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An Increase in the Galactic Planet Host Fraction Fails to Reproduce the Galactic Height Trend in Planet Occurrence

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that a time-dependent increase in the Milky Way's small-planet host fraction, whether stepped or gradual, cannot reproduce the steep decline in planet occurrence with height above the Galactic midplane, and that only…

desk verdict A transparent forward-modeling test that likely rules out gradual increases in the planet host fraction as the sole explanation for Z23's steep occurrence–height trend, but the exclusion leans on a shaky age–Zmax calibration. read the letter →

arxiv 2507.21250 v2 pith:YTHI3ICI submitted 2025-07-28 astro-ph.EP astro-ph.GAastro-ph.SR

Christopher Lam , Sarah Ballard , Sheila Sagear , Kathryne J. Daniel This is my paper
classification astro-ph.EPastro-ph.GAastro-ph.SR
keywords planetoccurrencegalacticheightplanetarysystempopulationsynthesisKepler-K2surveyTRILEGALsyntheticisochronestellaragesZmaxoscillationamplitudehostfractionevolution
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

Planet occurrence falls steeply with Galactic height in the Kepler–K2 sample, and metallicity gradients alone cannot fully account for it. This paper tests whether the missing ingredient could be a time-dependent planet host fraction: if planet formation boomed late in the Galaxy's history, young stars near the midplane would host more planets than older, kinematically heated stars that oscillate to greater heights. Using a population-synthesis code with step and gradual growth models for the host fraction, the authors find the effect is too weak. An increase in the host fraction cannot reproduce the observed occurrence–$Z_{\rm max}$ slope; even with idealized (about 1 Gyr) age uncertainties from a synthetic stellar population, gradual increases are ruled out, and only step increases with implausible endpoint fractions (near 1% or 100%) come close. If right, this narrows the search for the driver of the Galactic height trend to processes other than a simple late-time boost in planet formation.

What carries the argument

The machinery is a new planetary-system population-synthesis code, psps, combined with two ways of building the stellar sample. For the real sample, Kepler and K2 stars are taken from the homogeneous HU25 catalog, given isochrone ages from B20 and B25, and assigned a maximum vertical oscillation amplitude $Z_{\rm max}$ by integrating orbits in a Milky Way potential model with the Gala package. The synthetic sample is generated with TRILEGAL, whose built-in kinematic heating maps stellar age to height with much smaller age uncertainties. The host-fraction models are step functions or piecewise-linear ramps from a low early fraction $f_1$ to a present-day $f_2$ at a lookback time $t$, all normalized to a present-day 30–35% host fraction; psps assigns either dynamically compact cold multi-planet architectures or dynamically hot single or two-planet architectures, draws planets and transits, and applies Kepler and K2 detection sensitivity maps. The output is a completeness-corrected occurrence rate per height bin, fit to a power law $y = 100\,\eta\,Z_{\rm max}^{\tau}$, whose slope $\tau$ is compared with the Z23 trend.

What would settle it

Measure the age–$Z_{\rm max}$ relation for the joint Kepler–K2 sample using asteroseismic ages that are much more precise than the isochrone ages used here; if that relation turns out to be substantially steeper than the soft trend in the paper's Figure 3, the synthetic occurrence–height slopes would steepen and an increasing host fraction could reproduce the Z23 trend, undercutting the paper's central claim.

Watch

Extended reading notes

Core claim

The central claim is that a time-dependent planet host fraction $f$—rising from a primordial $f_1$ to a present-day $f_2$ either instantaneously or gradually—cannot, under the models tested, reproduce the steep decline in small-planet occurrence with $Z_{\rm max}$ measured by Zink et al. (2023, hereafter Z23). Applied to a joint Kepler–K2 sample with isochrone ages, almost every step and piecewise model yields an occurrence–height slope $\tau$ flatter than the observed $\tau \approx -0.28 \pm 0.08$, and the handful that come within one standard deviation require $f_1 \approx 1\%$ or $f_2 \approx 100\%$ at thresholds 2.2–3.2 Gyr ago. Using TRILEGAL synthetic stars with roughly 1 Gyr age uncertainties, gradual increases in $f$ are ruled out even in the idealized case, while the best step matches remain anchored at an extreme $f_2 = 100\%$. An independently derived Kepler-only occurrence–height trend has slope $-0.25 \pm 0.05$, close to the combined trend, and is somewhat easier for a step increase to match. The conclusion is that an increase in $f$ alone is insufficient; the paper suggests a time-evolving fraction of compact multi-planet systems, or separate $f$ histories for Super-Earths and Sub-Neptunes, as more flexible alternatives.

