New Python package to find, confirm, and characterize mean motion resonances

Abstract

<p>The study of orbital resonances allows for the constraint of planetary properties of compact systems. Mean motion resonance occurs when two or more planets repeatedly exchange angular momentum and energy as they orbit their host star, since the planets will always conjunct at the same point in their orbits. We can predict a system's resonances by observing the orbital periods of the planets, as planets in or near mean motion resonance have period ratios that reduce to a ratio of small numbers. However, a period ratio near commensurability does not guarantee a resonance; we must study the system's dynamics and resonance angles to confirm resonance. Because resonances require in-depth study to confirm, and because two-body resonances require a measurement of the eccentricity vector which is quite challenging, very few resonant pairs or chains have been confirmed. We thus remain in the era of small number statistics, not yet able to perform large population synthesis or informatics studies. To address this problem, we build a python package to find, confirm, and analyze mean motion resonances, primarily through N-body simulations. We verify our package by recovering the known resonances of Kepler-80 and Kepler-223. We then demonstrate the package’s functionality and potential by confirming new resonances, characterizing the mass-eccentricity degeneracy of Kepler-80g, and exploring the likelihood of an exterior giant planet in Kepler-80 and Kepler-223. We also study the formation history of K2-138 and constrain the planets’ masses and orbital parameters.</p>