Secular chaotic dynamics in hierarchical quadruple systems, with applications to hot Jupiters in stellar binaries and triples

Hierarchical quadruple systems arise naturally in stellar binaries and triples that harbour planets. Examples are hot Jupiters (HJs) in stellar triple systems, and planetary companions to HJs in stellar binaries. The secular dynamical evolution of these systems is generally complex, with secular chaotic motion possible in certain parameter regimes. The latter can lead to extremely high eccentricities and, therefore, strong interactions such as efficient tidal evolution. These interactions are believed to play an important role in the formation of HJs through high-eccentricity migration. Nevertheless, a deeper understanding of the secular dynamics of these systems is still lacking. Here, we study in detail the secular dynamics of a special case of hierarchical quadruple systems in either the '2+2' or '3+1' configurations. We show how the equations of motion can be cast in a form representing a perturbed hierarchical three-body system, in which the outer orbital angular-momentum vector is precessing steadily around a fixed axis. In this case, we show that eccentricity excitation can be significantly enhanced when the precession period is comparable to the Lidov-Kozai oscillation time-scale of the inner orbit. This arises from an induced large mutual inclination between the inner and outer orbits driven by the precession of the outer orbit, even if the initial mutual inclination is small. We present a simplified semi-analytic model that describes the latter phenomenon.