Title: Photodynamical Modeling of Exoplanet Systems: From Transit Timing Variations to Possibly Habitable Worlds
Abstract: Syzygies and gravitational perturbations create detectable signatures in the light curves of multi-planet transiting systems, ranging from subtle timing shifts to dramatic flux variations. This talk will address how transit photometry and transit timing variations constrain fundamental properties of exoplanets and their host stars, including planetary masses, radii, and orbital architectures, drawing on discoveries from the Kepler and TESS missions, and illustrating modeling degeneracies. I will present our team’s development of next-generation photodynamical models implemented in Julia, leveraging the language’s unique combination of rapid prototyping and high-performance computing. Our symplectic N-body integrator extends beyond traditional multi-planet systems to model circumbinary planets, hierarchical triple stellar systems, and potential exomoons. Technical challenges addressed include achieving numerical precision and computing accurate model derivatives essential for efficient optimization and Bayesian parameter estimation via Hamiltonian Monte Carlo and No U-Turn sampling. I may also discuss strategies for disentangling planetary signals from stellar variability noise. The talk will conclude with example applications to the TRAPPIST-1 system and our Solar System, focusing on the rocky planets within the habitable zone, and outlining future opportunities for detecting and characterizing Earth-like worlds.