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The Occurrence Rate of Nearby Planetary Companions to Hot Jupiters

By conducting a uniform search for nearby transiting companions in the first five years of TESS data, this study establishes a lower-limit occurrence rate of approximately 7.6% for such companions around hot Jupiters, providing critical constraints on the relative efficiency of disk migration versus high-eccentricity migration pathways while suggesting potential slight misalignments between hot Jupiters and their neighbors.

Original authors: Lizhou Sha, Andrew M. Vanderburg, Chelsea X. Huang, Samuel Christian, Kevin Burdge, Nicholas Saunders, Khalid Barkaoui, Alexander Belinski, Serge Bergeron, Zoë L. de Beurs, Allyson Bieryla, Karen A. C

Published 2026-07-17

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CC BY 4.0

Original authors: Lizhou Sha, Andrew M. Vanderburg, Chelsea X. Huang, Samuel Christian, Kevin Burdge, Nicholas Saunders, Khalid Barkaoui, Alexander Belinski, Serge Bergeron, Zoë L. de Beurs, Allyson Bieryla, Karen A. Collins, Giuseppe Conzo, Gareb Fernández-Rodríguez, Akihiko Fukui, Davide Gandolfi, Tristan Guillot, Joel D. Hartman, Kai Ikuta, David W. Latham, Jerome P. de Leon, Bob Massey, Gabriel Murawski, Felipe Murgas, Norio Narita, Mohammad Odeh, Enric Palle, Hannu Parviainen, Gabrielle Ross, Richard P. Schwarz, Gregor Srdoc, Chris Stockdale, Samuel N. Quinn, Ian A. Waite, Francis P. Wilkin, George Zhou

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

Imagine the universe as a giant, chaotic playground where planets are born. In our own solar system, the giant planets like Jupiter and Saturn live far away from the Sun, in the cold outer reaches. For a long time, scientists thought all giant planets were supposed to be there, too. But then, we started finding "Hot Jupiters"—giant gas planets that are scorching hot because they orbit incredibly close to their stars, sometimes closer than Mercury is to our Sun. The big mystery is: how did they get there? Did they form in place, or did they migrate inward?

The answer depends on how they moved. If a giant planet had a wild, violent journey involving gravitational slingshots and crashing into other planets, it would likely have destroyed any smaller neighbors along the way. It would be like a bull in a china shop; the smaller plates wouldn't survive. However, if the planet moved slowly and smoothly, like a boat gliding through calm water, it might have kept its smaller planetary friends nearby. So, by looking for these "little friends" orbiting close to the giant ones, astronomers can figure out which migration story is true. This paper is a massive detective hunt to see how many Hot Jupiters actually have these surviving neighbors.

The Great Hot Jupiter Neighborhood Search

In this study, a team of astronomers acted like cosmic real estate agents, scanning a huge list of stars to see if the "Hot Jupiters" living there had any roommates. They used data from NASA's TESS mission, which has been taking pictures of the sky for five years, looking for the tiny dips in starlight that happen when a planet passes in front of its star. They focused on finding small planets orbiting very close to the Hot Jupiters—specifically, planets with orbits shorter than 10 days.

The team started with a massive list of about 2,000 likely Hot Jupiters. They then ran a sophisticated computer search through the light curves (the brightness records) of these stars, looking for the tell-tale signs of a second, smaller planet. It was a bit like listening to a crowded party for a specific whisper; they had to filter out the noise of the giant planet's own transit and the star's natural flickering to hear the faint signal of a smaller companion.

After a rigorous vetting process to make sure they weren't seeing ghosts or false alarms, they found six confirmed systems where a Hot Jupiter has a nearby small companion. These systems include TOI-1408, TOI-5143, TOI-1130, TOI-2494, WASP-84, and TOI-2000. Interestingly, they didn't find the companions for some famous systems they expected to see, like WASP-47, likely because their specific search method wasn't sensitive enough to catch those particular signals.

