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Small and Close-In Planets are Uncommon Around A-type Stars

T0 review · 1 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A search of 20,257 A-type stars with TESS finds no reliable small planets with orbital periods under 10 days, placing 3-sigma upper limits far below those around cooler stars.

desk verdict First real constraint on small close-in planets around A-type stars; the null result and upper limits are solid enough to change the demographics picture, pending a targeted gravity-darkening injection test. read the letter →

arxiv 2411.13363 v2 pith:S7J4PSVX submitted 2024-11-20 astro-ph.EP astro-ph.SR

Steven Giacalone , Courtney D. Dressing This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords A-typestarsexoplanetoccurrenceratesTESSsurveytransitdetectionpipelinesub-NeptuneshotJupitersinjection/recoverycompletenessradiuscliff
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 tries to establish the first occurrence-rate measurement of small ($1\,R_\oplus < R_{\rm p} < 8\,R_\oplus$), close-in ($P_{\rm orb} < 10$ days) planets around A-type stars, a population that Kepler could not constrain. Using TESS data for 20,257 bright A-type stars and a custom transit-detection and vetting pipeline, the authors find no reliable planets in this size and period range. Through injection/recovery tests they measure the pipeline completeness and convert the null detection into $3\sigma$ upper limits: $2.2 \pm 0.4$ sub-Saturns, $9.1 \pm 1.8$ sub-Neptunes, and $186 \pm 34$ super-Earths per 1000 A-type stars. These limits are more than 3 times and 6 times lower than Kepler-era estimates for sub-Saturns and sub-Neptunes around Sun-like stars, suggesting small close-in planets become rare around hot stars. The paper also argues that the ratio of sub-Neptunes to hot Jupiters drops with stellar temperature, meaning the 'radius cliff' may flatten around early-type hosts.

What carries the argument

The load-bearing tool is a custom TESS transit pipeline whose completeness is calibrated by injection/recovery. The authors inject roughly 1,000,000 artificial transits into the raw light curves of the target stars, run the full detection and vetting chain, and grid the recovered fraction $R_{i,j}$ in planet-radius versus orbital-period cells; weighting by the geometric transit probability $p_{\rm geo,k}\approx R_{\star,k}/a_k$ yields the completeness map $C_{i,j}$. The occurrence-rate upper limit then follows from the binomial formula $f_{\rm cell,upper}=1-(1-CI)^{1/(n_{\rm trial}+1)}$ with $n_{\rm trial}=n_\star C$, applied separately to sub-Saturns ($4-8\,R_\oplus$), sub-Neptunes ($2-4\,R_\oplus$), and super-Earths ($1-2\,R_\oplus$). The overall measured completeness is only 7.2%, which explains why the null detection translates into a weak super-Earth limit but a relatively strong sub-Neptune limit.

What would settle it

Re-run the injection/recovery tests with gravity-darkened oblate-star transit models, using the measured rotation-rate distribution of A-type stars and a range of sky-projected spin-orbit angles, and measure the recovered fraction. If the completeness for sub-Neptunes falls below roughly 1%, the $3\sigma$ upper limit rises above 30 per 1000 stars and the claimed deficit relative to G-type stars disappears; detecting a population of small close-in planets around A-type stars with future surveys at rates comparable to FGK stars would also contradict the claim.

Watch

Extended reading notes

Core claim

The central discovery is a null result with quantitative force: no bona fide transiting planets with radii $1-8\,R_\oplus$ and periods $0.5-10$ days orbit the 20,257 A-type stars searched, and the completeness-corrected binomial upper limits place the occurrence rates of sub-Saturns, sub-Neptunes, and super-Earths at $<2.2$, $<9.1$, and $<186$ per 1000 stars at $3\sigma$. The sub-Saturn and sub-Neptune limits are over 3 and 6 times lower than the corresponding Kepler-derived rates for G-type stars, and the super-Earth limit is more than 1.5 times lower than for M dwarfs. The paper interprets this as evidence that small close-in planets cannot easily form at, migrate to, or survive at short orbital periods around A-type stars, and it notes the occurrence rate of sub-Neptunes appears to decline with stellar temperature faster than that of hot Jupiters, flattening the radius cliff.

