Revisiting the exoplanet radius valley with host stars from SWEET-Cat

By re-examining 1,405 exoplanets orbiting 1,221 stars with high-precision parameters from SWEET-Cat, this study confirms the existence of the radius valley and reveals its dependence on period, flux, stellar mass, and age, providing evidence that supports a core-powered atmospheric mass loss scenario while highlighting the need for improved stellar characterizations in future missions like PLATO.

The Gist

Imagine the universe as a massive, bustling city of planets. For a long time, astronomers noticed something strange about the "apartments" (planets) orbiting nearby stars. There seemed to be a distinct gap in the building sizes.

You had Super-Earths: small, rocky apartments, cozy and compact (about 1.5 times the size of Earth).
Then you had Sub-Neptunes: much larger, fluffy apartments wrapped in thick, puffy gas coats (about 2.5 times the size of Earth).

But right in the middle? There was a Radius Valley. It was like a "No Vacancy" sign hanging over the 2x-Earth-size apartments. Very few planets lived there.

This new paper, written by a team of astronomers, is like a team of expert building inspectors who just got brand-new, high-tech measuring tapes. They wanted to re-measure these planets to see if the "No Vacancy" sign was real, and more importantly, why that gap exists.

Here is the story of their discovery, explained simply:

1. The Old Tapes vs. The New Tapes

In the past, measuring these planets was like trying to measure a house while wearing foggy glasses. The astronomers knew the size of the planet relative to its star, but they weren't sure exactly how big the star was. If you guess the star is 10% bigger than it really is, your planet looks 10% bigger too.

This new study used a super-smart computer program called MAISTEP (think of it as a "Stellar GPS") combined with data from the European space telescope Gaia. They measured the stars with incredible precision.

• The Result: With these new, crystal-clear measurements, the "Radius Valley" didn't just exist; it looked deeper and clearer than before. The gap is real, but it's not completely empty; a few brave planets are still hanging out in the middle.

2. The Great Cosmic Shrink-Ray

The big question is: Why is there a gap? Why don't we see many planets that are exactly 2 times the size of Earth?

The paper suggests that planets are like balloons that slowly lose air over time.

• The Sub-Neptunes are the big, puffy balloons.
• The Super-Earths are the deflated, rocky cores left behind after the air is gone.
• The Valley is the transition zone where the balloon is losing its air but hasn't fully deflated yet.

The team looked at three main "knobs" that control how fast these balloons shrink:

A. The Distance Knob (Orbital Period)

• The Analogy: Imagine a campfire. If you sit right next to it (close to the star), you get roasted quickly. If you sit far away, you stay warm but don't burn.
• The Finding: Planets closer to their star lose their gas coats faster. So, the "gap" moves to smaller sizes for close-in planets. As you move further out, the gap shifts to larger sizes because those planets are safer and keep their gas longer.

B. The Star's Size Knob (Stellar Mass)

• The Analogy: A massive star is like a giant, roaring furnace. A smaller star is like a gentle heater.
• The Finding: Planets orbiting massive, hot stars tend to be larger on average. It seems that around bigger stars, the "balloons" (planets) start out puffier, so the gap between the rocky ones and the gas ones shifts to a larger size.

C. The Time Knob (Stellar Age)

• The Analogy: This is the most exciting part. Imagine a forest that changes over centuries. Young trees look different from old trees.
• The Finding: The team looked at young stars (less than 3 billion years old) vs. old stars (older than 3 billion years).
  • Young Systems: The gap is deep, and there are fewer "Super-Earths."
  • Old Systems: The gap gets shallower, and there are more Super-Earths relative to Sub-Neptunes.
  • What this means: Over billions of years, the puffy Sub-Neptunes are slowly losing their gas coats and turning into rocky Super-Earths. It's a slow-motion transformation. The "balloon" doesn't pop instantly; it slowly deflates over eons.

3. The "Core-Powered" Theory

There are two main theories about what causes this deflation:

1. Photoevaporation: The star blasts the planet with high-energy radiation (like a laser beam) and strips the gas away early in the planet's life.
2. Core-Powered Mass Loss: The planet's own internal heat (leftover from its birth) pushes the gas away, like a slow leak in a tire.

