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Three-Body Resonances Among Kepler Planets

Presentation #304.03 in the session “Orbital Resonance in Multi-Planet Systems”.

Published onJun 01, 2021
Three-Body Resonances Among Kepler Planets

Detailed analysis of systems with multiple planets near resonances has revealed the existence of three-body (mean-motion) resonances. Kepler-80 has a resonant chain of five planets with all threesomes in 3-body resonances, and Kepler-223 has a similar chain of four such planets. As with the Laplace resonance between the Galilean satellites, these three-body resonances involve a geometric repetition of conjunctions between three planets that exhibits stability through subtle mutual planetary perturbations. The strengths of three-body resonances are second-order in ratio of planetary masses to stellar masses, but the strongest 3-body resonances (“zeroth-order”) do not depend on either planetary eccentricities or inclinations, so their locations are not dependent on the rates of periapse precession or nodal regression, both of which are poorly constrained for the vast majority of Kepler planets. Nonetheless, period variations resulting from TTVs complicate the analysis of Kepler data (Lissauer et al., 2020 DDA, BAAS id. 2020n4i204p02). We present results of a study estimating the number of low-order, low-coefficient three-body resonances in the Kepler dataset and discuss interesting cases where detailed analysis implies resonant lock despite the nominal periods placing the system several standard deviations away from resonance.

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