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The impact of stripped cores on the frequency of Earth-size planets in the habitable zone

T0 review · 3 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Earth-size planets in the habitable zone of Sun-like stars may be four to eight times rarer than previously estimated, because short-period planets used in extrapolations are often stripped cores.

desk verdict A transparent re-analysis that makes a strong case that short-period small planets inflate eta_Earth; the four-to-eightfold drop is real, though the absolute 5-10% value depends on a separable model that the paper itself partly undermines. read the letter →

arxiv 1908.06192 v1 pith:HBUDLFL4 submitted 2019-08-16 astro-ph.EP

I. Pascucci , G. Mulders , E. Lopez This is my paper · ORCID
classification astro-ph.EP
keywords etaEarthhabitablezoneKepleroccurrenceratesstrippedcoresradiusvalleysub-Neptunesexoplanetdemographics
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 commonly quoted frequency of Earth-size planets in the habitable zone of Sun-like stars, $\eta_\oplus$, is inflated because the extrapolations lean on small short-period planets, many of which are probably sub-Neptune cores stripped by atmospheric loss. Re-fitting the Kepler DR25+Gaia sample with the same forward model but excluding planets with periods shorter than 12 or 25 days lowers $\eta_\oplus$ by a factor of roughly four to eight, to about 5-10%. The paper also shows that the occurrence of $1-1.8\,R_\oplus$ planets drops by about a factor of two between 10-day and 30-day orbits in the high-completeness regime, so the short-period population is not representative of longer-period rocky planets. If correct, this changes the expected yield of Earth analogues for future direct-imaging missions and redirects attention to quantifying stripped cores in young clusters.

What carries the argument

The load-bearing object is the separable broken power-law occurrence model $dN/d\log P\,d\log R = A f(P) f(R)$ (Eq. A1), implemented in the forward-modeling code epos, together with detection and vetting efficiency curves for the Kepler DR25+Gaia sample. The model assumes the period and radius distributions factor, with a broken power law in period (break near 10-12 days) and, for the full radius range, a broken power law in radius (break near 3.3 $R_\oplus$). Fitting this model to subsets with different minimum periods isolates the influence of short-period planets; the radius-valley evidence from photoevaporation models supplies the physical reason why those planets should be excluded.

What would settle it

Measure the occurrence of $1-1.8\,R_\oplus$ planets around Sun-like stars at orbital periods of 100-400 days with independent confirmation, for example via radial-velocity follow-up or long-period transit detections with TESS or PLATO. If the occurrence per log-period bin at those periods matches the extrapolation from periods shorter than 25 days, $\eta_\oplus$ would be near 40%; if it matches the authors' longer-period fit, $\eta_\oplus$ would be near 10%.

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Extended reading notes

Core claim

The central claim is that estimates of $\eta_\oplus$ are biased high by the inclusion of short-period small planets. Using a separable broken power-law model fit to the Kepler DR25 catalogue with Gaia DR2 stellar radii, the authors reproduce the standard result $\eta_\oplus \sim 41\%$ when fitting periods $2-400$ days. Restricting the same fits to periods beyond 12 or 25 days, where photoevaporation should be minimal, yields $\eta_\oplus \sim 4-11\%$, a fourfold to eightfold drop. The drop is driven by the slope of the radius distribution: at short periods the inferred occurrence of planets rises steeply toward Earth radii because that population is contaminated by stripped sub-Neptune cores, whereas at longer periods the small-planet occurrence is lower and flatter.

Load-bearing premise

The separable broken power-law model assumes the planet radius distribution seen at short periods, or at large radii, continues unchanged at the longer periods of the habitable zone; if the radius distribution shifts with orbital period (a period-radius correlation), the extrapolation could be biased.

Editorial extensions

If this is right

  • If $\eta_\oplus$ is 5-10 percent, the expected number of detectable Earth analogues around nearby Sun-like stars is several times smaller than the 20-40 percent baseline used in mission planning.
  • Future occurrence studies should fit periods starting beyond roughly 12-25 days, or explicitly model the stripped-core population, rather than extrapolating the full short-period sample.
  • Kepler's apparent lack of reliable habitable-zone candidates is consistent with a low true $\eta_\oplus$, not just incompleteness.
  • Observations of young clusters can quantify how many short-period sub-Neptunes lose their envelopes, providing a direct correction to the Kepler small-planet population.

