Detecting Planetary Oblateness in the Era of JWST: A Case Study of Kepler-167e

Planets may be rotationally flattened, and their oblateness thus provide useful information on their formation and evolution. Here we develop a new algorithm that can compute the transit light curve due to an oblate planet very efficiently and use it to study the detectability of planet oblateness (and spin obliquity) with the James Webb Space Telescope (JWST). Using the Jupiter analog, Kepler-167e, as an example, we show that observations of a single transit with JWST are able to detect a Saturn-like oblateness ($f=0.1$) with high confidence, or set a stringent upper limit on the oblateness parameter, as long as the planetary spin is slightly misaligned ($\gtrsim 20^\circ$) with respect to its orbital direction. Based on known obliquity measurements and theoretical arguments, it is reasonable to believe that this level of misalignment may be common. We estimate the sensitivity limit of JWST in oblateness detections and highlight the importance of better characterizations of cold planets in planning future JWST transit observations. The potential to detect rings, moons, and atmospheric species of the cold giants with JWST is also discussed.