Confirming Resonance in Three Transiting Systems

TL;DR

This study confirms resonance in five multi-planet systems through N-body simulations, revealing specific two-body and three-body resonances, and suggests these resonances likely formed without planetary migration.

Contribution

The paper provides a comprehensive dynamical analysis confirming resonances in multiple systems and clarifies their formation mechanisms, which is a novel application of N-body simulations to these systems.

Findings

Confirmed 3:2 resonance in Kepler-226c and Kepler-226d

Confirmed 3:2 resonance in Kepler-254c and Kepler-254d

Identified a 1:2:3 three-body resonant chain in Kepler-363

Abstract

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 multi-planet 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 non-resonant and which systems require additional follow-up analysis.