Secular and resonant dynamics of hierarchical and mildly hierarchical three-body systems
Mildly Hierarchical Triple Dynamics and Applications to the Outer Solar System
Three-body interactions show up throughout astrophysics, and the secular behavior of well-separated hierarchical triples is well understood, but less-separated ("mildly hierarchical") configurations are less explored. This paper works out the secular dynamics of a test particle in such a configuration, mapping where the secular approximation breaks down, locating resonant and chaotic regions of phase space, and identifying which configurations allow large swings in eccentricity and inclination. The results are applied to the outer solar system, showing that a hypothetical distant ninth planet on a low-inclination, polar, or counter-orbiting path could each help explain the observed orbital clustering of extreme trans-Neptunian objects.
High-Eccentricity Tidal Migration Driven by Secular Chaos in Wide-Binary Systems
Most models of high-eccentricity migration driven by a distant stellar companion use an idealized three-body setup, but real cold-Jupiter systems often carry additional planets or substellar companions. This paper studies hierarchical "3+1" systems—a stellar binary hosting a planet plus an intermediate companion—and shows that secular chaos, controlled by the ratio of the inner and outer Kozai–Lidov timescales, can drive migration even at fairly modest mutual inclinations, well below the classical Kozai–Lidov threshold. The model predicts resulting hot Jupiters on nearly polar orbits relative to both their host star and their outer companions.