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

This study demonstrates that a time-dependent increase in the planet host fraction alone is insufficient to reproduce the observed strong trend of planet occurrence with Galactic height in a combined Kepler-K2 sample, suggesting that additional factors such as more precise stellar ages and an evolving fraction of compact multi-planet systems are required to explain the data.

Original authors: Christopher Lam, Sarah Ballard, Sheila Sagear, Kathryne J. Daniel

Published 2026-06-26

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CC BY 4.0

Original authors: Christopher Lam, Sarah Ballard, Sheila Sagear, Kathryne J. Daniel

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Question: Why are planets harder to find on the "upper floors" of our galaxy?

Imagine the Milky Way galaxy as a massive, multi-story apartment building.

The Midplane (Ground Floor): This is the dense, metal-rich center of the galaxy where most stars are born.
Galactic Height (Upper Floors): As you go higher up (further from the center plane), the "air" gets thinner, and the stars are older and have fewer heavy elements (metals).

A recent study (Zink et al., 2023) found a strange pattern: The higher up you go in this galactic building, the fewer planets you find. It's as if the "upper floor" apartments are mostly empty, while the "ground floor" is packed with families.

Scientists know that planets usually like metal-rich environments (like a garden with rich soil). So, they assumed the drop in planets on the upper floors was just because the soil (metallicity) was poorer there.

But this paper says: "Not quite." The drop in soil quality isn't enough to explain why the upper floors are so empty. The authors wanted to test if something else was happening: Did the "birth rate" of planets change over time?

The Experiment: Testing the "Planet Birth Rate"

The authors asked: What if, in the past, it was very hard to make planets, and then suddenly (or gradually), it became much easier?

If planets were mostly born recently, and if those recent stars tend to live on the "ground floor" (because they haven't had time to drift up to the "upper floors" yet), that could explain the empty upper floors.

To test this, they built a virtual simulation (a "digital twin" of the galaxy) using a custom code called psps. They created two main types of scenarios:

The "Light Switch" Model (Step Function): Imagine a switch that was off for billions of years, and then suddenly flipped ON a few billion years ago. Suddenly, 95% of stars started having planets instead of just 1%.
The "Dimmer Switch" Model (Gradual Increase): Imagine the planet-making ability slowly turning up like a dimmer switch over time, going from a low setting to a high setting.

They ran these simulations against two different groups of stars:

Real Stars: Actual data from the Kepler and K2 telescopes, but with estimated ages (which can be a bit fuzzy, like guessing someone's age just by looking at them).
Fake Stars: A perfect, computer-generated population (TRILEGAL) where the ages are known exactly, to see if "fuzzy math" was the problem.

The Results: The "Birth Rate" Theory Fails

Here is what they found:

1. Turning up the "Planet Birth Rate" isn't enough.
Even when they simulated a massive explosion in planet formation (flipping the switch to 100% of stars having planets), the resulting trend was too flat.

Analogy: Imagine trying to explain why a city's traffic is heavy only on Main Street by saying "more people started driving cars recently." But even if everyone started driving, the traffic pattern didn't match the reality of the empty side streets. The simulation showed that simply having more planets today doesn't create the steep drop-off in planet numbers that we actually see on the "upper floors."

2. The "Fuzzy Age" wasn't the culprit.
The authors worried that maybe their real star data was just too messy (imprecise ages) to see the pattern. So, they ran the simulation with the "perfect" fake stars.

Result: Even with perfect data, the "birth rate" theory still failed to match the steepness of the real-world observation. The models were still too flat.

3. The "Step" vs. "Dimmer" Debate.
The only models that came close to matching the real data were the "Light Switch" models (sudden jumps) that happened very recently (about 2–3 billion years ago). However, these required impossible settings, like saying "0% of stars had planets in the past" and "100% have them now." This is physically unrealistic. The "Dimmer Switch" (gradual increase) models failed completely.

What Does This Mean?

The paper concludes that a simple increase in the number of planets over time cannot explain the pattern.

If you look at the galaxy as a building:

Old Theory: The upper floors are empty because the soil is bad (low metallicity).
This Paper's Finding: The soil isn't the only reason. Even if we assume planets started appearing everywhere recently, it still doesn't explain why the upper floors are so empty compared to the ground floor.

The "Next Steps" (According to the Authors)

The authors suggest that to solve this mystery, we might need to look at different factors, such as:

Different types of planets: Maybe the "birth rate" changed differently for small rocky planets vs. larger gas planets.
System stability: Maybe older planetary systems are getting "broken" or destroyed over time (like a house falling apart), rather than just new ones being built.
Galactic Events: Perhaps a specific cosmic event (like a dwarf galaxy crashing into the Milky Way) happened recently that changed the rules of planet formation, but we need more precise data to prove it.

In short: The paper is a "reality check." It tells us that the simple idea of "planets became more common recently" is not the whole story. The universe is more complex, and the reason planets are missing from the "upper floors" of our galaxy remains a puzzle.

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

Problem Statement
Recent observational results, specifically Zink et al. (2023) (hereafter Z23), have identified a strong trend where the occurrence rate of small planets (Super-Earths and Sub-Neptunes) around FGK dwarfs decreases significantly with increasing maximum vertical oscillation amplitude ( $Z_{max}$ ) from the Galactic midplane. While stellar metallicity is known to correlate with planet formation, the Galactic metallicity gradient alone is insufficient to explain the steepness of this observed decline. The central question addressed by this study is whether a time-dependent increase in the planet host fraction ( $f$ ) over the history of the Milky Way could reproduce the observed occurrence- $Z_{max}$ trend. The authors investigate if a "boost" in planet formation efficiency at some point in the Galaxy's past, combined with the kinematic heating of stellar orbits over time, can account for the deficit of planets at high Galactic heights.