The Big Numbers

Based on these six discoveries and the total number of stars they searched, the team calculated the "occurrence rate." This is the percentage of Hot Jupiters that have these nearby little friends. They found that (7.6+5.5 −3.8)% of Hot Jupiters have a nearby companion.

To put that in perspective, this number is a lower limit. It means that at least this many Hot Jupiters formed in a calm, quiet way (like disk migration or forming right where they are) that allowed their neighbors to survive. If the Hot Jupiters had formed via the violent, high-eccentricity migration method, these neighbors would have been kicked out or destroyed. So, this result suggests that the violent migration story isn't the only way these planets get to be so hot.

Are They Aligned or Tilted?

The paper also dug into the geometry of these systems. If the Hot Jupiter and its small neighbor are perfectly aligned, they orbit in the same flat plane. If they are tilted, they are like two hula hoops spinning at different angles. The team found that the small companions seem to be mostly aligned with the Hot Jupiters, which supports the idea of a calm formation history.

However, there is a tiny, tantalizing hint that they might be slightly tilted. The team noticed that four out of the nine Hot Jupiters with companions in their sample have "grazing" transits, meaning they only barely skim the edge of the star from our viewpoint. Statistically, finding this many grazing planets is a bit unlikely if everything is perfectly flat. This suggests there might be a slight, systematic tilt between the Hot Jupiter and its neighbor, perhaps a small remnant of a past migration event. But the paper is careful to say this is just a hint, not a proven fact, and more data is needed.

The Cold Companions

Finally, the team looked at whether these systems also have "cold" companions—planets orbiting much farther away. They found that about half of the Hot Jupiters with nearby small neighbors also seem to have these distant, cold companions. This is a bit of a puzzle. Usually, scientists think a distant companion is what kicks a Hot Jupiter inward via a violent migration. But here, the Hot Jupiters with nearby neighbors (who presumably didn't migrate violently) also have these distant companions. This suggests that just having a distant neighbor doesn't automatically mean a violent migration happened; the story of how these planets formed is more complicated than a simple "one cause, one effect" rule.

The Takeaway

In short, this paper tells us that Hot Jupiters aren't as lonely as we thought. About (7.6+5.5 −3.8)% of them have little planetary siblings living right next door. This discovery is a strong clue that at least some of these giants arrived at their scorching homes via a smooth, gentle journey rather than a chaotic, destructive one. While the numbers are still a bit fuzzy at the edges, the existence of these neighbors is a key piece of the puzzle in understanding how our universe builds its planets.

Technical Summary: The Occurrence Rate of Nearby Planetary Companions to Hot Jupiters

Problem Statement
The formation mechanisms of hot Jupiters (gas giants with orbital periods $P < 10$ days) remain a subject of debate, primarily distinguishing between dynamically disruptive high-eccentricity migration (HEM) and dynamically quiet pathways such as disk migration or in situ formation. A critical diagnostic for these pathways is the survival of nearby planetary companions. HEM is expected to disrupt or eject inner companions, whereas disk migration or in situ formation should preserve them. Previous estimates of the occurrence rate of such companions were limited by small sample sizes and a lack of positive detections, relying heavily on null results from the Kepler mission or small statistical samples. This study addresses the need for a robust, uniform search across a large statistical sample to constrain the relative efficiency of these formation pathways.

Methodology
The authors conducted a uniform search for short-period transiting companions to hot Jupiters using the first five years (Sectors 1–69) of TESS data.

