Secular Resonances in Nonrestricted Hierarchical Triple Systems

作者：Pan Tan, Xiyun Hou, Xinhao Liao, Wenlei Wang, Jingshi Tang · 发表于：The Astronomical Journal · 年份：2020 · DOI：10.3847/1538-3881/aba89c · 被引用次数：12 · 研究领域：Quantum chaos and dynamical systems、Astrophysics and Star Formation Studies、Nonlinear Photonic Systems

Abstract In this paper, the averaged Hamiltonian of a nonrestricted hierarchical triple system truncated at the third order is investigated. First, each secular resonant term is studied. For the well-studied secular quadrupole theory, it is analytically reformulated in a different manner in our work. The resonance width is numerically determined and displayed on the plane (also denoted as the plane). In terms of the octupole terms, we show that for a near-planar configuration of the system, considerable variations of both the eccentricities of the inner and outer orbits can be generated by a single resonant term. The resonance width for every secular resonant angle from the octupole terms is also numerically determined and displayed on the plane. The results show that an orbit flip with a near-perpendicular initial mutual inclination is possible for each secular resonance. By displaying the resonance widths of different resonant terms on the same plane, we intuitively show the overlap of different secular resonances. Then, the full averaged Hamiltonian with both quadrupole and octupole terms is investigated using the Poincaré surface of section, with a special focus on the orbit flip. For the cases we exploited, we find that the near-planar flip of the inner orbit can be either regular or chaotic while the outer orbit flip is generally chaotic.