🔭 astrophysics

Effect of tidal gravity and planetary rotation on the retrieved atmospheric abundances of close-in exoplanets

This study develops a framework to incorporate tidal and rotational gravity effects into atmospheric retrieval models, demonstrating that neglecting these factors for close-in exoplanets like WASP-12b and WASP-39b leads to significant underestimations of molecular abundances and transit depths, an effect that is partially suppressed by cloud cover.

Original authors: K. Arnav, Gopal Hazra

Published 2026-06-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: K. Arnav, Gopal Hazra

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 a planet as a giant, spinning top orbiting a blazing sun. For a long time, astronomers studying these "hot Jupiters" (giant planets very close to their stars) have made a simplifying assumption: they treated these planets as perfect, round balls with a steady, unchanging pull of gravity, just like a calm, non-spinning Earth.

This paper argues that this assumption is like trying to describe a spinning figure skater while ignoring the fact that they are spinning. In reality, two powerful forces are reshaping the "feel" of gravity on these close-in planets:

The Spin (Centrifugal Force): Because these planets spin incredibly fast (often as fast as they orbit), they bulge at the equator. This spinning creates a force that pushes outward, effectively making gravity feel weaker at the equator.
The Star's Hug (Tidal Gravity): The host star is so close that its gravitational pull stretches the planet like taffy. This tidal stretching also reduces the effective gravity felt by the atmosphere on the side facing the star.

The "Fluffy" Atmosphere Analogy

Think of a planet's atmosphere as a blanket wrapped around the planet.

Normal Gravity: If gravity is strong, the blanket is pulled tight and flat against the planet. It's thin and compact.
Reduced Gravity: When the spin and the star's pull weaken the gravity, the blanket becomes "fluffier." It puffs up and expands outward, covering a larger volume of space.

In the language of physics, this expansion is called an increase in the scale height. The paper shows that for planets like WASP-12b (which is very distorted) and WASP-39b (which is less distorted), this "fluffing up" changes how much light from the star is blocked when the planet passes in front of it (a transit).

What the Scientists Did

The researchers built a new computer model to act like a "gravity detective." They took existing data from two powerful telescopes—the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST)—and re-analyzed the atmospheres of WASP-12b and WASP-39b.

They ran the analysis twice for each planet:

The Old Way: Assuming the planet is a perfect sphere with normal gravity.
The New Way: Accounting for the "fluffiness" caused by the spin and the star's tidal pull.

The Findings: A Bigger "Shadow"

When they included the gravity corrections, they found that the "fluffy" atmosphere blocked more starlight than the "tight" atmosphere did.

For WASP-12b (the extreme case), the change in the amount of light blocked was significant, ranging from 150 to 500 parts per million (ppm). That's like noticing a tiny, specific change in the brightness of a lightbulb from a mile away.
For WASP-39b (the milder case), the change was smaller but still measurable, ranging from 60 to 180 ppm.

The "Recipe" Mix-Up

The most important part of the paper is what this means for the "ingredients" of the atmosphere. When astronomers look at the light passing through the atmosphere, they try to figure out how much water, carbon dioxide, methane, etc., is there. It's like trying to guess the recipe of a soup just by looking at its color.

The paper found that if you ignore the "fluffiness" (the reduced gravity), you get the wrong recipe:

The Mistake: If you assume the gravity is strong (the tight blanket), the model thinks the atmosphere is thinner than it really is. To explain the amount of light blocked, the model has to guess that there is less gas there.
The Correction: When you account for the "fluffiness" (the weak gravity), the model realizes the atmosphere is actually puffier. To explain the same amount of light, the model now calculates that there is more gas (higher abundance) than previously thought.

For example, in their tests, correcting for gravity changed the estimated amount of water and carbon monoxide in the atmosphere. For WASP-39b, even a small 1.8% reduction in gravity caused a noticeable shift in the calculated amounts of these gases.

The "Cloudy" Twist

The researchers also tested what happens if the planet has clouds. They found that clouds act like a lid on the soup. If a thick layer of clouds sits high up in the atmosphere, it hides the "fluffiness" below. In these cloudy models, the effect of the reduced gravity was suppressed, making it harder to detect the changes in the gas amounts.

The Bottom Line

This paper doesn't just say "gravity is different"; it says, "If you don't account for the spin and the star's pull, you are miscounting the ingredients in the atmosphere."

For Hubble (HST): The data wasn't quite sharp enough to see these differences clearly for the most extreme planet (WASP-12b), but the trend was there.
For Webb (JWST): The data is so precise that even for a planet with a small gravity change (WASP-39b), the new method reveals a different chemical recipe.

The authors conclude that as we get better telescopes, we must stop treating these planets as simple, round balls. We need to include the "spin" and the "stretch" in our calculations, or we will continue to misjudge the true composition of these distant worlds.