Load-bearing premise

The upper limits assume that the artificial transits used in injection/recovery tests—circular orbits, solar-metallicity limb darkening, and impact parameters drawn from $[0,0.9]$—look like real transits around A-type stars; if rapid rotation, gravity darkening, or other unmodeled effects make real transits shallower or more distorted, the true completeness is lower than 7.2% and the upper limits are biased downward.

Editorial extensions

If this is right

  • Small close-in planets are rarer around A-type stars than around G-type stars by factors of at least 3 (sub-Saturns) and 6 (sub-Neptunes), if the upper limits reflect the true rates.
  • The dearth of sub-Neptunes compared with hot Jupiters around A-type stars (ratio $< 3.1 \pm 0.8$, versus $12.9 \pm 3.9$ for G-type stars) suggests the radius cliff flattens with increasing host-star temperature.
  • Planets that do exist around A-type stars may be stripped to bare rocky cores by near-ultraviolet photoevaporation, leaving super-Earths that current TESS data cannot detect.
  • White dwarf pollution is unlikely to come from close-in planets that survive the main-sequence phase; the scarcity of small close-in planets around A-type stars supports a wide-separation origin for white dwarf contaminants.
  • The absence of sub-Saturn and sub-Neptune detections at $P<10$ days is consistent with formation and migration being inhibited interior to the dust sublimation radius (roughly $0.12$ AU around a typical A star).

Reading between the lines

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

  • If the deficit is real, the same mechanism should suppress planets at somewhat longer periods around A-type stars; the authors' dust-sublimation argument predicts a gradual onset rather than a sharp cutoff at 10 days, which future TESS cycles or PLATO could test by pushing to roughly 20-30 days.
  • The upper-limit methodology could be sharpened by injecting gravity-darkened transit models directly into the recovery tests; a factor-of-two change in completeness for the $4-8\,R_\oplus$ bin would shift the sub-Saturn limit to within a factor of about 2 of the G-star rate, so the claimed deficit is testable with modest modeling effort.
  • Applying the same pipeline to F-type stars would separate the stellar-temperature trend from survey-specific detection losses, since the A-type deficit is currently established against Kepler pipelines with different completeness functions.
  • The super-Earth upper limit of 186 per 1000 stars is too weak to constrain formation physics; detecting super-Earth cores around A-type stars would likely require combining TESS with radial-velocity or transit-timing follow-up, or waiting for a larger sample from extended TESS sectors.
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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

1 major / 4 minor

Summary. The paper presents the first occurrence-rate analysis of small (1–8 R_Earth), close-in (P_orb < 10 d) planets around A-type stars, using TESS full-frame-image light curves for 20,257 bright A-type stars. A custom BLS-based pipeline with automated and manual vetting yields no reliable planet candidates, and the authors characterize completeness with roughly one million injection/recovery tests that include the geometric transit probability. From the null detection they derive 3-sigma upper limits of 2.2 ± 0.4 sub-Saturns, 9.1 ± 1.8 sub-Neptunes, and 186 ± 34 super-Earths per 1000 A-type stars, and compare these with Kepler-based occurrence rates for FGKM stars. The paper discusses physical mechanisms (disk truncation, dust sublimation, photoevaporation, companions, stellar age) that could explain the inferred dearth and concludes that the occurrence rate of small close-in planets likely declines toward hotter stars, with the sub-Neptune-to-hot-Jupiter ratio possibly decreasing.