The Paper's Verdict:
The fact that the gap changes over billions of years (the "Time Knob") strongly supports the Core-Powered Mass Loss theory. If it were just the star's laser beam (Photoevaporation), the gas would have been stripped away very quickly in the first few million years, and the gap wouldn't change much as the stars got older.

Because the gap does change over time, it suggests the planets are slowly, steadily losing their atmospheres due to their own internal heat, a process that takes a very long time.

The Bottom Line

This study is a major step forward because it used the best possible tools to measure the stars. It confirms that the "Radius Valley" is a real feature of our universe, not just a measurement error.

More importantly, it tells us that planets are not static statues; they are dynamic, evolving worlds. A planet that starts as a puffy, gas-rich Sub-Neptune can, over the course of billions of years, slowly shrink and transform into a rocky Super-Earth. It's a cosmic journey of shrinking, driven by the planet's own internal heat, reshaping the population of worlds in our galaxy.

In short: The universe is full of planets that are slowly deflating, and this paper gave us the clearest map yet to see exactly where and how that deflation happens.

Technical Summary

Here is a detailed technical summary of the paper "Revisiting the exoplanet radius valley with host stars from SWEET-Cat" by Kamulali et al. (2026).

1. Problem Statement

The "radius valley" (or radius gap) is a bimodal distribution in the sizes of small exoplanets ($\lesssim 5 R_\oplus$), characterized by a deficit of planets with radii around $2 R_\oplus$. This feature separates **super-Earths** (rocky,$\lesssim 1.9 R_\oplus$) from **sub-Neptunes** (volatile-rich,$\gtrsim 2 R_\oplus$).

The physical origin of this valley is debated, with two primary competing mechanisms:

• Photoevaporation: High-energy stellar radiation strips atmospheres early in a system's life ($\sim 100$ Myr).
• Core-powered mass loss: Atmospheric escape is driven by the planet's internal cooling luminosity over gigayear (Gyr) timescales.

Previous studies have yielded conflicting results regarding whether the valley is empty or partially filled, and how its location depends on orbital period, stellar mass, and stellar age. These discrepancies often stem from uncertainties in host star parameters (radius, mass, age), which propagate directly into planetary radius calculations. This study aims to re-examine the radius valley using a large, homogeneous sample of host stars with highly precise fundamental parameters derived via machine learning.

2. Methodology

Data Sample:

• Source: The study utilizes the SWEET-Cat database, cross-matched with the NASA Exoplanet Archive.
• Selection: 1,221 main-sequence stars (hosting 1,405 confirmed planets) were selected. The sample was restricted to stars with effective temperatures ($T_{\text{eff}}$) between 4400–7500 K (FGK types) and radii between 0.62–2.75 $R_\odot$.
• Final Analysis Sample: After filtering for orbital periods $< 100$ days, planet radii between 1–4 $R_\oplus$, and relative uncertainties in planet-to-star radius ratios $< 10\%$, the final sample consisted of 893 confirmed planets hosted by 779 stars.

Stellar Parameter Derivation (MAISTEP):

• The authors employed MAISTEP (Machine learning Algorithms for Inferring STEllar Parameters), a grid-based ensemble machine learning tool.
• Inputs: Spectroscopic effective temperatures ($T_{\text{eff}}$), metallicities ([Fe/H]), and Gaia-based luminosities ($L$).
• Training: The model was trained on a grid of stellar evolutionary tracks (Moedas et al. 2024) covering masses from 0.7 to 1.75 $M_\odot$, incorporating atomic diffusion and specific nuclear reaction rates.
• Precision: This approach achieved median fractional uncertainties of 2% in stellar radius, 2% in stellar mass, and 27% in stellar age. This precision rivals asteroseismic measurements for a much larger sample size.

Planetary Radius Recalculation:

• Planetary radii ($R_p$) were recomputed using the formula $R_p = \rho \times R_\star$, where $\rho$ is the planet-to-star radius ratio from the NASA Exoplanet Archive and $R_\star$ is the new MAISTEP-derived stellar radius.
• This resulted in a median planetary radius uncertainty of 5%, a significant improvement over the $\sim 10\%$ typical of previous literature values.

