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 which 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, these quantities are often strongly degenerate and require sophisticated methods to convincingly constrain. We develop a new semi-analytic 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, 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 $f<0.23$, which corresponds to a rotation period of $P_{\mathrm{rot}}>13$h 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 modelled in transits, occultations, phase curves, transmission spectra and more.