Significance. If the result stands, this is an important step in exoplanet demographics, extending occurrence-rate measurements from FGKM stars to the previously unconstrained regime of A-type hosts. The strength of the paper is its unusually thorough injection/recovery setup, which injects into raw light curves and passes the signals through the same flattening, detection, and vetting stages used in the real search; the thresholds are mostly fixed a priori or taken from the literature, and the code is made public. The multi-stage vetting (SPOC comparison, secondary-eclipse search, centroid offsets, ExoFOP cross-matching, TRICERATOPS) is appropriately conservative. The upper limits are robust enough to exclude Sun-like occurrence rates for sub-Saturns and sub-Neptunes at high confidence, and the comparison to existing hot-Jupiter rates gives a physically interesting suggestion about the radius cliff. The super-Earth constraint is weak, as the authors clearly acknowledge.

major comments (1)
  1. [Section 4, Eqs. (8) and (15)] The completeness map is the load-bearing input for all occurrence-rate upper limits, but the injection/recovery tests assume spherical, uniformly bright stars with solar-metallicity limb darkening and impact parameters drawn from [0, 0.9]. Section 3.4 acknowledges that gravity darkening in rapidly rotating A-type stars can alter transit depth, shape, and duration, and argues qualitatively that the effect is minor for typical A-type stars. This argument is plausible but not quantified: if real transits are on average shallower or more distorted than the injected models, the true completeness would be lower than the measured 13.1%/3.2%/0.2% values, and the upper limits in Eq. (15) would be underestimated. I request either a targeted injection/recovery test using gravity-darkened transit models (e.g., following Barnes 2009 or Ahlers et al. 2020) for a representative subset of the sample, or a quantitative estimate of the maximum plausible completeness bias based on the sample's v sin i and oblateness distribution. The qualitative conclusion likely survives such a test, but the specific numbers in Section 6.1 should be placed on firmer footing.
minor comments (4)
  1. [Figure 11 caption] The caption labels the three panels as 'G-type (left), F-type (center), and A-type (left)', but the A-type panel is on the right; this is a typo that should be corrected.
  2. [Section 4 and Figure 9] The completeness values for the three radius regimes are reported as 13.2% ± 2.6%, 3.1% ± 0.6%, and 0.14% ± 0.03% in the text, while the Figure 9 caption states 13.1%, 3.2%, and 0.2%. These numbers should be reconciled.
  3. [Section 2] The phrase 'The lower T requirement removes very bright stars' is confusing because a lower T magnitude corresponds to a brighter star; the intended meaning becomes clear later, but the wording should be clarified (e.g., 'the T > 6 requirement removes saturated very bright stars').
  4. [Title and Abstract] The title and abstract use the definite phrase 'Small and Close-In Planets are Uncommon around A-type Stars', while the results are upper limits and the abstract itself repeatedly says 'may be'. Consider softening the title and the first abstract sentence to '...appear to be uncommon' or '...are not found in this sample', which better matches the statistical content.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the occurrence-rate upper limits follow from a null detection and an independently measured completeness map; self-citations are tools or context, not load-bearing inputs.

full rationale

The derivation chain from the TESS sample to the occurrence-rate upper limits is self-contained and does not reduce to its own inputs. The upper limits are computed from Equations 9–15 using only the sample size n*, the completeness C measured from injection/recovery tests (Equations 6–8), and the null detection nobs = 0. Equation 15 is a standard binomial inversion of a null result; no parameter is fitted to the target occurrence rate, and the reported limits are not defined in terms of the quantities they purport to predict. The completeness map is an independent measurement based on roughly one million injected transits, and while its assumptions (circular orbits, solar-metallicity limb darkening, impact parameters drawn from [0,0.9], spherical host stars) can be questioned, that is a model-dependence or correctness concern, not a circular reduction: the injected model is not defined in terms of the occurrence-rate upper limits. The comparison rates for FGKM stars are taken from external Kepler studies (Dressing & Charbonneau 2013, 2015; Kunimoto & Matthews 2020), and the hot-Jupiter comparison comes from Beleznay & Kunimoto (2022); none of these are fitted to A-star data. The self-citations are not load-bearing. TRICERATOPS is a published, externally validated vetting tool used to classify four TCEs; it does not appear in the occurrence-rate formula, and even if the two TRICERATOPS-rejected candidates were counted as real, the sub-Saturn rate would remain below the reported upper limit. The HD 56414 b discussion is contextual and does not feed into the upper-limit calculation. No uniqueness theorem or ansatz is imported from the authors' prior work to force the result. The central claim is therefore an empirical null detection combined with an independently characterized sensitivity, not a prediction that recovers its own inputs.