Analysis Techniques:

• Valley Fitting: The location and slope of the radius valley were quantified using the gapfit tool (Loyd et al. 2020) in 2D (Period, Flux, Mass, Age) and a 4D logistic regression model (incorporating Period, Mass, and Age simultaneously).
• Age Binning: Systems were divided into "Young" ($< 3$ Gyr) and "Old" ($\ge 3$ Gyr) to study evolutionary trends.
• Sample Matching: To control for selection biases when comparing age groups, Optimal Transport (OT) was used to create a property-matched subset of older systems with metallicity, radius, and mass distributions identical to the younger sample.

3. Key Results

A. Existence and Depth of the Valley

• The revised data confirms a partially filled radius valley near $2 R_\oplus$.
• The valley is deeper and better defined in this study compared to previous literature values. The valley metric ($V_A$) improved from 0.824 (literature) to 0.686 (this work), indicating a more pronounced gap due to reduced stellar parameter uncertainties.

B. Dependence on Orbital Parameters

• Orbital Period ($P$): The valley slopes downward toward longer periods. The fitted slope is $\alpha_{rv} = -0.12^{+0.02}_{-0.01}$.
• Incident Flux ($S_{\text{inc}}$): The valley slopes upward with increasing flux, with a slope of $\alpha_{rv} = 0.10^{+0.02}_{-0.03}$.
• These slopes are consistent with predictions from both photoevaporation and core-powered mass-loss models.

C. Dependence on Stellar Mass ($M_\star$)

• The valley shifts to larger radii as stellar mass increases, with a slope of $\alpha_{rv} = 0.19^{+0.09}_{-0.07}$.
• Sub-Neptunes show a stronger mass dependence ($\alpha_{sN} = 0.17^{+0.04}_{-0.04}$) compared to Super-Earths ($\alpha_{sE} = 0.11^{+0.05}_{-0.05}$). This suggests that higher-mass stars host slightly larger planets, likely due to larger core growth in more massive protoplanetary disks.

D. Dependence on Stellar Age ($\tau$)

• Valley Location: The valley shifts to larger radii and becomes shallower in older systems ($\ge 3$ Gyr). The 4D fit yields a weak positive age slope of $\gamma = 0.07^{+0.03}_{-0.04}$.
• Population Ratio ($N_E/N_N$): The ratio of Super-Earths to Sub-Neptunes increases with age:
  • Young ($< 3$ Gyr): $0.51^{+0.11}_{-0.08}$
  • Old ($\ge 3$ Gyr): $0.64^{+0.11}_{-0.11}$ (after OT matching).
• Sub-Neptune Size Evolution: Unlike theoretical predictions that sub-Neptunes should shrink significantly over time, the study found no significant decline in the average size of sub-Neptunes with age. The authors attribute this null result to the remaining uncertainties in stellar age estimates, despite the high precision of the radius/mass measurements.

4. Conclusions and Significance

Physical Interpretation:
The observed evolution of the radius valley over gigayear timescales—specifically the shift to larger radii and the increase in the Super-Earth to Sub-Neptune ratio in older systems—strongly supports the core-powered mass-loss scenario. This mechanism predicts continuous atmospheric erosion over Gyr timescales, whereas photoevaporation is expected to be most effective only in the first $\sim 100$ Myr. However, the authors note that photoevaporation cannot be entirely ruled out, as recent studies suggest UV radiation may persist longer than previously thought.

Methodological Impact:

• Precision: The study demonstrates that machine learning tools like MAISTEP, trained on high-fidelity stellar grids, can achieve stellar radius and mass precisions (2%) comparable to asteroseismology but for samples orders of magnitude larger.
• Age Sensitivity: The results highlight that stellar age is a critical, yet often noisy, parameter in exoplanet demographics. The lack of observed size shrinkage in sub-Neptunes underscores the need for more precise age determinations.

Future Outlook:
The findings motivate the need for improved stellar age measurements, which are expected from future missions like ESA's PLATO. The ability to resolve the radius valley's evolution over time is crucial for distinguishing between competing atmospheric loss mechanisms and understanding the formation and evolution of terrestrial planets.