Global Mean-Motion Resonances: Part II—Laplace-like Phase Angles to Facilitate Libration Searches in Multiplanetary N-body Simulations

We describe a method of determining three-body and four-body Laplace-like phase angles with the potential to librate about a mean value in multiplanet extrasolar systems. Unlike in past searches of N-body results, this method relies on global mean-motion resonances (MMRs) and takes into consideration the location of the most massive planet that defines the 1:1 global MMR in each (sub)system. We compiled lists of potentially librating phase angles and prevalent MMRs in 35 real multibody systems, and we discuss their properties in conjunction with recent investigations of librations discovered in sophisticated N-body simulations. We hope that our results will facilitate systematic libration searches in dynamical models of compact systems with three or more orbiting bodies.