Photo-dynamical Analysis of Circumbinary Multi-planet system TOI-1338: A Fully Coplanar Configuration with a Puffy Planet

ITOI-1338 is the first circumbinary planet (CBP) system discovered by TESS. It has one transiting planet at P ∼ 95 days and an outer non-transiting planet at P ∼ 215 days complemented by radial velocity (RV) observation. Here we present a global photodynamical modeling of the TOI-1338 system that self-consistently accounts for the mutual gravitational interactions between all known bodies in the system. As a result, the three-dimensional architecture of the system can be established by comparing the model with additional data from TESS Extended Mission and published HARPS/ESPRESSO RV data. We report an inconsistency of binary RV signal between HARPS and ESPRESSO, which could be due to the contamination of the secondary star. According to stability analysis, the RV data via ESPRESSO are preferred. Our results are summarized as follows: (1) The inner transiting planet is extremely coplanar to the binary plane, with a mutual inclination of ~0.°12, making it a permanently transiting circumbinary planet at any nodal precession phases; (2) The outer planet, despite its non-transiting nature, is also coplanar with the binary plane by ~9.1° (22° for the 99% upper limit). (3) The inner planet could have an extremely low density of 0.137 ± 0.026 g/cm3. With a TESS magnitude of 11.45, TOI-1338 b is an optimal circumbinary planet CBP for ground-based follow-up and transit spectroscopy.