Load-bearing premise

The whole test rests on the assumption that the measured age-to-maximum-height relation is tight and unbiased; if older stars do not systematically reach larger $Z_{\rm max}$ in the real sample, or if the true relation is much steeper than the soft isochrone-age trend, a time-dependent host fraction could produce the observed slope and the paper's main exclusion would weaken.

Editorial extensions

If this is right

  • If the paper's exclusion holds, any explanation of the occurrence–height trend must involve something beyond a simple age-dependent boost in the number of stars that host small close-in planets, such as separate host-fraction histories for Super-Earths and Sub-Neptunes or a time-evolving fraction of compact multi-planet systems.
  • The timing constraints narrow possible physical triggers: step thresholds that nearly match are 2.2–3.2 Gyr ago, so earlier Galactic events such as the Gaia-Enceladus merger and the first Sagittarius passage are disfavored as the dominant cause.
  • The independently derived Kepler-only occurrence–height slope agrees with the joint trend within uncertainties, indicating the effect is not an artifact of combining two surveys with different detection sensitivities.
  • A gradual rise in the planet host fraction is excluded even with age uncertainties as small as about 1 Gyr, which strengthens the conclusion that a sudden, relatively recent process is required if the host fraction participates at all.

Reading between the lines

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

  • An immediate extension would be to treat the fraction of intact compact multi-planet systems as a free parameter; since the paper's models are consistently too shallow, an increase in that fraction with time should steepen the predicted occurrence–$Z_{\rm max}$ trend and could remove the need for extreme $f_1$ or $f_2$ values.
  • The paper's timing constraints are conditional on the isochrone age–$Z_{\rm max}$ relation; a steeper relation, as may come from asteroseismic ages, would re-open the step and gradual models the paper excludes.
  • A larger uniformly aged K2 sample would be a useful check: the joint sample here contains only 141 K2 stars, and the K2 ages come from a planet-host-only catalog, so the relative weight of the two surveys in the observed trend is not yet measured as precisely as the Kepler part.
  • Replacing $Z_{\rm max}$ with the vertical action $J_z$, which correlates more tightly with age, is a natural next test; if the occurrence–height trend persists in $J_z$, a time-dependent host fraction would have to be reconsidered.
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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 / 5 minor

Summary. The paper asks whether an increase over time in the fraction of FGK stars hosting small close-in planets can explain the Zink et al. (2023) decline of planet occurrence with maximum Galactic height Zmax. The authors construct a real Kepler+K2 sample with isochrone ages from the HU25/B20/B25 catalogs and a synthetic TRILEGAL sample with much more precise ages, prescribe step and piecewise host-fraction histories f1→f2 at lookback time t (all normalized to a present-day host fraction of roughly 30-35%), synthesize planetary systems with the new psps code, apply Kepler/K2 completeness models, and fit a power law to occurrence versus Zmax. They find that most models produce slopes τ shallower than the observed τ=-0.28±0.08, with only extreme late-time step increases approaching the observed trend, and that gradual increases remain too shallow even in the TRILEGAL sample. A Kepler-only analysis yields a less steep observed trend that a step increase can match.

Significance. If the result holds, it demonstrates that a purely time-dependent planet host fraction is not sufficient to explain the Z23 occurrence–height trend, pointing toward size-dependent or architectural evolution as additional ingredients. The paper's strengths include the two independent sample constructions, the transparent listing of all model fits in Table 2, the public psps code, and the explicit acknowledgment in Section 4 that the weak age–Zmax relation is a possible source of dilution. However, the strength of the central exclusion is limited by the calibration of the age–Zmax mapping: in the real sample this mapping is built from large-uncertainty isochrone ages, and in the TRILEGAL experiment it is an assumed kinematic heating law rather than an empirically calibrated relation. The conclusion is plausible but conditional; robustness tests against these two points are needed before the exclusion can be regarded as fully established.