Reading between the lines

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

  • Beyond the paper: a low $\eta_\oplus$ strengthens the case that atmospheric loss sculpts the radius distribution, making the period-radius correlation a central observable for demographic models.
  • Beyond the paper: the same stripped-core bias may affect $\eta_\oplus$ estimates for M and K dwarfs, where short-period small planets are also used to anchor extrapolations.
  • Beyond the paper: if future surveys find that Earth-size planets at 0.9-2.2 year periods are as common as the short-period extrapolation predicts, the low $\eta_\oplus$ claim would be ruled out; this is directly testable with TESS or PLATO long-period detections.
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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 / 3 minor

Summary. The paper estimates the frequency of Earth-size planets in the habitable zone of Sun-like stars using the Kepler DR25 catalog with Gaia DR2 stellar parameters and the epos forward-modeling code. It fits a separable broken power-law occurrence model in period and radius over 2-400 days, then integrates the posterior over a conservative habitable zone (0.9-2.2 P⊕, 0.7-1.5 R⊕). The central comparison is between a fit that includes all short-period planets (Model#1, η⊕ ≈ 41%) and fits restricted to P > 12 or 25 days (Models#3-7, median η⊕ ≈ 5-12%). The authors interpret the drop as evidence that short-period small planets, many of which may be stripped sub-Neptune cores, bias η⊕ upward, and they propose young-cluster observations to quantify this contamination.

Significance. If the result holds, it materially lowers the expected yield of Earth analogues for future direct-imaging missions and sharpens the debate on the origin of the radius valley. The paper is methodologically transparent: the code is public, the MCMC setup is standard, several comparison models with different period and radius cuts are presented, and the binned inverse-efficiency occurrence rates in Figure 1 independently show that the small-planet population drops beyond ~10 days. However, the quantitative claim is sensitive to the assumed parametric form of the occurrence surface and to extrapolations beyond the fitted period range, and these dependencies are not fully quantified.

major comments (3)
  1. [Section 2.1, Eq. A1] The central result depends on the separable broken power-law model dN/dlogP dlogR = A f(P) f(R). This form forces the same period dependence on all planet radii. The manuscript itself cites a period-dependent radius valley (Section 1, R_valley ∝ P^-0.09) and Figure 1 shows that the occurrence of 1-1.8 R⊕ planets drops by roughly a factor of two from the ~10-day bin to the ~30-day bin while the 1.8-3.2 R⊕ occurrence rises by ~50%. Those trends cannot be represented simultaneously by a separable model; the fitted radius slope aR is an average over the fitted period range. Since the HZ lies at 0.9-2.2 P⊕ (well beyond most of the fitted data), applying that averaged slope to Earth-size planets at long periods is not justified. Please refit with a non-separable occurrence surface (e.g., a period-dependent radius break or slope), or otherwise demonstrate that the fourfold-to-eightfold drop survives when the radius distribution is measured in period bins that overlap the HZ.
  2. [Table 2] The claim of a 'fourfold to eightfold drop' is based on the median values of the posterior distributions. The 1σ uncertainties on the long-period models are large: Model#5 gives η⊕ = 5.9 +6.0 -3.5% and Model#6 gives 5.4 +7.0 -3.7%. At the upper 1σ boundary these values are ~12%, which is only a factor of ~3.3 below the Model#1 median of 40.6%; Model#4's upper bound gives a factor of ~2.5. The abstract's '~5-10%' similarly understates the posterior width. Please report the drop as a posterior distribution or with explicit uncertainty propagation, and adjust the abstract and text accordingly.
  3. [Section 2.1 and Appendix A] All fits are restricted to orbital periods P < 400 days, but the η⊕ integral is defined over 0.9-2.2 P⊕, i.e., up to ~800 days. The period power law (bP ≈ 0.14) is therefore extrapolated by a factor of two in period, and the radius distribution is assumed to remain fixed. No test is provided for this extrapolation. I request a sensitivity check: refit the long-period models using only P > 100 days or P > 200 days and recompute η⊕, or otherwise bound the systematic error from the period extrapolation.
minor comments (3)
  1. [Figure 1] The sentence in Section 2.1 describing Figure 1 ('Note that the small planets' ~30 days bin has an even higher survey completeness that the bin at 120 days...') is grammatically awkward and should be rephrased for clarity.
  2. [Section 3] The discussion of 'core-powered mass loss correlates with the bolometric luminosity of the star' would benefit from a more precise statement of whether the relevant quantity is stellar luminosity or a more specific function of stellar properties.
  3. [Appendix A] The statement that 'the typical uncertainty in planet radius is included in these Monte Carlo simulations but it is not propagated in the detection efficiency or vetting' leaves it unclear how much the reported uncertainties are affected; a brief justification or a sensitivity test would improve the presentation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the low-η⊕ result is a data-driven refit comparison, not a self-fulfilling derivation.

