62 Earth radii times (P_orb / 1 day) to the power +0.01. The measurement chain starts with a second-degree polynomial tying stellar radius to absolute K_s magnitude, calibrated on a spectroscopically analyzed subsample of APOGEE spectra and applied to all host stars. The same KDE locates the gap, and a bootstrapped gap-fitting procedure (used in prior FGK analyses) sets the slope and its uncertainty. Models are compared by their predicted R_gap versus P_orb power-law slopes.

What would settle it

Take the same 218 planets, compute per-mission detection efficiencies from injected transits, reweight each planet by the inverse efficiency, and refit the gap slope. If the completeness-corrected slope moves outside the +0.01 plus-or-minus 0.04 band, the claimed flatness is a selection artifact rather than a physical signal.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the M-dwarf radius gap is essentially stationary in orbital period. From 218 small planets (R_p < 4 Earth radii) around 161 M dwarfs detected by the Kepler, K2, and TESS missions, the valley in the radius distribution falls between about 1.6 and 2.0 Earth radii, with a power-law slope dlog R_gap/dlog P_orb = +0.01 (+0.03, -0.04), an intercept giving R_gap about 1.62 Earth radii at one day, and zero slope within uncertainties. This is 2-3 sigma different from the -0.10 slope reported for FGK hosts. In the period-radius plane the gap separates a rocky super-Earth peak (1.2-1.6 Earth radii) from a sub-Neptune peak (2.0-2.4 Earth radii); in density

Load-bearing premise

The flat slope rests on assuming that combining Kepler, K2, and TESS detections without completeness corrections does not bias the period-radius distribution; the authors state that these corrections are not applied.

Editorial extensions

If this is right

The M-dwarf radius gap sits at about 1.6-2.0 Earth radii over orbital periods from below a day to 100 days, so any theory of small-planet evolution must reproduce a period-independent gap for low-mass stars.
Photoevaporation and core-powered mass loss alone predict a gap that slides downward with period, so they cannot be the sole sculptors of the M-dwarf radius gap.
Pebble-accretion models that include photoevaporation and inward migration are the only tested models with a near-flat slope, pointing to pebble accretion as more important in disks around M dwarfs than around FGK stars.
The sub-Neptune desert begins near 120 times Earth's insolation for M dwarfs, much lower than about 650 for FGK stars, indicating the desert edge depends on host-star mass.
The density gap near 0.9 Earth densities separates rocky planets from sub-Neptunes, and the sub-Neptune group splits into gas-rich low-density planets and volatile-rich water worlds.

Reading between the lines

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

If completeness corrections were applied to the three-survey sample, the period distribution of detections could steepen or flatten the slope. This is the most direct check of the paper's central number.
The flat-slope interpretation implies that inward-migrated M-dwarf sub-Neptunes should show signs of pebble-fed volatile enrichment, which atmospheric spectroscopy of the densest sub-Neptunes could test.
The host-mass dependence of the sub-Neptune desert edge predicts a smooth gradient across K and M stars; combining this sample with K-dwarf samples could confirm the trend.
If pebble accretion dominates around M dwarfs, the radius gap around even lower-mass brown-dwarf hosts should be flatter still and shifted to lower radii, but no current sample tests that prediction.

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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

The short version: this is a useful, honest paper that probably has the right qualitative answer—a flat or near-flat radius-gap slope for M dwarfs—but the specific quantitative claim (m = +0.01, quoted as 2–3 sigma different from FGK) is not yet nailed down. The slope is fit on a three-mission sample without completeness corrections, and the fitting pipeline is a little ad hoc. I would send it to a competent referee, but I would want the completeness issue addressed before putting strong weight on the slope.

What is genuinely new: the homogeneous stellar radius scale from APOGEE spectra, applied to 218 planets around 161 M dwarfs, is a real step forward. The radii are cross-checked against previous measurements, and the R*-MKs calibration is presented transparently with covariance. The paper also does a fair job comparing to formation models, and it does not wildly overinterpret—except maybe the abstract's 'water worlds' phrasing, which the text itself walks back with the mass-radius degeneracy.

Soft spots, in order of importance. (1) The completeness issue is load-bearing, not cosmetic. Section 6.1 explicitly says no completeness corrections are applied because the sample combines Kepler, K2, and TESS; Section 6.2.1 then fits the gap slope on that same uncorrected sample. The defense that period distributions are 'similar' does not address the joint radius–period completeness surface. The stress-test concern is plausible: if small planets at long periods are under-detected, the apparent gap can tilt positive and create the flat slope. That needs an injection-recovery test or at least a per-mission completeness-weighted check. (2) Averaging two different fitting methods (the KDE line and gapfit) with no stated justification is odd; the paper should adopt one principled approach or show the result is robust to the choice. (3) The FGK comparison relies on literature slopes from a different pipeline—fine, but the 2–3 sigma claim is only as good as cross-survey comparability. (4) The 'water worlds' conclusion is stated more strongly in the abstract than the text supports, though the text itself acknowledges the degeneracy.

