Planets are not perfect spheres. For example, Jupiter's equatorial radius is larger than its polar radius by 7%, and this aspherical shape is due to the fast spin of Jupiter, as one day on Jupiter is only 10 hr long. The shape of a planet therefore provides a measure of the rate and the orientation of its spin, which are ultimately related to the formation and evolution history of the planet as well as the planetary system.
Solar System giant planets in front of the Sun. Because of the fast spin, a planet’s equatorial radius is usually larger than its polar radius. This is most extreme for Saturn, whose equatorial radius is larger than its polar radius by 10%.
How to detect planetary shape with the transit technique?
For transiting exoplanets, it is possible to constrain their shape and spin obliquity from the transit light curve. When a planet passes between us and its host star, it blocks a certain fraction of the flux from the host star, causing a characteristic transit light curve. The transit light curve of an oblate planet deviates slightly from that of a spherical planet with the same cross-sectional area, primarily when the planet enters (i.e., ingress) and exits (i.e., egress) the stellar disk in the sky plane. The detection of such a deviation requires exceptional level of photometric precision. For a Jupiter-sized planet transiting a Sun-like star, the amplitude of the oblateness signal is no more than 200 parts per million (ppm), and it lasts no more than a few hours.
When a Jupiter-sized exoplanet with an oblate shape transits a Sun-like star, the light curve deviates from the transit of a spherical planet with the same cross-sectional area by no more than 200 ppm, and the deviation concentrates in the ingress and the egress parts of the light curve. Here we have used one year as the orbital period of the planet.
An extremely low-density planet spins slow
Based on observations from the James Webb Space Telescope (JWST), a recent paper led by Tsinghua astronomers has constrained the shape---and ultimately the spin rate---of a super-puff planet Kepler-51d. Kepler-51d is a very low-density planet with a mass of about 6 Earth masses and a radius of about 9 Earth radii. Low-density planets are easily distorted by rotation, making Kepler-51d an ideal target for oblateness detections. Using JoJo, a code developed by the team to efficiently compute the transit light curve due to an oblate planet, the team showed that the projected shape of Kepler-51d was consistent with being spherical. Relating the non-detection of planetary oblateness to the spin rate, the team inferred that the rotation period of this super-puffy planet should be longer than 33 hours. This is longer than the rotation period of any of the giant planets in the Solar System, meaning that Kepler-51d is spinning very slowly. This study is the first time that a physically meaningful constraint on the shape and spin rate of a mature exoplanet is obtained.
The paper has been published in Astrophysical Journal Letters. Tsinghua DoA graduate student Quanyi Liu is the first author, and Associate Professor Wei Zhu is the corresponding author. Other co-authors are from Osaka University, Pennsylvania State University, Caltech JPL, and NASA Goddard. The work of the Tsinghua team was supported by the National Natural Science Foundation of China.
Paper link: https://doi.org/10.3847/2041-8213/ad8f39
JoJo code link: https://github.com/Flippedx/JoJo