Confirming Resonance in Three Transiting Systems

Although resonant planets have orbital periods near commensurability, resonance is also dictated by other factors, such as the planets' eccentricities and masses, and therefore must be confirmed through a study of the system's dynamics. Here, we perform such a study for five multiplanet systems: Kepler-226, Kepler-254, Kepler-363, Kepler-1542, and K2-32. For each system, we run a suite of N-body simulations that span the full parameter space that is consistent with the constrained orbital and planetary properties. We study the stability of each system and look for resonances based on the libration of the critical resonant angles. We find strong evidence for a two-body resonance in each system; we confirm a 3:2 resonance between Kepler-226c and Kepler-226d, confirm a 3:2 resonance between Kepler-254c and Kepler-254d, and confirm a three-body 1:2:3 resonant chain between the three planets of Kepler-363. We explore the dynamical history of two of these systems and find that these resonances most likely formed without migration. Migration leads to the libration of the three-body resonant angle, but these angles circulate in both Kepler-254 and Kepler-363. Applying our methods to additional near-resonant systems could help us identify which systems are truly resonant or nonresonant and which systems require additional follow-up analysis.