How Many Transiting Giant Planets Can JWST Search for Moons and Rotational Oblateness?

Observations with the James Webb Space Telescope (JWST) can, in principle, detect moons and rotational oblateness of giant exoplanets through subtle distortions of transit light curves. The most favorable planets are expected to be on wide orbits (0.3 AU) where moons and rapid rotation are more likely to survive tidal evolution. No unambiguous detections have yet been reported. Here, we forecast the number of systems with sufficiently favorable properties to allow for secure detections, using JWST noise models, analytic detectability scalings, giant-planet occurrence rates, and the Gaia star catalog. For planets orbiting 0.9--1.6,M stars and a noise model based on demonstrated JWST performance, single-transit observations should be capable of detecting Jupiter-like rotational oblateness in several known systems and of order 10 systems yet to be discovered, if obliquities are typically 10. A similar number of systems are favorable for Ganymede-sized moons, if such moons are common. The yields can increase to tens or hundreds of systems if lower-mass host stars are included or if JWST can achieve photon-limited performance. Time-correlated noise on 1--10 hr timescales can strongly suppress these yields; a noise floor of a few tens of parts per million is enough to hide oblateness or moons in many otherwise favorable systems. Successful searches will therefore require both a more complete census of long-period transiting giant planets and low levels of instrumental systematics and stellar variability.