The citation pattern looks fine. The paper builds on prior work by Gaidos, Van Eylen, Cloutier & Menou, and the self-references to the authors' spectral synthesis methods are legitimate since those methods are published and applied consistently.

Bottom line: this paper deserves a serious referee. The central claim is plausible and the sample is valuable, but the completeness sensitivity analysis is a must before publication, and the slope-averaging procedure should be cleaned up. If those are addressed, this will be a useful reference for the M-dwarf radius gap discussion.

Referee Report

3 major / 4 minor

Summary. This paper constructs a sample of 218 small transiting exoplanets around 161 M dwarf hosts from Kepler, K2, and TESS. Stellar radii for 48 APOGEE stars are used to build an R*-MKs calibration, which is applied to the full sample to derive uniform planetary radii. The radius distribution shows a gap at ~1.6–2.0 R⊕, a nearly flat slope of the gap with orbital period (m=+0.01) and with insolation, and a sub-Neptune desert at Sp~120 S⊕. Using published masses for 51 planets, the paper finds a density gap at about 0.9 ρ⊕ and two subgroups of sub-Neptunes. The flat slope is interpreted as evidence for pebble accretion and inward migration being more important around M dwarfs.

Significance. If the flat slope is robust, this is an important constraint on models of planet formation and evolution, and it would support a stellar-mass dependence of the gap-shaping mechanisms. The homogeneous stellar radii from APOGEE spectroscopy and the public table of derived radii are valuable contributions. However, the headline slope is measured from an uncorrected mixture of three missions, and the fitting procedure is not fully transparent; these issues must be addressed before the conclusions can be accepted. The density analysis, though based on a small mass sample, provides useful comparison with earlier M-dwarf results.

major comments (3)

[§6.1, §6.2.1] The headline slope m=+0.01 is measured from the Full sample without any completeness correction, as explicitly stated in §6.1. The three missions have different photometric precision, cadence, and follow-up confirmation; a period-dependent loss of small planets at long orbital periods would systematically tilt the fitted gap position toward larger Rp with P, potentially turning a true FGK-like negative slope into the observed flat/positive slope. The defense that period distributions are 'similar' across missions does not constrain the joint Rp–P completeness. Please provide an injection-recovery or per-mission completeness test, or state the bias direction quantitatively; for example, repeat the slope fit using the K2/TESS subsamples and a Kepler-only sample with existing completeness maps.
[§6.2.1] The adopted slope is the unweighted average of two different fits: a KDE minimum-sum slope (-0.01) and a gapfit slope (+0.02). Because the difference between the two is comparable to the quoted bootstrap uncertainty, the averaged value is not a well-defined estimator, and the bootstrap uncertainties from gapfit do not include the scatter between the two methods. Please report both fits separately, explain why averaging is appropriate, and use a single method for the baseline result. This is load-bearing because the 2–3σ difference from the FGK slope (-0.10) depends on the exact central value and uncertainty.
[§6.2.1 (FGK comparison)] The paper states that the M-dwarf slope differs at '2–3σ' from the FGK value of ~-0.10, but no statistical comparison is shown. The FGK slope is taken from literature analyses that use different samples, completeness treatments, and fitting algorithms; these differences are not propagated into the claimed significance. Please provide a quantitative comparison (e.g., a bootstrap or Monte Carlo test that includes both slope uncertainties and, ideally, a consistent re-analysis of an FGK sample with the same pipeline), or temper the claim accordingly.

minor comments (4)

[Figure 8 caption] The middle panel caption sequentially calls the green line 'Martinez+19 (FGK), Van Eylen+21 (M dwarfs)' and then references 'Van Eylen et al. (2018) for M dwarfs' in the text. Please reconcile the year and the source of the M-dwarf slope.
[§6.2.2] The sub-Neptune desert edge at Sp~120 S⊕ versus ~650 S⊕ for FGK hosts is based on a visual reading of the KDE plot. A quantitative definition of the desert edge (e.g., a fitted boundary or a minimum-density contour) would make the comparison more objective.
[§6.3, Figure 11] The division of the 51-planet density sample into three peaks is presented as a robust feature. Given the small N, an explicit test for bimodality/trimodality (e.g., likelihood-ratio or GMM comparison) would strengthen the claim.
[Throughout] The paper would benefit from a table column or stated flag indicating which planets come from each mission, so readers can assess subsample robustness of the slope and desert results.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the radius-gap slope is measured from data and compared with external models; self-citations are methodological and not load-bearing.

