Secular Dynamics of Three-Body Systems and the Origins of Retrograde Hot Jupiters

We consider the secular-perturbation expansion of the classical Hamiltonian equations of motion for three mutually gravitating bodies, and we use the formalism to study the dynamical evolution of hierarchical three-body systems to octupole-level accuracy. Our study is partly motivated by recent observations of exoplanetary systems, which may include two giant planets strongly perturbing each other gravitationally on secular timescales. These systems display a rich array of dynamics not present in the commonly adopted quadrupolelevel models. In particular, long-period, large-amplitude oscillations in the eccentricity e1 and inclination i1 of the inner orbit have been observed. In some cases the inner orbit may even become retrograde, providing a possible explanation of the “retrograde Hot Jupiters” that have been observed recently in several systems. We study in some detail the mechanisms giving rise to such retrograde orbits and we propose a model that may apply to the entire phase space. We find that the probability to induce a flip in the inner binary is highly dependent on the maximum inner orbit eccentricity e1 reached during the dynamical evolution of the system. We also find that the probability to reach high eccentricities increases with time and, as a result, the probability for a flip approaches unity (formally, over an infinite time) above a certain threshold in e1,max. Finally we show that the relationship between the quadrupole– and octupole–level secular timescales plays an important role in setting the probability to reach high eccentricities (over some finite time) and thus to flip the inner orbit.