Von Zeipel-Lidov-Kozai secondary resonances can enhance the excitation of planetary eccentricity

Abstract

The von Zeipel-Lidov-Kozai (ZLK) effect has been applied to a wide range of dynamical circumstances, covering satellites and planets to supermassive black holes, in order to explain physical phenomena. The evolution of periodic orbit families associated with ZLK resonance under the octupole-level approximation exhibits distinctly different dynamical structures from the standard ZLK effect. In particular, bifurcations of periodic-orbit families commonly exist in planetary systems with a wide range of mass ratios. It is shown that such a phenomenon of bifurcation is triggered by ZLK secondary resonance, which is a new dynamical mechanism that has not appeared in previous studies. Numerical analysis shows that ZLK secondary resonance leads to a stronger excitation of eccentricity and/or inclination than the standard ZLK effect and that the level of enhancement is dependent on the initial eccentricity. The technique of perturbative treatments is adopted to study dynamical structures of ZLK secondary resonances, showing that there is an excellent agreement between analytical structures arising in phase portraits and numerical structures arising in Poincaré sections. Phase-space structures are produced for actual exoplanetary systems including HAT-P-11, HAT-P-13, and HAT-P-44, where large excitation of planetary eccentricity and/or inclination is expected due to the emergence of ZLK secondary resonance.