full rationale

The claimed derivation chain is not circular. Stellar radii for the APOGEE subsample are derived from spectra, Gaia distances, and bolometric corrections; these radii define an R*-M_Ks calibration that is then applied to the broader sample. Planetary radii follow from Rp = sqrt(delta F) * R*, and the radius-gap slope is fit to the resulting Rp-Porb distribution. Nothing in this chain defines the gap slope in terms of the models that are later invoked; the statement that the flat slope 'agrees with pebble accretion models' is a comparison, not a derivation from the model. The paper's self-citations (Souto et al. 2018, 2020; Wanderley et al. 2023, 2024, 2025) concern spectral-synthesis methodology and companion papers, not the radius-gap measurement, and they do not smuggle in the target result. The explicit statement in Section 6.1 that 'we do not apply completeness corrections to our results' is a real limitation for the slope's physical interpretation, but it is a selection-bias/correctness risk, not circularity: the slope is not mathematically forced by the completeness assumption, and it could in principle be tested with injection-recovery weighting. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' own work, and no equation reduces to its inputs by construction. The central slope m=+0.01 is an empirical measurement with external model comparison, so the paper is self-contained against external benchmarks for the purpose of this assessment.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. It relies on a fitted stellar radius calibration, a fitted gap slope, and several domain assumptions about the spectral synthesis scale, the extrapolation of the calibration, and the absence of selection bias. The water-world interpretation is an assignment of known planets to existing compositional models.

free parameters (3)

R*-MKs calibration coefficients = a0=1.7420, a1=-0.2925, a2=0.0123
Three coefficients fit to the 48-star APOGEE sample; used to derive stellar radii and hence planetary radii for all 161 hosts.
radius gap power-law slope m = +0.01 (+0.03, -0.04)
Fitted to the radius-period KDE/gapfit; this is the central claim that the slope is flat.
radius gap intercept y0 = +0.21
Intercept of the radius-period gap fit, equivalent to R_gap = 1.62 Earth radii at P_orb = 1 day.

assumptions (6)

domain assumption Spectral synthesis methodology from Wanderley et al. 2023/2024 and Souto et al. 2018/2020 yields correct Teff and log g for the APOGEE M dwarfs.
Stellar radii and the calibration rely on these values; the methodology is cited from prior papers, not re-derived here.
domain assumption Stefan-Boltzmann radii with Mann et al. bolometric corrections and Bailer-Jones et al. distances are accurate for this M-dwarf sample.
Luminosity and R* assume the Mann et al. bolometric correction scale and Gaia distances are correct.
domain assumption The quadratic R*-MKs calibration from 48 APOGEE stars applies to all 161 full-sample hosts.
Assumes no unmodeled dependence (e.g. metallicity, age) within the same MKs range, as stated in Section 4.
domain assumption KDE and gapfit reliably recover the true gap location and slope from the uncorrected sample.
The slope measurement assumes the KDE/gapfit method and bootstrap represent the true gap, not sample selection.
domain assumption Selection effects from combining Kepler, K2, and TESS without completeness corrections do not bias the radius-period relation.
The authors explicitly do not apply completeness corrections in Section 6.1; the flat-slope claim depends on this assumption.
domain assumption Zeng et al. 2019 mass-radius models allow reliable composition classification.
Water world versus rocky plus H2 atmosphere classification assumes these models and the acknowledged degeneracy.

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Cite this review

Pith. "Pith review of An Analysis of the Radius Gap in a Sample of Kepler, K2 and TESS exoplanets orbiting M Dwarf Stars." pith.science (2026). https://pith.science/paper/HPLTARCN

@misc{pith2026250901930,
  author       = {Pith},
  title        = {Pith review of: An Analysis of the Radius Gap in a Sample of Kepler, K2 and TESS exoplanets orbiting M Dwarf Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HPLTARCN}},
  note         = {Machine review of arXiv:2509.01930}
}