Methodology
The authors developed a novel planetary system population synthesis code, psps, to simulate synthetic planetary populations around a sample of FGK dwarfs. The methodology involved the following steps:

Stellar Samples: Two distinct stellar samples were constructed to test the robustness of the results against age uncertainties:
- Real Sample: A joint Kepler and K2 sample (22,184 stars) drawn from the Hardegree-Ullman et al. (2025) catalog, cross-matched with isochrone ages from Berger et al. (2020b, 2025). $Z_{max}$ values were calculated using Gaia DR3 kinematics and a Galactic potential model via the Gala package.
- Synthetic Sample: A TRILEGAL population synthesis sample (49,109 stars) tuned to resemble the Kepler and K2 fields. This sample provided an "optimistic" scenario with arbitrarily precise stellar ages and known kinematic heating models, allowing the authors to isolate the effects of age precision from the physical models.
Time-Dependent Occurrence Models: The study tested two families of models for the evolution of the planet host fraction ( $f$ ) as a function of stellar age (lookback time):
- Step Functions: A sudden jump from an initial fraction $f_1$ to a present-day fraction $f_2$ at a specific lookback time $t$ .
- Piecewise Functions: A gradual linear increase from $f_1$ to $f_2$ starting at time $t$ .
- All models were constrained to yield a present-day planet host fraction of $\sim30-35\%$ , consistent with observational constraints.
Population Synthesis and Observation: Using psps, the authors generated planetary systems based on the prescribed $f$ for each star. Systems were assigned architectures (compact multi-planet systems vs. single planets) and orbital parameters (eccentricity, inclination) based on existing demographic constraints (e.g., Lam & Ballard 2024). The synthetic populations were then "observed" using inverse detection efficiency methods (IDEM) that accounted for the geometric transit probability and the specific sensitivity functions of the Kepler and K2 missions.
Analysis: The simulated occurrence rates were binned by $Z_{max}$ (100–1000 pc) and fitted with a power law ( $y \propto Z_{max}^\tau$ ) to determine the slope ( $\tau$ ) and normalization ( $\eta$ ). These results were compared against the observed trend from Z23 ( $\tau \approx -0.28$ ).

Key Results

Insufficiency of Host Fraction Increases: The study finds that increasing the planet host fraction ( $f$ ) over time, whether instantaneously or gradually, is generally insufficient to reproduce the steepness of the observed occurrence- $Z_{max}$ trend.
Model Constraints:
- For the real Kepler-K2 sample, the vast majority of models produced slopes ( $\tau$ ) that were too shallow (closer to 0) compared to the observed $\tau \approx -0.28$ . The models that came closest to matching the trend required extreme, physically implausible parameters (e.g., $f_1 \approx 1\%$ or $f_2 \approx 100\%$ ) and step times ( $t$ ) restricted to a narrow window between 2.2 and 3.2 Gyr ago.
- For the TRILEGAL synthetic sample (with precise ages), the results were similar. While a late-time instantaneous rise in $f$ could match the Z23 slope, it again required tuning to theoretical extrema ( $f_1=1\%$ or $f_2=100\%$ ). This suggests that even with perfect age precision, a simple increase in $f$ cannot single-handedly drive the observed trend.
Kepler-Only Analysis: When analyzing only the Kepler field (which has a different age distribution and lacks the K2 data), the derived occurrence- $Z_{max}$ slope was similar to the joint sample. A step increase in $f$ matched this Kepler-only trend slightly better, but the fundamental difficulty in reproducing the steepness remained.
Role of Age Precision: The comparison between the real and synthetic samples indicates that the inability of the models to match the trend is not primarily due to insufficient precision in stellar age measurements. Even with idealized ages, the "gradual increase" models were ruled out, and "step" models required unrealistic parameters.

Significance and Claims
The paper concludes that the observed strong negative correlation between small planet occurrence and Galactic height cannot be explained solely by a time-dependent increase in the fraction of stars hosting planets. The authors state that while a late-time boost in $f$ (specifically a step function occurring 2–3 Gyr ago) can marginally reproduce the trend, it requires tuning to the physical limits of the model (e.g., nearly 100% of stars hosting planets today).

The authors argue that the discrepancy implies that other factors must be at play. They suggest that future models might achieve a better fit by:

Distinguishing between Super-Earths and Sub-Neptunes (as Z23 found the trend is driven primarily by Sub-Neptunes).
Allowing the fraction of "intact" compact multi-planet systems to evolve over time, rather than keeping it constant.
Investigating physical mechanisms that either enhance recent planet formation or progressively disrupt older systems (e.g., via stellar flybys, galactic tides, or changes in ISM turbulence).

The study emphasizes that the canonical picture of local metal enrichment as the sole link between Galactic context and planet demographics is insufficient in the Gaia era. The results highlight the need to connect Galactic-scale dynamical history (mergers, satellite infalls) with local processes affecting protoplanetary disks and system stability to fully explain exoplanet demographics.

The Big Question: Why are planets harder to find on the "upper floors" of our galaxy?

The Experiment: Testing the "Planet Birth Rate"

The Results: The "Birth Rate" Theory Fails

What Does This Mean?

The "Next Steps" (According to the Authors)

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