full rationale

The central claim—that η⊕ drops four- to eightfold when short-period planets are excluded—is obtained by refitting the same separable broken-power-law occurrence model (Eq. A1) to different Kepler DR25+Gaia subsamples (Models #1–#7) and integrating the resulting posterior over a fixed HZ box. The comparison is a data statement: the difference between Models #1/#2 (P>2 days) and Models #3–#7 (P>12 or P>25 days) comes from the fitted power-law slopes (Tables 1 and 2), not from any equation that defines η⊕ in terms of the conclusion. The exclusion thresholds are motivated by photoevaporation models, but the numerical drop is not forced by that motivation; it is an empirical finding that the fitted radius slope flattens or flips when short-period small planets are removed. The M18 and Lopez & Rice self-citations introduce the code and the qualitative concern, but the model equations are restated in Appendix A and the fitted parameters are new to this paper, so the load-bearing result has independent content. The separable f(P)f(R) assumption is a real robustness risk, but a modeling limitation, not a circular reduction.

Assumptions & free parameters 14 free parameters · 6 assumptions · 0 invented entities

All model parameters are fitted to the same Kepler data that define the planet population, so the HZ eta is an extrapolation of fitted trends rather than an independent measurement. The paper introduces no new physical entities. The main burden is carried by the separable power-law assumption and by the theoretical prior that short-period small planets are stripped cores.

free parameters (14)
  • eta normalization Model#1 = 4.6+1.0/-1.1 (percent)
    Number of planets per star integrated over fitted period and radius range; fitted by MCMC to DR25+Gaia data.
  • P_break Model#1 = 11+6/-3 days
    Broken power-law break in orbital period; fitted to the 2 to 400 day sample.
  • a_P Model#1 = 1.6+0.6/-0.3
    Period power-law index for P < P_break; fitted.
  • b_P Model#1 = 0.3+0.1/-0.2
    Period power-law index for P > P_break; controls the long-period extrapolation toward the HZ.
  • R_break Model#1 = 3.4+0.2/-0.3 R_Earth
    Broken power-law break in planet radius; fitted.
  • a_R Model#1 = -0.3+0.2/-0.2
    Radius power-law index for small planets; drives the high eta when short periods are included.
  • b_R Model#1 = -7+2/-2
    Radius power-law index for large planets; fitted.
  • eta normalization Model#4 = 2.7+0.5/-0.3 (percent)
    Normalization for the fit that excludes periods below 12 days and radii below 1 R_Earth.
  • b_P Model#4 = 0.14+0.07/-0.07
    Single period power-law index in Model#4; controls the long-period extrapolation toward the HZ.
  • R_break Model#4 = 3.2+0.2/-0.3 R_Earth
    Radius break in the fit that excludes short-period planets.
  • a_R Model#4 = 1.0+0.5/-0.5
    Radius power-law index for small planets in Model#4; the sign flip relative to Model#1 is the main driver of the eta drop.
  • b_R Model#4 = -6+2/-2
    Radius power-law index for large planets in Model#4; fitted.
  • Minimum period threshold 12 days = 12 days
    Hand-chosen to sit at the known orbital period break for sub-Neptunes; not data-fitted in the usual sense but a selection choice.
  • Minimum period threshold 25 days = 25 days
    Hand-chosen to sit beyond the period where photoevaporation is expected to be minimal; drives the low-eta models.
assumptions (6)
  • domain assumption Kepler DR25 completeness and vetting efficiency curves (Robovetter score >= 0.9) accurately represent the survey's sensitivity.
    Used to weight the likelihood in epos; if incorrect, the fitted occurrence rates and hence eta are biased.
  • domain assumption The occurrence rate is separable in orbital period and planet radius: dN/dlogP dlogR = A f(P) f(R).
    Eq. A1; rules out period-radius correlations, which are known to exist in the radius valley.
  • domain assumption Broken power laws in period and radius are adequate functional forms over the fitted ranges.
    Appendix A; the shape of the tail at long periods and small radii controls the HZ extrapolation.
  • domain assumption Short-period small planets are largely stripped cores of sub-Neptunes, as predicted by photoevaporation and core-powered mass-loss models.
    Section 1 and Section 3; this motivates the exclusion of P < 25 day planets and the interpretation of the result.
  • domain assumption The conservative habitable zone definition of Kopparapu et al. (2013) is correct for Sun-like stars.
    Section 2; eta is defined by integrating over 0.9 to 2.2 P_Earth and 0.7 to 1.5 R_Earth.
  • domain assumption The Gaia DR2 revised stellar radii and the selection of dwarf stars are accurate.
    Section 2.1; the sample of 119,220 dwarfs underpins all fits.

