Chaotic von Zeipel-Lidov-Kozai Oscillations of Binary System around Rotating Supermassive Black Hole

TL;DR

This paper studies the complex dynamics of binary systems orbiting rotating supermassive black holes, revealing conditions for stable and chaotic von Zeipel-Lidov-Kozai oscillations and orbital flips.

Contribution

It introduces a novel framework using Fermi-Walker transport to analyze vZLK oscillations in binary-black hole systems around Kerr black holes, highlighting chaotic behaviors.

Findings

Regular vZLK oscillations in hard binaries

Chaotic vZLK oscillations in soft binaries

Orbital flips at high initial inclinations

Abstract

In this paper, we investigate the dynamics of a binary system that orbits a rotating supermassive black hole. Our approach employs Fermi-Walker transport to construct a local inertial reference frame, and to set up a Newtonian binary system. We consider a scenario in which a circular geodesic observer is positioned around a Kerr black hole, and thereby derive the equations of motion governing the binary system. To eliminate the interaction terms between the center of mass (CM) of the binary and its relative coordinates, we introduce a small acceleration for the observer. This adjustment leads to the CM closely following the observer's orbit, deviating from a circular geodesic. Here, we first focus on elucidating the stability conditions in a hierarchical triple system. Subsequently, we discuss the phenomenon of von Zeipel-Lidov-Kozai (vZLK) oscillations, which manifest when the binary system is compact and the initial inclination exceeds a critical angle. In hard binary systems, these oscillations exhibit regular behavior, while in soft binary systems, they exhibit a chaotic character, characterized by irregular periods and amplitudes, albeit remaining stable. Additionally, we observe an orbital flip under circumstances of large initial inclination. As for the motion of the CM, we observe deviations from a purely circular orbit that transform into stable yet chaotic oscillations characterized by minute amplitude variations.