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

The central result rests on the accuracy of the injection/recovery completeness, the fidelity of injected transits to real ones, and the correctness of the false-positive classification. These are domain assumptions rather than fitted parameters; no free parameters are fitted to make the upper limits match a target.

free parameters (3)
  • Minimum knot distance for light curve flattening = 0.5 days
    Chosen visually using real TESS light curves with injected transits (Section 3.1). This hand-tuned value affects whether real transits are preserved during flattening and thus the pipeline completeness.
  • Systematic uncertainty on stellar mass and radius = 20%
    Adopted in Section 4 to account for TIC parameter precision; used in completeness uncertainties. Conservative for >99% of the sample, but chosen by the authors.
  • Maximum impact parameter for injected transits = 0.9
    Injected transits use b drawn uniformly from [0, 0.9], which the authors note slightly overestimates completeness (Section 4 footnote 8). The bias is stated to be negligible, but the choice is a modeling decision.
assumptions (6)
  • domain assumption The transit detection pipeline's noise model is correct: after flattening, residual noise is approximately Gaussian and independent, so the BLS SDE, S/N, Delta BIC, and chi-squared statistics are valid discriminators.
    Section 3 relies on these statistics to select and vet TCEs; non-Gaussian systematics could either produce false alarms or hide real transits.
  • domain assumption TIC stellar parameters (Teff, R*, M*) are sufficiently accurate for sample selection and for converting transit depth to planet radius.
    Sample selection and radius cuts use TIC values; the authors partially validate with Gaia DR3 but systematic offsets remain (Section 2).
  • domain assumption The injected transit model (batman with quadratic limb darkening from Claret 2017, circular orbit, uniform b up to 0.9) faithfully represents real transits around A-type stars.
    Section 4 injection/recovery uses this model; if real transits are significantly distorted by gravity darkening or eccentricity, completeness estimates change.
  • domain assumption The manual vetting steps and TRICERATOPS correctly classify all true planets as candidates and all astrophysical false positives as false.
    Section 3.3 relies on TRICERATOPS FPP thresholds from Giacalone et al. (2021); three surviving TCEs have FPP>92%, but the probability of a false classification is non-negligible.
  • domain assumption The sample of 20,257 stars are predominantly main-sequence A-type stars; the ~18% with R* < 1.7 R_sun are not a large population of evolved subdwarfs that would bias the interpretation.
    Section 2 discusses sdA stars, but keeping them assumes the consensus that they are metal-poor main-sequence stars.
  • standard math Binomial statistics are the correct model for the null detection counting experiment.
    Equation 12 defines the binomial likelihood used for upper limit calculation.

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Pith. "Pith review of Small and Close-In Planets are Uncommon Around A-type Stars." pith.science (2026). https://pith.science/paper/S7J4PSVX

@misc{pith2026241113363,
  author       = {Pith},
  title        = {Pith review of: Small and Close-In Planets are Uncommon Around A-type Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S7J4PSVX}},
  note         = {Machine review of arXiv:2411.13363}
}
abstract

The Kepler and K2 missions enabled robust calculations of planet occurrence rates around FGKM-type stars. However, these missions observed too few stars with earlier spectral types to tightly constrain the occurrence rates of planets orbiting hotter stars. Using TESS, we calculate the occurrence rate of small ($1 \, R_\oplus < R_{\rm p} < 8 \, R_\oplus$), close-in ($P_{\rm orb} < 10$ days) planets orbiting A-type stars for the first time. We search a sample of 20,257 bright ($6 < T < 10$) A-type stars for transiting planets using a custom pipeline and vet the detected signals, finding no reliable small planets. We characterize the pipeline completeness using injection/recovery tests and determine the $3\sigma$ upper limits of the occurrence rates of close-in sub-Saturns ($4 \, R_\oplus < R_{\rm p} < 8 \, R_\oplus$), sub-Neptunes ($2 \, R_\oplus < R_{\rm p} < 4 \, R_\oplus$), and super-Earths ($1 \, R_\oplus < R_{\rm p} < 2 \, R_\oplus$). We find upper limits of $2.2 \pm 0.4$ sub-Saturns and $9.1 \pm 1.8$ sub-Neptunes per 1000 A-type stars, which may be more than $3\times$ and $6\times$ lower than Kepler-era estimates for Sun-like stars. We calculate an upper limit of $186 \pm 34$ super-Earths per 1000 A-type stars, which may be more than $1.5\times$ lower than that for M dwarfs. Our results hint that small, close-in planets become rarer around early-type stars and that their occurrence rates decrease faster than that of hot Jupiters with increasing host star temperature. We discuss plausible explanations for these trends, including star-disk interactions and enhanced photoevaporation of planet atmospheres.

