Quadrupole and octupole order resonances in non-restricted hierarchical planetary systems
arXiv:2207.05362 · doi:10.1093/mnras/stac1757
Abstract
Nonrestricted hierarchical three-body configurations are common in various scales of astrophysical systems. Dynamical structures of the quadrupole-order resonance (the von Zeipel-Lidov-Kozai resonance) and the octupole-order resonance (the apsidal resonance) under the nonrestricted hierarchical planetary systems are investigated in this work by taking advantage of perturbative treatments. Under the quadrupole-order Hamiltonian model, the distribution of libration and circulation regions as well as the distribution of flipping region are analytically explored in the parameter space spanned by the conserved quantities. The fundamental frequencies of system are produced and then the nominal location of octupole-order resonance is identified. From the viewpoint of perturbative theory, the quadrupole-order Hamiltonian determines the unperturbed dynamical model and the octupole-order Hamiltonian plays an role of perturbation to the quadrupole-order dynamics. The resonant Hamiltonian for octupole-order resonances is formulated by means of averaging theory, giving rise to a new constant of motion. Phase portraits are produced to analyse dynamical structures of octupole-order resonance, including resonant centres, saddle points, dynamical separatrices and islands of libration. By analysing phase portraits, it is found that there are four branches of libration centre and eight libration zones in the considered space. Applications to orbit flips show that there are five flipping regions.
arXiv commentAccepted for publication in MNRAS, 20 pages, 15 figures
References in corpus (23)
- The Eccentric Kozai-Lidov Effect and Its Applications
- Origins of Hot Jupiters
- Hot Jupiters from Secular Planet--Planet Interactions
- Secular Dynamics in Hierarchical Three-Body Systems
- The Kozai Mechanism and the Evolution of Binary Supermassive Black Holes
- On the Formation of Hot Jupiters in Stellar Binaries
- The Eccentric Kozai Mechanism for a Test Particle
- Long-Term Cycling of Kozai-Lidov Cycles: Extreme Eccentricities and Inclinations Excited by a Distant Eccentric Perturber
- Eccentricity growth and orbit flip in coplanar hierarchical three body systems
- Hot Jupiters from Coplanar High-eccentricity Migration
- Secular Evolution of Hierarchical Planetary Systems
- Warm Jupiters from secular planet-planet interactions
- Chaos in the Test Particle Eccentric Kozai-Lidov Mechanism
- Double-Averaging Can Fail to Characterize the Long-Term Evolution of Lidov-Kozai Cycles & Derivation of an Analytical Correction
- Extreme orbital evolution from hierarchical secular coupling of two giant planets
- Orbital flips in hierarchical triple systems: relativistic effects and third-body effects to hexadecapole order
- Analytic computation of the secular effects of encounters on a binary: features arising from second-order perturbation theory
- Higher-order effects in the dynamics of hierarchical triple systems. Quadrupole-squared terms
- The eccentric Kozai-Lidov effect as a resonance phenomenon
- Properties of von Zeipel-Lidov-Kozai oscillations in triple systems at the quadrupole order: relaxing the test particle approximation
- A systematic study about orbit flips of test particles caused by eccentric von Zeipel-Lidov-Kozai effects
- Analytic computation of the secular effects of encounters on a binary: third-order perturbation, octupole, and post-Newtonian terms; steady-state distribution
- An Analytic Solution to the Kozai-Lidov Evolution Equations