major comments (3)
  1. [Sections 2.1.2–2.1.3, Figs. 3 and 6, Section 4] The central exclusion rests on how steeply stellar age maps to Zmax. In the real sample this map is only a 'soft positive trend' built from isochrone ages with mean upper uncertainties of 2.8 Gyr (Kepler) and 5.6 Gyr (K2), and the 30 redraws resample the same posteriors, so they cannot correct a systematic flattening if old high-Zmax stars are assigned younger ages. In the TRILEGAL experiment the age precision is high, but the age–Zmax link is not empirical: it is the adopted heating law h_z=z0(1+t/t0)^α with α=5/3 and a two-step star-formation history. If the true age–Zmax gradient is steeper—the paper itself cites asteroseismic estimates of ~4 Gyr/kpc—the same f1→f2 histories would yield steeper occurrence–Zmax slopes, potentially bringing gradual models within 1σ of Z23. The paper flags this possibility in Section 4, but it does not quantify it. I request a sensitivity test (for example, rerunning the TRILEGAL experiment with alternate α values or with an empirically calibrated age–Zmax relation) before the claim that gradual models are ruled out 'even with very precise ages' is accepted.
  2. [Section 3.3, Fig. 12, and Abstract/Conclusion] The abstract's unqualified statement that 'an increase in f is insufficient to reproduce the strength of the observed trend' is in tension with the paper's own Kepler-only analysis: the step model {f1=20%, f2=100%, t=2.2 Gyr} yields τ=-0.20±0.07 against the derived Kepler-only observed τ=-0.25±0.05, which the authors call a relatively good match. The joint-sample exclusion therefore depends on the K2 component, which after all cuts contains only 141 stars, and whose completeness maps are shot-noise dominated (Section 2.4, Fig. 8). The authors should either demonstrate that the joint exclusion is robust to K2 sample size and noise (for example, by jackknifing over K2 campaigns or repeating the analysis without K2), or qualify the central claim so that it applies to the joint sample but not to the Kepler-only trend.
  3. [Section 2.2 and Section 3.1, Table 2] The argument that testing the limits f1=1% and f2=100% 'sets the maximum slope' of the occurrence–Zmax trend for any given t is asserted but not demonstrated. Table 2 contains no model with both f1=1% and f2=100% simultaneously; the models with t=2.7 and t=3.2 Gyr have f1=1%, f2=95% and f1=1%, f2=75%, respectively. If the true steepest model compatible with the present-day host-fraction constraint lies outside the tested grid, the claim to 'rule out entire t' intervals is stronger than the evidence. The authors should either show that the predicted τ is monotonic in f1 and f2 (decreasing as f1 decreases and f2 increases), or perform a small optimization over the (f1,f2) plane for each threshold t.
minor comments (5)
  1. [Figure 1 caption and Section 2.1.1] The text interprets a KS p-value of 7e-4 as indicating 'a very high probability' that the two age distributions are drawn from the same population; with large samples, small p-values can accompany small distribution differences, so the p-value alone does not support the phrase used. Please rephrase in terms of the small CDF separation or report an effect size.
  2. [Equation (8), Section 3.1] The normalization states dlnZmax = 0.0011, but five evenly log-spaced bins from 100 to 1000 pc imply dlnZmax ≈ 0.46; please clarify whether this is a typo or whether a different binning was used, since it affects the reported normalization η.
  3. [Figure 12 caption vs. Section 3.3] The Figure 12 top-panel caption says the model is {f1=5%, f2=80%, t=9.5 Gyr}, while the text describes the matched model as {f1=20%, f2=100%, t=2.2 Gyr}; these are inconsistent and should be reconciled.
  4. [Figure 7 and Section 2.2] The model parameters are sometimes written without units (for example 't=1.7' rather than '1.7 Gyr ago'); please label the lookback time consistently in the figure insets and table headers.
  5. [Figure 5 caption] The histogram panel for 'height' compares TRILEGAL instantaneous height with HU25-B20-B25 Zmax; the caption notes this but using different vertical coordinates in the same normalized panel can mislead readers. Please state explicitly in the caption that the two quantities are not directly comparable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the time-dependent host-fraction models are forward-modeled against the independent Zink et al. (2023) trend, with f1, f2, and t anchored only to the externally measured present-day host fraction.