abstract

Planetary radii are derived for 218 exoplanets orbiting 161 M dwarf stars. Stellar radii are based on an analysis of APOGEE high-resolution near-IR spectra for a subsample of the M-dwarfs; these results are used to define a stellar radius-M$_{\rm K_{\rm s}}$ calibration that is applied to the sample of M-dwarf planet hosts. The planetary radius distribution displays a gap over R$_{\rm p}$$\sim$1.6-2.0 R$_{\oplus}$, bordered by two peaks at R$_{\rm p}$$\sim$1.2-1.6 R$_{\oplus}$ (super-Earths) and 2.0-2.4 R$_{\oplus}$ (sub-Neptunes). The radius gap is nearly constant with exoplanetary orbital period (a power-law slope of m=$+0.01^{+0.03}_{-0.04}$), which is different (2-3$\sigma$) from m$\sim$$-$0.10 found previously for FGK dwarfs. This flat slope agrees with pebble accretion models, which include photoevaporation and inward orbital migration. The radius gap as a function of insolation is approximately constant over the range of S$_{\rm p}$$\sim$20-250 S$_{\oplus}$. The R$_{\rm p}$-P$_{\rm orb}$ plane exhibits a sub-Neptune desert for P$_{\rm orb}$$<$2d, that appears at S$_{\rm p}$$>$120 S$_{\oplus}$, being significantly smaller than S$_{\rm p}$$>$650 S$_{\oplus}$ found in the FGK planet-hosts, indicating that the appearance of the sub-Neptune desert is a function of host-star mass. Published masses for 51 exoplanets are combined with our radii to determine densities, which exhibit a gap at $\rho_{\rm p}$$\sim$0.9$\rho_{\oplus}$, separating rocky exoplanets from sub-Neptunes. The density distribution within the sub-Neptune family itself reveals two peaks, at $\rho_{\rm p}$$\sim$0.4$\rho_{\oplus}$ and $\sim$0.7$\rho_{\oplus}$. Comparisons to planetary models find that the low-density group are gas-rich sub-Neptunes, while the group at $<$$\rho_{\rm p}$$>$$\sim$0.7$\rho_{\oplus}$ likely consists of volatile-rich water worlds.

Figures

Figures reproduced from arXiv: 2509.01930 by the authors.

**Figure 1.** The observed APOGEE spectrum and best-fit syntheses for two studied M dwarfs, covering the effective temperature range of our sample. From top to bottom: the first, second, and third chip of the APOGEE spectrum are shown. Using the spectroscopic parameters and stellar radii obtained previously in this study, we derived a calibration between the M dwarf stellar radius and the MKs absolute magnitude. In [PITH_FULL_I… view at source ↗

**Figure 2.** Kiel Diagram showing the effective temperatures and surface gravities derived in this study (blue circles), along with ASPCAP DR17 results for the same stars (grey xs). Physical log g values computed using the relations in Mann et al. (2019) are shown as orange triangles. Typical uncertainties are shown at the top right. The DR17 log g results are systematically lower than ours and roughly flat with the effective … view at source ↗

**Figure 3.** A comparison between the derived effective temperatures from this work with results obtained with the ASPCAP pipeline from APOGEE DR17. The dashed lines represent offsets of ± 100 K. stellar radii errors of all of these. For each realization, there is a different set of coefficients and a covariance matrix, which are used to derive stellar radii errors as a function of MKs [PITH_FULL_IMAGE:figures/full_fig_p006… view at source ↗

Figures from the paper (7 more)

**Figure 5.** Figure 5: From left to right: distribution of Gaia distances from Bailer-Jones et al. (2021), MKs absolute magnitudes, and stellar radii for the 161 M dwarfs in our Full sample. As a comparison we also show the histograms for the APOGEE sample delineated in white. with planetary…

**Figure 6.** Figure 6: Comparison between the planetary radii from this work with results from the literature. Blue, orange, and grey circles are radii obtained from the ExoFOP TOI Program, KOI DR25 (Thompson et al. 2018), and other works from the literature. The x=y relation is shown by the…

**Figure 7.** Figure 7: Distribution of the derived planetary radii for our Full sample is shown in blue. The grey dashed line indicates the minimum probability density at 1.78 R⊕ for a KDE associated with the Full sample. The histogram of the planetary radii distribution, obtained from the …

**Figure 8.** Figure 8: The top panel shows the distribution of the derived planetary radii as a function of orbital periods along with the associated KDE. The middle and bottom panels show the same KDE, along with our radius gap relation (black solid line), and uncertainties (grey region). …

**Figure 9.** Figure 9: Distribution of the derived planetary radii as a function of insolation, along with the associated KDE. radius gap, resulted in a near-perfect division in the ρpPorb plane, where the sub-Neptunes had smaller mean densities and “rocky” exoplanets had larger values of ρ…

**Figure 10.** Figure 10: Left panel: exoplanetary radii as a function of orbital periods, where sample exoplanets, having masses available, which fall on the “rocky” side of the gap are colored in gold, while those falling on the sub-Neptune side of the gap are colored in blue. Grey xs are ex…

**Figure 11.** Figure 11: Left panel: density histogram of our exoplanetary sample with available masses from the literature. The dashed lines indicate the boundaries for segregating exoplanets into three groups. Middle panel: Derived planetary radii as a function of planetary mass, along with…

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