Confirming and characterizing the five-planet resonant chains of K2-138 and Kepler-80

The Kepler and K2 missions have discovered hundreds of systems with multiple transiting exoplanets which hold tremendous potential for understanding the formation and evolution of planetary systems. While many of these systems contain planet pairs with period ratios near mean motion resonances, very few resonances have been confirmed because it can be difficult to constrain the eccentricity vector of transiting planets. While a two-body resonance is hard to confirm, a multi-body resonance or a chain of resonances is much easier to constrain. In addition, such a study can also constrain the planetary masses and orbits since the planets are gravitationally perturbing one another. We present such a study here. We forward model the lightcurves of two compact systems with suggested resonance chains, K2-138 and Kepler-80, and subsequently determine the planetary masses and orbital parameters of all of their planets. We then explore the resonant behaviour of each system. We find that both systems have five planets interlocked in a resonant chain, something previously confirmed for four planets of Kepler-80 but never for K2-138. We also find that the systems and their dynamic behaviour are consistent with in situ formation and compare our results to another resonant chain system, TRAPPIST-1.