A General, differentiable transit model for ellipsoidal occulters: derivation, application, and forecast of planetary oblateness and obliquity constraints with JWST

Increasingly precise space-based photometry uncovers higher-order effects in transits, eclipses, and phase curves that can be used to characterize exoplanets in novel ways. The subtle signature induced by a rotationally deformed exoplanet is determined by the planet’s oblateness and rotational obliquity, which provide a wealth of information about a planet’s formation, internal structure, and dynamical history. However, oblateness and obliquity are often strongly degenerate and require sophisticated methods to convincingly constrain. We develop a new semianalytic model for an ellipsoidal object occulting a spherical body with arbitrary surface maps expressed in terms of spherical harmonics. We implement this model in an open-source Jax-based Python package eclipsoid (https://github.com/shishirdholakia/eclipsoid), allowing just-in-time compilation and automatic differentiation. We then estimate the precision obtainable with JWST observations of the long-period planet population and demonstrate the best current candidates for studies of oblateness and obliquity. We test our method on the JWST NIRSpec transit of the inflated warm Neptune WASP-107 b and place an upper bound on its projected oblateness of f < 0.23, which corresponds to a rotation period of P_rot > 13 hr if the planet is not inclined to our line of sight. Further studies of long-period exoplanets will necessitate discarding the assumption of planets as spherical bodies. Eclipsoid provides a general framework allowing rotational deformation to be modeled in transits, occultations, phase curves, transmission spectra, and more.