full rationale

The paper's central claim is a falsification test, not a fit. The model parameters f1, f2, and t are hand-scanned and normalized to the externally measured present-day planet-host fraction of 30–35% (Zhu et al. 2018); they are never fit to the target occurrence–Galactic-height slope. The Z23 trend (τ = -0.28±0.08 after the authors' re-fit) is an external observed benchmark, and the modeled yields are compared to it after independent completeness corrections. The 'steepest possible' bounding argument (f1=1%, f2=100%) is a model-derived limit, not an input assumption equivalent to the conclusion. The only self-referential element is the constant hot/cold system fraction adopted from Lam & Ballard (2024), but that is an externally published empirical prior, not a parameter fitted in this paper; the authors explicitly identify relaxing the intact fraction as future work, showing it is an assumption rather than a circular reduction. Likewise, the weak age–Zmax relation is explicitly flagged as a potential systematic (Section 4) and is a measurement/calibration limitation, not a case where an equation reduces to itself. No step in the derivation chain equates the target result to an input by construction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The core model family is a grid of hand-chosen f1, f2, t combinations. These are not fitted to the target occurrence-height trend, but the breadth of the grid limits the strength of the exclusion: only extreme f1/f2 combinations approach the observed slope.

free parameters (4)
  • f1 (primordial host fraction) = 0.01 to 0.20 across 13 models
    Chosen by hand for each step/piecewise model; together with f2 and t constrained by the external requirement that the present-day host fraction be 30-35%.
  • f2 (present-day host fraction) = 0.35 to 1.00 across 13 models
    Set to the extreme limits (e.g., 100%) in several models to maximize the occurrence-height slope; not fitted to the target trend.
  • t (threshold lookback time) = 1.7 to 8.2 Gyr ago
    Iterated by hand to span the plausible range; the models that survive have t between 2.2 and 3.2 Gyr.
  • intact STIPs fraction = 18% ± 10% (normal prior)
    Drawn from a normal distribution around the prior measurement of Lam & Ballard (2024); held constant with age; not fitted to the Z23 trend.
assumptions (6)
  • domain assumption Age-Zmax relation from Gala orbits and isochrone ages is a valid proxy for galactic height history.
    Section 2.1.2: the bottom panel of Figure 3 shows only a 'soft positive trend'; the entire exclusion depends on older stars reaching larger Zmax.
  • domain assumption TRILEGAL's two-step star formation history and kinematic heating (h_z = z0(1+t/t0)^alpha) describe the Milky Way thin disk.
    Section 2.1.3: the idealized sample assumes precise ages and built-in scale-height evolution; if the real disk heated differently, the synthetic-sample conclusions could change.
  • domain assumption Present-day planet host fraction around FGK dwarfs is 30-35%.
    Section 2.2: from Zhu et al. (2018); all models are normalized to this external value.
  • domain assumption Fraction of dynamically cool compact multi systems is ~18% and independent of age.
    Section 2.3: from Lam & Ballard (2024), a self-cited prior result; holding it constant removes a degree of freedom that could otherwise steepen the trend.
  • domain assumption Detection completeness maps (Thompson 2018, Zink 2021) and the inverse detection efficiency method are valid per Zmax bin.
    Section 2.4: the recovered yields are adjusted with these maps; errors in them propagate directly into the model slopes.
  • domain assumption The Milky Way is 13.7 Gyr old.
    Section 2.2: sets the lookback time scale for the models.

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Cite this review

Pith. "Pith review of An Increase in the Galactic Planet Host Fraction Fails to Reproduce the Galactic Height Trend in Planet Occurrence." pith.science (2026). https://pith.science/paper/YTHI3ICI

@misc{pith2026250721250,
  author       = {Pith},
  title        = {Pith review of: An Increase in the Galactic Planet Host Fraction Fails to Reproduce the Galactic Height Trend in Planet Occurrence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YTHI3ICI}},
  note         = {Machine review of arXiv:2507.21250}
}
read the original abstract

While stellar metallicity has long been known to correlate with planetary properties, the galactic metallicity gradient alone does not account for the observed strong trend in planet occurrence with Galactic height. In this study, we investigate the observable effect of a time-dependent planet occurrence rate upon a sample of stars selected uniformly from the Kepler and K2 surveys. Using a novel planetary system population synthesis code, psps, we impose several prescriptions for a time-variable planet host fraction, f, in which a primordial f1 either instantaneously or gradually increased to a present-day f2. We then simulate the expected small planet occurrence rate around FGK dwarfs as a function of galactic height. Finally, we compare the modeled trends to the observed result from the missions themselves. We find that using a joint Kepler-K2 sample with isochrone ages, an increase in f is insufficient to reproduce the strength of the observed trend between occurrence and Galactic height. We show that not all of this is due to insufficient age precision: using a synthetic stellar population from the TRILEGAL framework, we show that even with very precise ages, we can rule out models of gradually increasing f. We also derive the Kepler occurrence-height relation and find that an increase in f is better able to match this trend. An analysis using more precise ages and incorporating an evolving compact multi fraction could furnish a realistic relation in planet occurrence with Galactic height that matches the observed Kepler-K2 trend.

