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Orbit Refinement of WASP-18 b and Evidence Against the Existence of WASP-18 c

This study refines the orbital parameters of the exoplanet WASP-18 b using extensive transit and radial velocity data while providing strong evidence against the existence of the previously proposed companion, WASP-18 c, by finding no significant variations to support its presence.

Original authors: Avinash Salguneswaran Nediyedath, Kyle A. Pearson, Tara Fetherolf, Andre O. Kovacs

Published 2026-06-02

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CC BY 4.0

Original authors: Avinash Salguneswaran Nediyedath, Kyle A. Pearson, Tara Fetherolf, Andre O. Kovacs

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, cosmic clockwork. For years, astronomers have been trying to tune the gears of a specific system called WASP-18, which features a massive "hot Jupiter" planet (WASP-18 b) zooming incredibly close to its star. But there was a mystery: some scientists thought there might be a second, hidden planet (WASP-18 c) tugging on the first one, causing it to arrive slightly early or late, like a runner being pushed by a friend.

This paper is like a team of master clockmakers who decided to check the gears with the most precise tools available to see if that second planet actually exists.

Here is what they found, broken down simply:

1. The "Super-Stopwatch" (Refining the Orbit)

First, the team wanted to make sure they knew exactly when the main planet, WASP-18 b, would pass in front of its star. To do this, they didn't just look at one or two observations. They gathered 205 different "snapshots" of the planet's transit from a massive collection of data. This included:

Space telescopes: Like TESS and CHEOPS, which act like high-powered binoculars in space.
Ground telescopes: Observations from regular telescopes on Earth and even data from citizen scientists (regular people helping out).
Old records: Data stretching back nearly 20 years.

By combining all this, they created a "super-stopwatch." They calculated the exact moment the planet crosses the star and how long its orbit takes with incredible precision.

The Result: They can now predict when the planet will transit in the year 2030 with an error margin of just 2.4 seconds. That's like predicting a train arrival time 4 years in the future and being off by less than the time it takes to blink.

2. The "Ghost Planet" Hunt (Searching for WASP-18 c)

With this super-precise schedule in hand, they looked for the "ghost planet," WASP-18 c.

The Theory: If a second planet existed, it would act like a gravitational tug-of-war. It would pull on WASP-18 b, making it arrive a few seconds early or late depending on where the second planet was. This is called a "Transit Timing Variation" (TTV).
The Search: The team looked at the timing data and also listened to the "heartbeat" of the star (using radial velocity measurements, which detect the star wobbling back and forth).
The Findings: They found no evidence of a second planet.
- When they looked at the timing data, the "wobbles" they saw earlier turned out to be just noise—like static on a radio—caused by mixing data from different sources with different schedules. When they looked only at the clean, continuous data from space, the "ghost" disappeared.
- When they listened to the star's wobble, the signals they found didn't match the rhythm expected for a planet like WASP-18 c.

The Analogy: Imagine you are trying to hear a whisper (the second planet) in a crowded room. Earlier, people thought they heard the whisper because of the background chatter. But this team put on noise-canceling headphones (using only the best data) and realized the "whisper" was just the room's background noise. The whisper wasn't there.

3. The "Elastic Band" (Measuring the Planet's Shape)

While looking for the second planet, the team also measured something called the Love number ( $k_2$ ).

The Concept: Imagine the planet is a giant, squishy rubber ball. As it zooms around its star, the star's gravity stretches the ball slightly, like an elastic band. The "Love number" tells us how squishy or rigid that ball is.
The Result: They calculated this number with high precision ($0.62199$), giving us a better understanding of what the planet is made of and how it reacts to its star's gravity.

The Bottom Line

The paper concludes that WASP-18 c likely does not exist. The signals that made people think it was there were just illusions caused by imperfect data.

However, the work wasn't in vain. By creating this ultra-precise "super-stopwatch" for the main planet, the team has given future astronomers a perfect map. This will help space telescopes (like the upcoming ARIEL mission) know exactly when to look at WASP-18 b to study its atmosphere, ensuring they don't miss a single moment of the show.