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Pith. "Pith review of The impact of stripped cores on the frequency of Earth-size planets in the habitable zone." pith.science (2026). https://pith.science/paper/HBUDLFL4

@misc{pith2026190806192,
  author       = {Pith},
  title        = {Pith review of: The impact of stripped cores on the frequency of Earth-size planets in the habitable zone},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HBUDLFL4}},
  note         = {Machine review of arXiv:1908.06192}
}
abstract

The frequency of Earth-size planets in the habitable zone of Sun-like stars, hereafter $\eta_\oplus$, is a key parameter to evaluate the yield of nearby Earth analogues that can be detected and characterized by future missions. Yet, this value is poorly constrained as there are no reliable exoplanet candidates in the habitable zone of Sun-like stars in the Kepler field. Here, we show that extrapolations relying on the population of small ($< 1.8\,R_\oplus$) short-period ($< 25\,$days) planets bias $\eta_\oplus$ to large values. As the radius distribution at short orbital periods is strongly affected by atmospheric loss, we re-evaluate $\eta_\oplus$ using exoplanets at larger separations. We find that $\eta_\oplus$ drops considerably, to values of only $\sim 5-10$%. Observations of young ($< 100$ Myr) clusters can probe short-period sub-Neptunes that still retain most of their envelope mass. As such, they can be used to quantify the contamination of sub-Neptunes to the population of Kepler short-period small planets and aid in more reliable estimates of $\eta_\oplus$.

Figures

Figures reproduced from arXiv: 1908.06192 by the authors.

Figure 1
Figure 1. Upper panel: DR25+Gaia candidate list, color coded by survey completeness. The sample includes only dwarfs and planet candidates with a Robovetter score ≥ 0.9. The grey rectangle delineates the HZ, no reliable planet can￾didate is detected inside the HZ. Occurrence rates using the inverse detection efficiency method are also provided for nine period and two radius bins (black rectangles). For clarity these values ar… view at source ↗
Figure 2
Figure 2. epos posterior orbital period (top) and planet radius distributions (bottom) for Model#1. Black vertical dashed lines indicate the range in planet period and radius that epos fits. Red points with errorbars show the occurrence rates calculated with the inverse detection efficiency method. A biased version of the posterior planet radius distribution, assuming no planets below a completeness of 0.03%, is shown in gree… view at source ↗
Figure 3
Figure 3. epos posterior orbital period distribution (top) and planet radius distribution (bottom) for Model#4. Sym￾bols as in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: shows the epos posterior orbital period and planet radius distributions for a model analogue to Model#1 but with the fit restricted in planet period (2-200 days) and radius (1-6 R⊕). This new model results in the same best fit solutions as Model#1, that is why it is no…

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