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Exoplanet Occurrence Rate with Age for FGK Stars in Kepler

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that the occurrence rate of Kepler exoplanets around FGK stars shows no statistically significant trend with stellar age between 1.5 and 8 Gyr, after correcting for Kepler's detection efficiency.

desk verdict A careful null result that is not yet verified because age-label noise is not propagated into the rates. read the letter →

arxiv 2501.13809 v1 pith:XVANFGE5 submitted 2025-01-23 astro-ph.EP astro-ph.SR

Maryum Sayeed , Ruth Angus , Travis Berger , Yuxi (Lucy) Lu , Jessie Christiansen , Daniel Foreman-Mackey , Melissa Ness This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords exoplanetoccurrenceratestellarageisochronefittinggyrochronologyKeplersurveyinversedetectionefficiencyFGKstarsplanetevolution
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 asks whether the number of planets per star changes as Sun-like stars age from 1.5 to 8 billion years. Using two independent age indicators — isochrone fitting and gyrochronology (rotation slowdown) — and correcting for how easily Kepler would have detected each planet, the authors find no statistically significant trend in occurrence rate with age. A mild decreasing trend, within about 1.5–2.5σ, appears only for low-mass, metal-rich stars, which dominate the sample. The authors read this as a hint that planetary systems may lose planets over time through scattering or ejection, but state that accurate ages and larger samples are needed to settle the question.

What carries the argument

The carrying mechanism is the inverse detection efficiency method, in which the observed number of planets per star in each age bin is divided by the average Kepler detection completeness $\bar{Q}$ of the stars in that bin, giving $\Gamma_i = n_{i,\mathrm{planets}}/(N_{i,\mathrm{stars}}\bar{Q}_i)$. The completeness itself is the product of three probabilities, $Q = P_{\mathrm{geom}} P_{\mathrm{det}} P_{\mathrm{win}}$: the chance of a geometric transit, the chance the transit-search pipeline detects the signal, and the chance that enough transits fall in the observing window. The age binning is provided by two published stellar age catalogs, isochrone ages from stellar evolution models and gyrochronology ages from rotation slowdown, and the trend is quantified with weighted least-squares regression using inverse errors as weights.

What would settle it

Re-analyze the same 235 planets and 2658 stars with asteroseismic ages accurate to about 10 percent and recompute the binned occurrence-rate slope; if the slope is significantly negative (p < 0.05), the paper's conclusion of no trend with age would be refuted.

Watch

Extended reading notes

Core claim

The paper's central discovery is a null result with a hint. After correcting 235 confirmed or candidate Kepler planets for pipeline incompleteness using the inverse detection efficiency method, the occurrence rate of planets with radii 0.2–20 Earth radii and periods 0.2–100 days around 2658 FGK stars is consistent with being constant between 1.5 and 8 Gyr. The weighted least-squares slopes are −0.03 ± 0.04 per gigayear for isochrone ages and −0.01 ± 0.02 per gigayear for gyrochronology ages, with p-values of 0.45 and 0.73. Only when the sample is split into mass and metallicity bins does a decreasing slope emerge, for low-mass (0.8–1.0 solar masses), metal-rich ([Fe/H] 0.0–0.5 dex) stars, and even there the p-value is 0.2–0.4, so the decline is not statistically significant. The intended contribution is to show that any age-driven decline in planet occurrence over multi-gigayear timescales is weak at most and possibly confined to one stellar subpopulation.

Load-bearing premise

The result depends on one load-bearing assumption: the assigned stellar ages are accurate enough that stars binned into 1.5–8 Gyr groups preserve the true age ordering, since the paper's own comparison shows isochrone and gyrochronology ages disagree by a median absolute deviation of 1.05 Gyr and average isochrone age errors are 56%.

Editorial extensions

If this is right

  • If the null result is correct, the number of detectable planets around Sun-like stars does not change measurably between 1.5 and 8 billion years, so destructive processes like engulfment, scattering, and ejection must be too rare to leave a population-level signature.
  • The slope uncertainties (−0.03 ± 0.04 and −0.01 ± 0.02 per gigayear) set an upper limit on any real decline in occurrence rate over this age range.
  • The mild decline seen for low-mass, metal-rich stars, if real, would point to dynamical instability preferentially removing planets from that subgroup.
  • Because age errors are large enough to shuffle stars between bins, the null result also means that a genuine age trend cannot be ruled out until more precise ages are available.