Figures

Figures reproduced from arXiv: 2507.21250 by the authors.

Figure 1
Figure 1. — Cumulative distribution functions of Gaia DR2 isochrone ages for the B20 sample, split between hosts (solid) and non-hosts (dashed). A KS test shows that these age distributions are very likely drawn from essentially the same population, satis￾fying our check that the use of purely host ages from B25 does not introduce a selection bias. in Z23). We then cross-match the HU25 Kepler catalog with B20 and the HU25 K2 … view at source ↗
Figure 2
Figure 2. — Top left: HR diagram of the HU25 Kepler, B20, and HU25-B20 cross-matched samples after culling by T eff, log g, [Fe/H], and age (for B20). Top right: Same as top, but for the culled HU25 and B25 K2 samples and their cross-match. Bottom left: Kiel diagram of HU25 Kepler, B20, and HU25-B20. Bottom right: Kiel diagram of HU25 K2, B25 K2, and HU25-B25 K2. TABLE 1 Number of stars after each stage of data preparation Da… view at source ↗
Figure 3
Figure 3. — Top: Kiel diagram of the combined HU25-B20-B25 sample, color-coded by age. Top and right marginalized histograms show the Teff and log g distributions, respectively. The median Teff and log g are 5703 K (MAD of 215 K) and 4.356 dex (MAD of 0.089 dex), respectively. Bottom: We observe a soft positive trend between isochrone age and Zmax, as calculated by the Gala (Price-Whelan 2017; Price-Whelan et al. 2020) softwa… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: — Galactic latitudes and longitudes for our combined HU25-B20-B25 Kepler−K2 sample (gray), the K2 TRILEGAL search field (blue), and the Kepler TRILEGAL search field (orange). TRILEGAL search field dots are scaled to be 10 deg2 (even if the fields themselves are not qui…
Figure 5
Figure 5. Figure 5: — Normalized histograms of key parameters for the HU25-B20-B25 Kepler−K2 sample (gray) and the TRILEGAL Kepler−K2 sample (purple). Note that the “height” histogram refers to instantaneous height for TRILEGAL and Zmax for HU25-B20-B25. The medians and median absolute de…
Figure 6
Figure 6. Figure 6: — Top: Kiel diagram of the TRILEGAL Kepler-K2 sam￾ple, color-coded by age. Top and right marginalized histograms show the Teff and log g distributions, respectively. Bottom: Age￾Zmax relation for the TRILEGAL Kepler-K2 sample. Note that height for the TRILEGAL is the i…
Figure 7
Figure 7. Figure 7: — Galactic sculpting models, characterized by step and piecewise functions with a lower planet-host fraction after some event in the Milky Way’s past led to an increase in planet hosts among Sun-like stars. We also include a control model that holds the planet host fra…
Figure 8
Figure 8. Figure 8: — Detection sensitivity maps were constructed by injecting a geometrically transiting planet at each period and radius bin for 1000 random Kepler stars or the entirety of the K2 stars in each Zmax bin. Here we show four representative sensitivity maps: lowest-Zmax bin …
Figure 9
Figure 9. Figure 9: — Planet occurrence versus Zmax for the step function planet occurrence models, shown in insets. We consider only planets with period 1 < Pp < 40 days and radius 1.2 R⊕ < Rp < 4 R⊕. All models are constrained to produce a present-day planet host fraction of approximate…
Figure 10
Figure 10. Figure 10: — Planet occurrence versus Zmax for six piecewise models with t separated by 1 Gyr. Models, shown in insets, prescribe a flat planet host fraction f1 until a time t at which this fraction gradually rises to some current f2. Favored models are shaded in gray. Top left:…
Figure 11
Figure 11. Figure 11: — Planet occurrence versus Zmax for four step and four piecewise models using the TRILEGAL synthetic stellar sample. Favored models are shaded in gray.Top left: Piecewise, f1=15%, f2=100%, t=3.2 Gyr. Top right: Piecewise f1=1%, f2=100%, t=4.2 Gyr. Second row left: Pie…
Figure 12
Figure 12. Figure 12: — Top: Planet occurrence versus Zmax for a fiducial step function model applied to just the Kepler sample. The model used here is f1=5%, f2=80%, t=9.5 Gyr. Using only the Kepler field, it is clear we require a broken power law to better model the occurrence-Zmax trend…

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