Irregular Fixation: I. Fixed points and librating orbits of the Brown Hamiltonian
arXiv:2407.05122 · doi:10.1093/mnras/stae1833
Abstract
In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel-Lidov-Kozai (ZLK) oscillations. Stable systems with a mild hierarchy, where the period ratio is not too small, require an additional corrective term, known as the Brown Hamiltonian, to adequately account for their long-term evolution. Although the Brown Hamiltonian has been used to accurately describe the highly eccentric systems on circulating orbits where the periapse completes a complete revolution, the analysis near its elliptical fixed points had been overlooked. We derive analytically the modified fixed points including the Brown Hamiltonian and analyse its librating orbits (where the periapse motion is limited in range). We compare our result to the direct three-body integrations of millions of orbits and discuss the regimes of validity. We numerically discover the regions of orbital instability, allowed and forbidden librating zones with a complex, fractal, structure. The retrograde orbits, where the mutual inclination is , are more stable and allowed to librate for larger areas of the parameter space. We find numerical fits for the librating-circulating boundary. Finally, we discuss the astrophysical implications for systems of satellites, stars and compact objects. In a companion paper (paper II), we apply our formalism to the orbits of irregular satellites around giant planets.
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References in corpus (35)
- The Eccentric Kozai-Lidov Effect and Its Applications
- IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits
- Secular Dynamics in Hierarchical Three-Body Systems
- Head-on collisions of white dwarfs in triple systems could explain type Ia supernova
- Suppression of extreme orbital evolution in triple systems with short range forces
- Black hole and neutron star mergers in galactic nuclei
- Black Hole and Neutron Star Binary Mergers in Triple Systems: Merger Fraction and Spin-Orbit Misalignment
- A close-pair binary in a distant triple supermassive black-hole system
- Planets Transiting Non-Eclipsing Binaries
- Double-Averaging Can Fail to Characterize the Long-Term Evolution of Lidov-Kozai Cycles & Derivation of an Analytical Correction
- A Statistical Solution to the Chaotic, Non-Hierarchical Three-Body Problem
- Quasi-secular evolution of mildly hierarchical triple systems: analytics and applications for GW-sources and hot Jupiters
- Direct Imaging Discovery of a Jovian Exoplanet Within a Triple Star System
- Generalized Hill-Stability Criteria for Hierarchical Three-Body Systems at Arbitrary Inclinations
- On the Secular Behavior of Irregular Satellites
- Chaotic dynamics of wide triples induced by galactic tides: a novel channel for producing compact binaries, mergers, and collisions
- Higher-order effects in the dynamics of hierarchical triple systems. Quadrupole-squared terms
- An Analytical, Statistical Approximate Solution for Dissipative and non-Dissipative Binary-Single Stellar Encounters
- Compact-Object Mergers in the Galactic Center: Evolution in Triaxial Clusters
- Origin of (2014) MU69-like Kuiper-belt contact binaries from wide binaries
- The Hamiltonian for von Zeipel-Lidov-Kozai oscillations
- Secular dynamics of binaries in stellar clusters II: dynamical evolution
- Properties of von Zeipel-Lidov-Kozai oscillations in triple systems at the quadrupole order: relaxing the test particle approximation
- Flux-based statistical prediction of three-body outcomes
- The Stationary Points of the Hierarchical Three Body Problem
- Testing the Flux-based statistical prediction of the Three-Body Problem
- Empirical Stability Boundary for Hierarchical Triples
- A Simple Random-Walk Model Explains the Disruption Process of Hierarchical, Eccentric 3-Body Systems
- Binaries are softer than they seem: Effects of an external potential on the scattering dynamics of binaries
- The Wide-Binary Origin of The Pluto-Charon System
- Extreme close approaches in hierarchical triple systems with comparable masses
- Librating Kozai-Lidov Cycles with a Precessing Quadrupole Potential are Analytically Approximately Solved
- An Analytic Solution to the Kozai-Lidov Evolution Equations
- Analytic understanding of the resonant nature of Kozai Lidov Cycles with a precessing quadrupole potential
- Natural dynamical reduction of the three-body problem