Reading between the lines

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

  • The paper treats age as a discrete binning variable and does not propagate age errors into the occurrence-rate uncertainty budget; a hierarchical model that propagates age uncertainties could convert the null into a quantitative upper limit on planet-loss rates.
  • The 1.05 Gyr median absolute deviation between the two age indicators suggests that requiring cross-agreement between isochrone and gyrochronology ages might yield a cleaner, though smaller, sample for detecting trends.
  • The dependence of the absolute occurrence rate on the choice of mean, median, or mode detection efficiency implies that absolute rates are less reliable than the relative trend, which the paper argues is stable.
  • A direct extension would be to split the sample by planet radius or orbital period to see whether the age trend differs for hot Jupiters, sub-Neptunes, and super-Earths, which the current sample size does not allow.
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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

4 major / 5 minor

Summary. The paper measures Kepler exoplanet occurrence rates as a function of stellar age for FGK stars using two age indicators: isochrone ages from Berger et al. (2020) and gyrochronology ages from Lu et al. (2024). Restricting to 2,658 stars with both age estimates and 235 confirmed or candidate planets, the authors apply the inverse detection efficiency method with Kepler DR25 pipeline completeness to estimate occurrence rates in five log-spaced age bins between 1.5 and 8 Gyr. They report no significant trend in the full sample (slopes of -0.033 +/- 0.038 Gyr^-1 for isochrone ages and -0.009 +/- 0.023 Gyr^-1 for gyrochronology ages), and a tentative decreasing trend for low-mass, metal-rich stars. The paper discusses possible dynamical explanations, including planet engulfment, planet-planet scattering, and planet ejection, and urges caution due to age uncertainties and small sample size.

Significance. If the central null result is robust, it would usefully constrain the long-term evolution of close-in planetary systems around FGK stars, suggesting that any net loss of planets over 1.5-8 Gyr is small. The analysis has several genuine strengths: it is an independent application of public Kepler completeness data, it uses two different age indicators on the same stellar sample, and it explicitly isolates mass and metallicity as confounders. The inverse detection efficiency computation is transparent and closely follows established methodology. However, the significance of the result is currently limited by the fact that the dominant uncertainty in the problem, the stellar age, is not propagated into the binned occurrence rates, slopes, or p-values. The paper itself acknowledges this gap in Section 4.2. A null result based on age bins that may be heavily contaminated by misassigned stars is not yet a falsifiable statement about the age dependence of occurrence rates.