Technical Summary: Effect of Tidal Gravity and Planetary Rotation on the Retrieved Atmospheric Abundances of Close-in Exoplanets

Problem Statement
Modern atmospheric retrieval frameworks for exoplanets typically rely on simplifying assumptions, including spherical symmetry and constant surface gravity. However, for close-in, tidally locked exoplanets, the effective gravity experienced by the atmospheric limb is significantly modified by two physical mechanisms: the centrifugal acceleration arising from rapid planetary rotation and the tidal acceleration induced by the host star's gravitational field. These forces reduce the net effective gravity, thereby altering the atmospheric scale height and the vertical distribution of molecular abundances. While these effects are known to influence planetary shape and dynamics, they are generally not incorporated into current atmospheric retrieval codes. This omission raises the question of whether neglecting centrifugal and tidal corrections introduces measurable biases in the inferred atmospheric parameters, particularly as observational precision transitions from the Hubble Space Telescope (HST) to the James Webb Space Telescope (JWST).

Methodology
The authors developed a combined framework to incorporate centrifugal and tidal gravity corrections into the forward modeling and retrieval of exoplanet atmospheres using the POSEIDON retrieval code.

Analytical Framework: The study derives a corrected effective gravitational acceleration ( $g'$ ) by subtracting the centrifugal term ( $\frac{1}{2}\omega^2 R$ ) and the characteristic axial tidal acceleration ( $2GM_*R/a^3$ ) from the standard surface gravity ( $g$ ). This modified gravity is used to calculate the atmospheric pressure scale height ( $H = kT/\mu g'$ ).
Forward Modeling: Synthetic transmission spectra were generated for two target planets: WASP-12b (a highly irradiated ultra-hot Jupiter with strong tidal/rotational effects) and WASP-39b (a planet with high-quality JWST data but smaller gravity corrections). The forward models compared spectra generated with standard gravity versus those with $g'$ corrections.
Retrieval Analysis: Atmospheric retrievals were performed on:
- WASP-12b: Using HST/WFC3 G141 transmission spectroscopy (1.0–1.8 $\mu$ m).
- WASP-39b: Using JWST/NIRSpec PRISM transmission spectroscopy (0.4–5.4 $\mu$ m).
- Synthetic Experiments: To isolate the detectability of gravity-induced effects, controlled synthetic retrievals were conducted for WASP-39b with artificially reduced effective gravity (20%, 30%, and 50% reductions).
Model Variations: The study tested the robustness of these effects under different atmospheric assumptions, including isothermal cloud-free models, non-isothermal pressure-temperature (P-T) profiles, and models with grey cloud decks.

Key Results

Forward Model Impact: The inclusion of tidal and rotational corrections increases the effective atmospheric scale height, leading to an increase in transit depth. For WASP-12b, where gravity is reduced by ~~15.8%, the transit depth increases by 150–500 ppm for major molecules. For WASP-39b, with a smaller gravity reduction (~~1.8%), the variation is 60–180 ppm.
Retrieval Biases (WASP-12b): Retrievals using HST data showed systematic shifts in the retrieved log-mixing ratios when gravity corrections were included. Specifically, the inferred abundance of H $_2$ O shifted from -3.22 to -2.64, and NH $_3$ from -6.08 to -6.57. However, due to the limited signal-to-noise ratio and resolution of HST data, these shifts were not statistically significant within the 1 $\sigma$ credible intervals.
Retrieval Biases (WASP-39b): Despite the small natural gravity correction for WASP-39b, the high precision of JWST data revealed systematic shifts in retrieved parameters. The CO abundance showed a shift approaching the 1 $\sigma$ boundary.
Synthetic Gravity Reduction: Controlled experiments on WASP-39b demonstrated that as the effective gravity reduction increases, the shifts in retrieved log-mixing ratios become more pronounced and statistically significant.
- At a 20% gravity reduction, CO abundance shifted by ~0.3 dex.
- At a 50% reduction, shifts exceeded the 2 $\sigma$ confidence level for multiple species.
Model Dependencies:
- Non-Isothermal Profiles: Introducing flexible P-T profiles increased parameter degeneracies, allowing the retrieval to redistribute opacity between temperature structure and abundances, which altered the magnitude of the gravity-induced shifts but did not eliminate them.
- Clouds: The presence of a grey cloud deck suppressed the combined effect of rotation and tidal gravity. Clouds truncate the transmission spectrum at higher pressures, effectively reducing the observable scale height and diminishing the sensitivity of the spectrum to gravity modifications.

Significance and Conclusions
The paper concludes that neglecting centrifugal and tidal gravity corrections can lead to biased inferences of atmospheric abundances, particularly for close-in, fast-rotating planets where effective gravity is significantly reduced. While current HST data lacks the precision to robustly detect these biases for strongly distorted planets like WASP-12b, the study demonstrates that JWST-quality data is sensitive enough to detect these effects, even for planets with smaller gravity corrections like WASP-39b.

The authors assert that as the field moves toward high-precision observations of highly distorted systems (e.g., WASP-121b, WASP-76b, NGTS-10b), incorporating these gravity corrections into retrieval frameworks will be essential for achieving physically consistent and accurate atmospheric characterizations. The study highlights that these corrections interact non-trivially with other atmospheric parameters, such as cloud properties and thermal profiles, and that their inclusion is necessary to avoid misinterpreting the chemical composition of close-in exoplanets.