Non-resonant Kepler planetary systems

Identifying potentially resonant systems could help guide future observations and enhance our understanding of planetary formation scenarios. We develop and apply an algebraic method to determine which Kepler two-planet systems cannot be in a first-fourth order resonance, given the current, publicly available data.

This method identifies when any potentially resonant angle of a system must circulate. We identify and list 70 near-resonant systems which cannot actually reside in resonance, assuming a widely used formulation for deriving planetary masses from their observed radii and that these systems do not contain unseen bodies that affect the interactions of the observed planets. This work strengthens the argument that a high fraction of exoplanetary systems may be near resonance but not actually in resonance.