major comments (4)
  1. [§4.2, Table 1, Figure 3] The central null claim is not established because age uncertainties are not propagated into the binned rates or the regression. Section 4.2 states that age uncertainties average 56% for the isochrone sample and that bin assignment 'has a major effect on the rate of planets per star.' Table 1 lists mean isochrone age errors of 2.35-4.83 Gyr against bin widths of roughly 0.6-2.3 Gyr, and Figure 1 shows an RMS disagreement of 1.79 Gyr between the two age scales. The reported slopes and p-values in Table 2 are therefore conditional on the age labels being correct; with this level of label noise, even a real trend would be attenuated toward zero. A sensitivity test is required, for example Monte Carlo resampling of stellar ages from their reported uncertainties and recomputing the binned occurrence rates and slopes, or a forward model of bin-assignment probabilities.
  2. [§4.1, Table 2, Figure 5B] The low-mass metal-rich result is reported inconsistently. The text states that the gyrochronology sample in Figure 5B has a slope of -0.044 +/- 0.036 and describes the trend as 'significant in slope,' while Table 2 lists a slope of -0.055 +/- 0.018 with p = 0.205. These values cannot both be correct, and the description 'significant in slope' contradicts the reported p-value. Because this subpanel is the only tentative decreasing trend and motivates the dynamical-evolution discussion in Section 5, the numbers and language must be reconciled.
  3. [§3.3, §4.1, Eq. (12)] The weighted least squares regression uses the inverse of sigma_Gamma as weights rather than the inverse variance 1/sigma_Gamma^2. This is not the standard WLS prescription and changes the relative contribution of the five bins to the fitted slope and p-value. The authors should either use inverse-variance weights or explicitly demonstrate that the slopes and p-values are unchanged under the alternative weighting.
  4. [§3.2, Eq. (9)] The inverse detection efficiency step in Eq. (9) divides the observed planets-per-star rate by the mean efficiency Qbar_i, where Qbar_i is the mean over the Rp-P grid and then over stars. The paper notes in Section 3.2 that the per-star Q distribution is right-skewed, with mean, median, and mode differing substantially. The appropriate correction is not obviously the mean of Q over all stars rather than, for example, a per-planet inverse-efficiency sum. The authors state that the relative shape of the occurrence-rate distribution is unaffected by the choice of summary statistic, but they do not show this quantitatively; they should provide the slopes and p-values under mean, median, and mode Q, or use per-planet inverse efficiencies.
minor comments (5)
  1. [§3.1] The text before Eq. (6) contains a typo: 'Guassian' should be 'Gaussian.'
  2. [§1] The citation 'Fernandes et al. (submitted)' appears in the introduction but is not included in the reference list; please add the reference or remove the citation.
  3. [§4.1] The statement that the lack of metal-poor older stars in Figure 4D could be caused by a detection bias 'in Lu et al. (2021)' appears to refer to the gyrochronology catalog of Lu et al. (2024); please verify and correct the citation.
  4. [§2] The sample selection section says the FGK definition follows Kunimoto & Matthews (2020), but the effective-temperature range is quoted without a citation to the original source; a brief reference would help the reader.
  5. [Figure 3] The caption says 'error bars indicate Binomial errors' and 'propagated error'; using lower-case 'binomial' would improve consistency with standard nomenclature, and it would be helpful to state explicitly that the propagated errors do not include age uncertainty.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the occurrence-rate computation is an independent application of public Kepler completeness data, and the coauthored age catalogs are externally benchmarked inputs rather than the result being derived.

full rationale

Equation 9 computes occurrence rate as the observed planet-to-star ratio in each age bin divided by the mean Kepler pipeline detection efficiency for that bin. The completeness model is taken from Burke et al. (2015) and Christiansen et al. (2020), and the planet sample comes from the public Q1-17 DR25 catalog; neither is fitted to the age trend being reported. The slopes and p-values are obtained directly from the binned corrected rates via weighted least squares, so the null result is not a construction artifact. No equation in the paper defines age, detection efficiency, or slope in terms of the occurrence rate, and no parameter is fitted to the occurrence-rate-age relation and then renamed as a prediction. The main self-citations, Berger et al. (2020) and Lu et al. (2024), supply the stellar-age labels. These are pre-existing catalogs with external benchmarks described in the cited papers (open clusters, asteroseismic ages, wide binaries), and they are not derived from or fitted to the occurrence-rate data; using them is a methodological dependency rather than a circular argument. The paper explicitly flags the large age uncertainties and their effect on bin assignment as a limitation that could hide a real trend, which weakens the strength of the null claim but does not make the derivation circular. The tentative dynamical-evolution interpretation in Section 5 is explicitly framed as a hint and is not used as an input to the analysis. Accordingly, no load-bearing step reduces to its own inputs, and no circular step can be identified with the required specificity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on two external age catalogs from the same research network, the Kepler pipeline completeness model, and several unstated modeling choices: uniform grid weighting for Q, zero eccentricity, and no false-positive correction for candidates. No new physical entities are introduced. The age-accuracy assumption is the heaviest burden and is acknowledged in the paper.