Sample Selection: From the TESS Objects of Interest (TOI) catalog, the team selected $\approx 2000$ likely hot Jupiters ( $P < 10$ days, $8 \le R_p/R_\oplus < 30$ ). They refined stellar parameters using spectral energy distribution (SED) fitting to Gaia DR3 and 2MASS photometry and filtered out known false positives (e.g., eclipsing binaries, spectroscopic binaries) to establish a clean sample of $N_{HJ} = 1849$ systems.
Search Pipeline: The team employed the MIT Quick Look Pipeline (QLP) light curves. They utilized a Box Least-Squares (BLS) algorithm to search for additional transits after masking the known hot Jupiter transits and detrending the light curves.
Vetting: Signals with a signal-to-noise ratio (S/N) $> 7$ underwent rigorous vetting, including visual inspection of folded light curves, BLS spectra, and difference imaging to rule out false positives (e.g., background eclipsing binaries, scattered light).
Detection Efficiency: An injection-recovery simulation was performed, injecting 10,000 simulated companions per host star with radii $R_p \sim U(1, 4) R_\oplus$ and periods $P \sim U(0.25, 10)$ days. The recovery fraction was fitted to a scaled Gamma cumulative distribution function (CDF) as a function of theoretical transit S/N to determine observational completeness.
Statistical Framework: The occurrence rate ( $\eta$ ) was calculated using a Bayesian framework. The number of trials ( $n$ ) was defined as the effective sample size (ESS), derived by summing the average detection efficiencies of simulated companions across all systems and correcting for the estimated false positive rate of the hot Jupiter sample. The number of successes ( $s$ ) was the count of confirmed detections.

Key Contributions and Results

Detection of Companions: The pipeline identified six systems with nearby transiting companions: TOI-1408 c, TOI-5143 b, TOI-1130 b, TOI-2494 b, WASP-84 c, and TOI-2000 b. Notably, some known systems (e.g., WASP-47, TOI-4468) were not detected by this specific pipeline due to signal characteristics or data gaps, but these were accounted for in the analysis.
Occurrence Rate: Accounting for observational completeness and detection efficiency, the authors derived an intrinsic occurrence rate for nearby companions ( $0.25 \text{ d} \le P < 10 \text{ d}$ , $1 \le R_p/R_\oplus < 4$ ) of $(7.6^{+5.5}_{-3.8})\%$ . This represents the fraction of hot Jupiters that possess a nearby companion, conditioned on the hot Jupiter's existence.
Dependence on Mutual Inclination: The study explicitly modeled the dependence of the occurrence rate on the mutual inclination distribution between the hot Jupiter and its companion.
- Assuming a well-aligned system (Rayleigh distribution with $\sigma = 1.8^\circ$ ), the rate is $(7.6^{+5.5}_{-3.8})\%$ .
- Assuming a maximally misaligned (isotropic) distribution, the rate rises to $(37^{+19}_{-17})\%$ .
- Comparing the transit-derived rate with rates derived from Transit Timing Variations (TTVs) by Wu, Rice, & Wang (2023) suggests that the case of maximal misalignment is disfavored, implying that hot Jupiters with companions are likely mostly aligned.
Grazing Transits: The authors noted that four of the nine hot Jupiters with inner companions exhibit grazing transits. Statistical analysis suggests this may indicate a slight preferential misalignment between the hot Jupiter and its inner companion, though the significance is marginal ( $p \approx 0.075$ ).
Cold Companions: A review of radial velocity (RV) data indicates that hot Jupiters with nearby companions may host cold outer companions at a rate similar to the general hot Jupiter population, challenging the simple narrative that outer companions are the sole trigger for HEM.

Significance
The paper establishes a lower limit on the fraction of hot Jupiters that formed via dynamically quiet pathways (disk migration or in situ formation) at approximately 7.6%. Because high-eccentricity migration is expected to destroy nearby companions, the existence of these systems rules out HEM for at least this fraction of the population. The authors argue that if simulations suggest only a fraction of companions survive disk migration over long timescales, the true fraction of hot Jupiters formed via quiet pathways could be significantly higher (potentially $\approx 20\%$ ).

The study emphasizes that while hot Jupiters remain relatively "lonely" compared to small short-period planets (which have a much higher companion occurrence rate), the presence of even a small population of companions provides a crucial constraint on formation theories. The results suggest that while HEM may be the dominant pathway, it is not the exclusive one, and comprehensive characterization of system architectures (including obliquities and long-period companions) is necessary to fully resolve the relative prevalence of hot Jupiter formation channels.

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