Isles of regularity in a sea of chaos amid the gravitational three-body problem

Abstract

The three-body problem (3BP) poses a longstanding challenge in physics and celestial mechanics. Despite the impossibility of obtaining general analytical solutions, statistical theories have been developed based on the ergodic principle. This assumption is justified by chaos, which is expected to fully mix the accessible phase space of the 3BP. This study probes the presence of regular (i.e. non chaotic) trajectories within the 3BP and assesses their impact on statistical escape theories. Using numerical simulations, we establish criteria for identifying regular trajectories and analyse their impact on statistical outcomes. Our analysis reveals that regular trajectories occupy up to 32% of the phase space, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. Integration errors manifest as numerical chaos, artificially enhancing the mixing of the phase space and affecting the reliability of individual simulations, yet preserving the statistical correctness of an ensemble of realizations. Our findings underscore the challenges in applying statistical escape theories to astrophysical problems, as they may bias results by excluding the outcome of regular trajectories. This is particularly important in the context of formation scenarios of gravitational wave mergers, where biased estimates of binary eccentricity can significantly impact estimates of coalescence efficiency and detectable eccentricity.

15 pages, 13 figures, accepted for publication in Astronomy & Astrophysics

References in corpus (13)

• Three Classes of Newtonian Three-Body Planar Periodic Orbits
• Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length
• Chaos and Lévy Flights in the Three-Body Problem
• Correlation of macroscopic instability and Lyapunov times in the general three-body problem
• Chaos in self-gravitating many-body systems: Lyapunov time dependence of $N$ and the influence of general relativity
• Flux-based statistical prediction of three-body outcomes
• From hydrodynamics to N-body simulations of star clusters: mergers and rotation
• On the relationship between instability and Lyapunov times for the 3-body problem
• Searching for the extra-tidal stars of globular clusters using high-dimensional analysis and a core particle spray code
• Discreteness effects, $N-$body chaos and the onset of radial-orbit instability
• Analytic Modelling of Binary-Single Encounters: Non-Thermal Eccentricity Distribution and Gravitational-Wave Source Formation
• Chaos in the vicinity of a singularity in the Three-Body Problem: The equilateral triangle experiment in the zero angular momentum limit
• Measurement of three-body chaotic absorptivity predicts chaotic outcome distribution

Cited by in corpus (5)

• Interactions among binary black holes in star clusters: Eccentric gravitational wave captures and triple formation
• Partial suppression of chaos in relativistic three-body problems
• Binary-single interactions with different mass ratios
• The formation of periodic three-body orbits for Newtonian systems
• Exploring the parameter space of hierarchical triple black hole systems