free parameters (2)
  • Age bin edges = 1.5, 2.096, 2.930, 4.095, 5.723, 8.000 Gyr
    Five logarithmically spaced bins chosen by hand; the null result and the tentative subsample trend depend on this coarse binning, especially with typical age errors of 56%.
  • Mass and metallicity bin edges = 0.8/1.0/1.2 Msun and -0.5/0.0/0.5 dex
    Chosen by hand; the only tentative trend, in low-mass metal-rich stars, is defined by these boundaries, and the sample size per bin is small.
assumptions (5)
  • domain assumption The Kepler pipeline completeness model (Pdet, Pgeom, Pwin) from Burke et al. (2015) and Christiansen et al. (2020) correctly describes detection efficiency for this sample.
    Used throughout Section 3.1 to compute Q; if the completeness model is wrong for this stellar sample, the corrected occurrence rates and their age trend are biased.
  • domain assumption Circular orbits (e=0) for all planets when computing Pgeom and transit duration.
    Stated in Section 3.1 and discussed in Section 4.2; known to change absolute rates by about 10% but assumed not to change the age trend.
  • domain assumption B20 and L24 ages are calibrated and accurate enough for binning.
    The entire analysis relies on these two catalogs; Section 2 and 4.2 note large disagreements and mean age errors of 56%, so this assumption is weak.
  • ad hoc to paper The planet population is uniform over the log Rp-log P grid when averaging per-star detection efficiency.
    The study computes a per-star mean Q over 3660 grid cells and then averages over stars in Section 3.2. This implicitly weights all grid cells equally, which is not true for the actual planet distribution; a proper completeness correction would weight by the intrinsic Rp-P distribution.
  • domain assumption Candidate planets without confirmation have the same reliability as confirmed planets.
    The sample includes confirmed and candidate Kepler planets in Section 2 with no false-positive probability correction, which can bias absolute occurrence rates.

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Cite this review

Pith. "Pith review of Exoplanet Occurrence Rate with Age for FGK Stars in Kepler." pith.science (2026). https://pith.science/paper/XVANFGE5

@misc{pith2026250113809,
  author       = {Pith},
  title        = {Pith review of: Exoplanet Occurrence Rate with Age for FGK Stars in Kepler},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XVANFGE5}},
  note         = {Machine review of arXiv:2501.13809}
}
abstract

We measure exoplanet occurrence rate as a function of isochrone and gyrochronology ages using confirmed and candidate planets identified in Q1-17 DR25 Kepler data. We employ Kepler's pipeline detection efficiency to correct for the expected number of planets in each age bin. We examine the occurrence rates for planets with radii $0.2 \leq Rp \leq 20$ R$_\oplus$ and orbital periods $0.2 \leq P \leq 100$ days for FGK stars with ages between $1.5-8$ Gyr using the inverse detection efficiency method. We find no significant trend between occurrence rate and stellar ages; a slight, decreasing trend (within $1.5-2.5$ $\sigma$) only emerges for low-mass and metal-rich stars that dominate our sample. We isolate the effects of mass and metallicity on the occurrence rate trend with age, but find the results to be inconclusive due to weak trends and small sample size. Our results hint that the exoplanet occurrence rate may decrease over time due to dynamical instability from planet-planet scattering or planet ejection, but accurate ages and larger sample sizes are needed to resolve a clear relation between occurrence rate and age.

Figures

Figures reproduced from arXiv: 2501.13809 by the authors.

Figure 1
Figure 1. Left: Stellar sample from B20 and L24 on an Hertzprung–Russell diagram before and after quality cuts. Middle: Age distribution of isochrone and gyrochronology ages for 2658 stars in both sets. Right: Comparison of gyrochronology and isochrone ages with an RMS of 1.79 Gyr. The red points show the median isochrone and gyrochronology age within age bins where error bars show the 16th and 84th percentile of isochrone ag… view at source ↗
Figure 2
Figure 2. Integrated detection efficiency for the full sample of 2658 with available isochrone and gyrochronology ages stars over a grid of orbital period and planet radii. Contours and gridlines are shown for reference. transit duration, τdur, we interpolate within a grid of 141 robCDPP values, to estimate the noise (σcdpp) for that duration, where transit duration takes as input Porb, a, e, and R⋆, and is defined as, τdur =… view at source ↗
Figure 3
Figure 3. Planet occurrence rate as a function of isochrone (blue, dashed line) and gyrochronology (black, solid line) ages. Left: detection efficiency, Q, per age bin where the error bars are the standard deviation of Q in each bin. Middle: number of planets per star where error bars indicate Binomial errors (Equation 10). Right: occurrence rate of planets per age bin where the error bars indicate propagated error (Equation … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Distribution of stellar isochrone mass (top) and spectroscopic metallicity (bottom) with isochrone (left) and gyrochronology (right) ages where the colour indicates the number of data points in each bin, with equal number of bins across the four distributions. These di…
Figure 5
Figure 5. Figure 5: Planet occurrence rate as a function of isochrone (blue, dashed line) and gyrochronology (black, solid line) ages in groups of stellar mass and metallicity. The text indicates the number of observed planets in each bin. The mass increases from top to bottom, and the me…

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Pith tools

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