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Determining the Host Stars of Planets in Binary Star Systems with Asterodensity Profiling: Investigating the Canonical Radius Gap

This study employs asterodensity profiling to probabilistically determine the host stars of 15 exoplanets in binary systems, revealing that while observational biases favor circumprimary identification, the resulting host assignments suggest the canonical radius gap is less pronounced in binary star systems than previously assumed.

Original authors: Nathanael Burns-Watson, Kendall Sullivan, Adam Kraus

Published 2026-04-09

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CC BY 4.0

Original authors: Nathanael Burns-Watson, Kendall Sullivan, Adam Kraus

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 Picture: The "Missing Middle" in the Universe

Imagine you are looking at a collection of marbles from all over the universe. You notice something strange: there are lots of tiny marbles (like Earth) and lots of big, fluffy marbles (like Neptune), but almost no marbles in the middle size.

Astronomers call this the "Radius Gap." It's like a bakery that only sells tiny cupcakes and giant cakes, but refuses to make medium-sized ones. Scientists think this happens because planets in the "middle" size either lose their gas and shrink down to become rocky, or they keep their gas and puff up into giants.

The Mystery: What About the "Couple" Stars?

For a long time, we only studied planets orbiting single stars (like our Sun). But about half of all stars in our galaxy are actually binary systems—two stars dancing around each other, like a couple holding hands.

Recently, astronomers looked at planets in these "couple" star systems and found something weird: The Radius Gap seemed to disappear. There were suddenly lots of "medium-sized" planets.

The Problem: When we look at these binary stars through our telescopes, they often look like a single blurry dot of light. We don't know which star the planet is actually orbiting.

The Assumption: We usually assume the planet orbits the bigger, brighter star (the "Primary").
The Risk: If the planet is actually orbiting the smaller, dimmer star (the "Secondary"), our math is wrong. Because the smaller star is dimmer, the planet would have to be much bigger to block the same amount of light.

Think of it like this: If you see a shadow on a wall, you can guess how big the object casting it is. But if you don't know how far away the light source is, your guess could be way off. If the planet is orbiting the dimmer star, it might actually be a giant gas planet, not a medium-sized one.

The Detective Work: The "Density Fingerprint"

The authors of this paper wanted to solve this mystery. They asked: "Are these medium-sized planets actually orbiting the big star, or are they hiding around the small star?"

To find out, they used a technique called Asterodensity Profiling. Here is the analogy:

Imagine you are trying to guess which of two people (a heavy bodybuilder and a light gymnast) is running on a treadmill. You can't see them, but you can feel the vibration of the floor.

If the floor vibrates heavily, it's the bodybuilder.
If it vibrates lightly, it's the gymnast.

In space, when a planet passes in front of a star, it creates a "wiggle" in the star's light. The shape of that wiggle tells us the density of the star (how heavy and compact it is).

The big star has one density.
The small star has a different density.

By measuring the wiggle in the light, the astronomers could calculate the star's density and match it to the correct star. It's like matching a fingerprint to a suspect.

What They Found

The team looked at 15 planets in 10 binary star systems. They ran the numbers to see if the planets were orbiting the big star or the small star.

The "Smoking Gun": For 5 of the planets, the density fingerprint was a perfect match for the big star. These planets are definitely orbiting the primary star.
The "Fuzzy Match": For the other 10 planets, the fingerprints were too blurry to tell for sure. The stars were too similar in size, or the data wasn't sharp enough.
The Result: They found no clear evidence that these planets were orbiting the small, dimmer stars.

The Conclusion: The Gap is Still There (Maybe)

Because they couldn't prove that the planets were orbiting the small stars (which would have made them look huge), the authors concluded that the Radius Gap is likely still present in binary systems.

The "missing middle" planets probably aren't missing; they just look different because we were measuring them wrong. When you correct for which star they orbit, they likely fit right back into the gap, just like they do around single stars.

Why This Matters

This paper is a bit of a reality check. It tells us that just because data looks weird (like a filled-in gap), it doesn't mean the laws of physics have changed. Sometimes, it just means we haven't figured out which star the planet is hanging out with yet.

The Takeaway: The universe still loves its tiny rocky planets and its giant gas planets, but it's still figuring out how to make the medium-sized ones. And to solve that puzzle, we need to know exactly which star is the parent!

1. Problem Statement

The "radius gap" (or Fulton gap) is a well-established feature in the exoplanet population distribution, characterized by a scarcity of planets with radii between $\sim1.8$ and $2.0 R_\oplus$ . This gap is thought to distinguish between rocky super-Earths and gaseous sub-Neptunes. However, recent studies of planets in binary star systems (e.g., Sullivan et al. 2023) suggested this gap might be "filled in" or absent in binaries.

A critical confounding factor in these previous studies is the assumption that all transiting planets orbit the primary (brighter) star. In unresolved binary systems, if a planet actually orbits the secondary (fainter) star, its inferred radius is significantly underestimated because the transit depth is diluted by the primary star's flux. Correcting for this flux dilution would increase the planet's radius, potentially shifting it out of the radius gap.

The Core Question: Do planets in binary systems truly lack a radius gap, or is the apparent filling of the gap an artifact of misidentifying host stars? To answer this, the authors needed to probabilistically determine whether specific planets orbit the primary or secondary star.

2. Methodology

The authors employed Asterodensity Profiling, a technique that compares the stellar density derived from transit lightcurve fitting ( $\rho_{\star, \text{transit}}$ ) with independent spectroscopic density estimates ( $\rho_{\star, \text{spec}}$ ).

