Large-scale chaos in restricted hierarchical triples driven by short-range forces

Abstract

Context: The eccentric von Zeipel-Lidov-Kozai effect, which is widely applied to diverse astrophysical settings, can drive the inner binary to extremely high eccentricities, where short-range forces such as general relativity (GR) become prominent. Aims: Poincare surfaces of section show that GR effects reshape phase-space structures, giving rise to a widespread and large-scale chaotic sea. This work aims to uncover the underlying mechanism of GR-enabled chaos. Methods: The dynamical structures are studied within an adiabatic framework, where an adiabatic invariant is constructed. Phase portraits, defined by the level curves of this invariant, establish analytical boundaries for the chaotic domains. Numerical simulations are subsequently performed to map orbital flips, maximum eccentricities, and Fast Lyapunov Indicators (FLI) across the initial eccentricity-inclination parameter space. Results: Phase portrait analysis demonstrates that GR precession introduces an uncertainty zone near polar inclinations, where trajectories crossing this zone inherently become chaotic. Leveraging this framework, the chaotic boundaries across the full parameter space are analytically derived, yielding excellent agreement with numerical maps of flipping orbits, maximum eccentricity, and FLI. Conclusions: In the presence of short-range forces, flipping orbits accompanied by extreme eccentricity excitation are fundamentally chaotic, and the underlying mechanism of large-scale chaos originates from the periodic passage of trajectories through the uncertainty zone in phase space over secular timescales.