Figures

Figures reproduced from arXiv: 2411.13363 by the authors.

Figure 1
Figure 1. Coordinates and properties of the 20,257 A-type stars that are used in this study. In the top-most panel, each point is a star, with color indicating the number of sectors it has been observed by TESS [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. 2D histogram of the stars in our sample, binned according to their 1-hour combined differential photometric precisions (CDPPs) and their TESS magnitudes. Most stars in the sample have CDPPs between 0.1 and 1 parts per thou￾sand. main sequence and have lost significant fractions of their envelopes as they expanded (most likely due to strip￾ping from a close-in degenerate companion; Heber 2009), and cool subdwarfs, wh… view at source ↗
Figure 3
Figure 3. Visualization of sinusoid test described in Section 3.2. The black points show the phase-folded data of the event detected by the BLS periodogram. The solid light blue curves show the best-fit sinusoid models and the dashed dark blue curves show the best-fit transit models. The left-side panel shows the results for TIC 238597883 (TOI-1004), which strongly favors the transit model, and the right-side panel shows the … view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Visualization of event symmetry test described in Section 3.2. The left-side panels show the phase-folded events detected by the BLS periodogram. The right-side panels compare the binned pre-midpoint (blue circles) and post-midpoint (red squares) data. The top two pane…
Figure 5
Figure 5. Figure 5: Periods and depths of TCEs detected by the automated pipeline described in Section 3.2. The points are divided into two categories: red circles, which were determined to be false alarms or false positives in the SPOC comparison vetting test (Section 3.3.1), and blue sq…
Figure 6
Figure 6. Figure 6: Visualization of signals that fail the manual secondary eclipse search. The left-side panel shows the signal detected in the light curve of TIC 126449150, which has a convincing secondary eclipse. The phase-folded light curve is shifted by half of the detected period s…
Figure 7
Figure 7. Figure 7: Visualization of the centroid offset test for TIC 177120452, which was found to have 2.5-day signal by the TCE detection pipeline. Left: The difference image of the TESS sector 7 data of the star, which shows a clear offset 3 pixels (approximately 1′ ) to the east. TIC…
Figure 8
Figure 8. Figure 8: Phase-folded light curves of the four signals discussed in Section 3.3.5, binned to 2-minute intervals for clarity. Best-fit transit models with 1σ uncertainties are shown in blue. After fitting the signal around TIC 120155231 with a transit model, we determined the pl…
Figure 9
Figure 9. Figure 9: Pipeline sensitivity (top) and completeness (bottom) for different planet radii and orbital periods for our sample of 20,257 stars. The color of each cell corresponds to the value displayed within. Uncertainties in sensitivity are Poisson errors associated with injecte…
Figure 10
Figure 10. Figure 10: Calculated 3σ upper limits on the occurrence rates of sub-Saturns (4 R⊕ < Rp < 8 R⊕; top), sub-Neptunes (2 R⊕ < Rp < 4 R⊕; middle), and super-Earths (1 R⊕ < Rp < 2 R⊕; bottom) with Porb < 10 days around A-type stars from TESS data (black). Error bars on the 3σ upper l…
Figure 11
Figure 11. Figure 11: Occurrence rates for super-Earths, sub-Neptunes, sub-Saturns, and hot Jupiters for G-type (left), F-type (center), and A-type (left) stars. Blue data are from Kunimoto & Matthews (2020), green data are from Beleznay & Kunimoto (2022), and black data are the 3σ upper l…

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