Data Selection:

Sample: 15 transiting exoplanets across 10 binary systems from the Sullivan et al. (2023) catalog.
Criteria: Systems with $\le 2$ planets, orbital periods $P < 31.6$ days, and planets that would fall within the canonical radius gap ( $\pm 0.2 R_\oplus$ of the gap function) if they were orbiting the primary star.
Exclusions: Triple systems, highly variable stars, and systems with poor initial fits were removed.

Analysis Pipeline:

Lightcurve Processing: Used Kepler PDCSAP flux data (30-minute cadence). Applied flux contamination corrections ( $f_{pri}$ and $f_{sec}$ ) to generate separate lightcurves for the hypothetical primary and secondary host scenarios.
Transit Modeling: Used exoplanet and pymc3 to fit transit models. Parameters included period ( $P$ $P$ ), transit time ( $t_0$ $t_{0}$ ), limb darkening ( $u_0, u_1$ $u_{0}, u_{1}$ ), radius ratio ( $r/R_\star$ $r / R_{⋆}$ ), impact parameter ( $b$ $b$ ), and stellar density ( $\rho_\star$ $ρ_{⋆}$ ).
- Assumed circular orbits ( $e=0$ ) due to short periods.
- Used a No-U-Turn Sampler (NUTS) for efficient MCMC sampling.
Host Identification (Bayesian Framework):
- Likelihood ( $P(B|A)$ ): Calculated the overlap between the transit-derived density posterior and the spectroscopic density priors for both the primary and secondary stars.
- Prior ( $P(A)$ ): Modeled the single-star planet radius distribution (Fulton et al. 2017) using a generalized gamma function. Crucially, the radius gap (1.5–2.0 $R_\oplus$ ) was masked in the prior to ensure the analysis was agnostic to the gap's existence. The prior naturally favored smaller planets (which are more common), which statistically favored primary hosts (as secondary hosts would imply larger, less common radii).
- Posterior ( $P(A|B)$ ): Combined the likelihood and prior using Bayes' Theorem to determine the probability of a planet being circumprimary vs. circumsecondary.

Validation:

KOI-1300: Analyzed as a test case with a known planet. The method correctly identified it as circumprimary with 99.9% probability.
Cadence Test: Compared 30-minute vs. 60-second cadence data. Found that while 60-second data offers higher sampling, its lower signal-to-noise ratio (S/N) resulted in broader, less precise density posteriors. The authors opted for 30-minute data for the full sample.

3. Key Contributions

Probabilistic Host Assignment: Developed a rigorous Bayesian framework to assign host stars in unresolved binaries without requiring spatial resolution or radial velocity confirmation for every target.
Re-evaluation of the Radius Gap in Binaries: Directly tested the hypothesis that the radius gap is absent in binaries by correcting planet radii based on the most probable host star.
Quantification of Biases: Demonstrated that physical and observational biases (flux dilution making secondary-hosted planets harder to detect and appear larger) heavily favor the detection of circumprimary planets, leading to ambiguous results for many systems.

4. Results

Host Star Probabilities:
- Unambiguous Circumprimary: 5 planets (including 2 in the radius gap subsample: KOI-2289.02 and KOI-3401.01) had posterior probabilities $>0.95$ of orbiting the primary.
- Ambiguous: The remaining 10 planets had posterior probabilities between 0.3 and 0.7, meaning the host star could not be definitively identified.
- No Unambiguous Circumsecondary: No planet was found to be unambiguously orbiting the secondary star.
Radius Distribution:
- When summing the posterior probabilities, the sample suggests $\sim66\%$ of planets are circumprimary and $\sim34\%$ are circumsecondary.
- Even after correcting radii based on these probabilities, the radius gap remains occupied. The distribution of planets in binaries still shows a lack of planets in the 1.8–2.0 $R_\oplus$ range, similar to single-star systems.
- The "filled gap" observed in previous studies (Sullivan et al. 2023) was largely an artifact of assuming all planets orbit the primary, which underestimated the radii of potential secondary-hosted planets. However, even with corrections, the gap does not disappear; it remains populated.

5. Significance and Limitations

Significance:

The study confirms that the canonical radius gap is likely not absent in binary star systems, contrary to some previous interpretations.
It highlights the necessity of host-star identification for accurate exoplanet demographics.
It suggests that the formation mechanisms (e.g., photoevaporation or core-powered mass loss) creating the radius gap operate similarly in binaries and single stars, at least for the sample analyzed.

Limitations:

Ambiguity: The method struggles when the primary and secondary stars have similar densities (common in equal-mass binaries) or when the transit impact parameter ( $b$ ) is poorly constrained, leading to broad density posteriors.
Sample Size: The analysis was limited to 15 planets in 10 systems due to computational constraints and data quality.
Data Cadence: The reliance on Kepler's 30-minute cadence (due to S/N issues with 1-minute data) limited the precision of the density estimates. Future missions like PLATO (with high S/N and high cadence) or ARIEL (multi-band photometry) could resolve these degeneracies.

Conclusion:
While the asterodensity profiling method has limitations in near-equal mass binaries, this work provides preliminary confirmation that the radius gap persists in binary systems. The apparent "filling" of the gap in previous studies was likely due to uncorrected flux dilution and misidentification of host stars, rather than a fundamental difference in planet formation physics between single and binary systems.