Technical Summary: Orbit Refinement of WASP-18 b and Evidence Against the Existence of WASP-18 c

Problem Statement
The WASP-18 system, hosting a hot Jupiter (WASP-18 b) on a 0.94-day orbit, has been the subject of conflicting claims regarding the existence of a second planetary companion, WASP-18 c. Initially proposed by Pearson (2019) based on observed transit timing variations (TTVs), the existence of WASP-18 c was later challenged by Cortés-Zuleta et al. (2020), leaving the system's architecture controversial within the NASA Exoplanet Archive. Furthermore, while the system is a prime target for atmospheric characterization due to its extreme equilibrium temperature and strong day-night contrast, precise long-term ephemerides are required to schedule future observations with facilities like JWST and the upcoming ARIEL mission. Previous studies have yielded null results for orbital decay, suggesting high stellar tidal quality factors or alternative energy dissipation channels, yet the dynamical stability and potential perturbations from a second body remain to be rigorously tested with an expanded dataset.

Methodology
The authors conducted a comprehensive re-analysis of photometric and spectroscopic data spanning nearly 20 years.

Photometric Data: The study utilized 205 transit light curves derived from space-based observations (TESS sectors 2, 3, 29, 30, 69, and 96; and 12 CHEOPS transits) and ground-based observations (80 transits from Exoplanet Watch, the Exoplanet Transit Database, ExoClock, and literature sources including Patra et al. 2020 and Bouma et al. 2019).
Spectroscopic Data: The analysis incorporated 449 radial velocity (RV) measurements from five spectrographs: CORALIE, HARPS, HIRES, PFS, and ESPRESSO. This included previously unpublished archival ESPRESSO data acquired in 2021.
Analysis Techniques:
- Ephemeris Refinement: Light curves were processed using the EXOTIC pipeline with custom detrending and limb-darkening modeling. A Bayesian nested sampling approach (Ultranest) was used to derive mid-transit times and orbital periods.
- TTV Search: Lomb-Scargle periodograms were applied to the O-C (Observed minus Calculated) residuals of the combined and TESS-only datasets to search for periodic signals indicative of a companion.
- Radial Velocity Modeling: A modified Keplerian model including an apsidal precession term ( $\dot{\omega}$ ) was fitted to the RV data using the emcee affine-invariant ensemble sampler. The model accounted for instrument offsets and jitter, with the anomalistic period fixed to decouple degeneracies.
- Love Number Estimation: The refined orbital solution was used to calculate the second-order gravitational Love number ( $k_2$ ).

Key Contributions and Results

Refined Ephemeris: The authors derived a high-precision ephemeris for WASP-18 b with a mid-transit time of $T_0 = 2460933.096346 \pm 0.000022$ BJDTDB and an orbital period of $P = 0.94145252 \pm 1.1 \times 10^{-8}$ days. Forward-propagating this ephemeris to January 1, 2030, yields a timing uncertainty of only 2.41 seconds.
Apsidal Precession and Love Number: The RV analysis confirmed a stable apsidal precession rate of $\dot{\omega} = 0.009034 \pm 0.000010^\circ$ /day, consistent with previous literature but with improved precision due to the extended baseline. This allowed for a precise calculation of the planetary Love number, $k_2 = 0.62199 \pm 0.0011$ .
Evidence Against WASP-18 c:
- Photometric TTVs: While the combined ground-and-space dataset showed peaks exceeding the 99% false alarm probability (FAP), these signals disappeared when the analysis was restricted to the high-precision, continuous TESS-only data. The authors attribute these peaks to aliasing effects from inhomogeneous ground-based sampling rather than astrophysical origins.
- Radial Velocity Residuals: Periodogram analysis of RV residuals revealed no significant periodicity corresponding to the proposed ~2.1-day orbit of WASP-18 c. Detected peaks were identified as harmonics or noise-driven aliases.
- Conclusion on WASP-18 c: The lack of consistent periodic signals in both TTV and RV datasets, combined with the failure to detect a signal at the predicted period, leads the authors to conclude that the claimed WASP-18 c signal is likely spurious.

Significance
The paper asserts that its primary significance lies in providing a robust, high-precision baseline for the WASP-18 b orbit, which is essential for scheduling future space telescope observations (specifically ARIEL and the Habitable Worlds Observatory) and for accurately interpreting atmospheric data. By falsifying the existence of the previously proposed WASP-18 c, the study resolves a long-standing controversy in the system's architecture, suggesting that the system is likely dominated by the single hot Jupiter and its interaction with the host star, rather than complex multi-body dynamics. The work emphasizes that reported deviations in transit timing must be distinguished from artifacts of insufficiently constrained orbital periods before attributing them to additional perturbers.

1. The "Super-Stopwatch" (Refining the Orbit)

2. The "Ghost Planet" Hunt (Searching for WASP-18 c)

3. The "Elastic Band" (Measuring the Planet's Shape)

The Bottom Line

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