Multi-Body Resonances in Extrasolar Systems

Utilizing a recently revised catalog of exoplanets detected by the Kepler space telescope, we aim to identify planetary systems that exhibit three or more planets in orbital resonance. An orbital resonance occurs when planetary bodies orbiting the same object have orbital periods in a first- or second-order integer ratio (e.g., 2:1, 3:2, 5:3). These resonances play a significant role in the gravitational dynamics of a system, stabilizing or destabilizing orbits and providing insight into system formation. Using Python scripts we created to identify systems for potential resonances, we identified 91 systems with at least one planet triple that could potentially be in resonance. We identify triple-body resonances by checking whether two planets in a system have orbital periods close to a two-body resonance and then determining if one of these planets also forms another two-body resonance with a third planet in the system. We ran simulations of the multiplanet systems of interest using an established Python package (Rebound) to model the planetary dynamics and gravity of these systems. By deriving the initial orbital parameters and using precise planetary radius measurements and an empirical mass-radius relation, we estimate the masses of planets for the dynamical simulations. Using these orbital parameters, we confirm orbital resonances by analyzing the planets' simulated mean motions multiplied by calculated integer coefficients. Through simulating the dynamics of these systems, we corroborated the resonant configurations of Kepler Object of Interest (KOI)-500 discovered by MacDonald et al. (2016), KOI-730 discovered by Fabrycky et at. (2011), and KOI-2086 discovered by Jontof-Hutter et al. (2016). We also find evidence of potential resonances in KOI-351 and KOI-707. Future studies of these systems could confirm whether they are truly in resonance. Our methodology may also prove fruitful when applied to data from the ongoing Transiting Exoplanet Survey Satellite (TESS) mission.