Dynamics of Binary System around a Supermassive Black Hole :Binary Scattering and Eccentric vZLK Oscillations

TL;DR

This paper investigates the complex dynamics of binary systems around supermassive black holes, revealing new regimes of scattering and oscillations influenced by tidal effects and black hole spin.

Contribution

It introduces a unified framework for understanding tidal interactions and eccentric vZLK oscillations in binary systems near SMBHs, highlighting new scattering regimes and dynamical behaviors.

Findings

Identified four scattering regimes based on binary semi-major axis.

Discovered that tidal effects can cause strong eccentricity excitation and chaos.

Described a new scattering-type vZLK oscillation mechanism.

Abstract

We study the dynamics of a binary orbiting a supermassive black hole (SMBH), focusing on both binary scattering in unbound orbits and eccentric von Zeipel-Lidov-Kozai (vZLK) oscillations in bound orbits. The motion is described in a local inertial frame in Kerr spacetime, where tidal effects are encoded in the Riemann curvature. For unbound (parabolic and hyperbolic) orbits, we identify four scattering regimes-adiabatic, tidally affected, chaotic, and disruptive-depending on the binary semi-major axis. As the binary becomes softer, tidal interactions near periapsis lead to strong eccentricity excitation, large changes in the orbital parameters, and eventually chaotic behavior or tidal disruption, with a sensitive dependence on the argument of periapsis. For eccentric bound (elliptic) orbits, the vZLK mechanism differs qualitatively from the standard one, although the $z$-component of the angular momentum in the local inertial frame remains approximately conserved. The evolution proceeds on a dynamical timescale and exhibits step-like changes driven by repeated periapsis passages, which can be interpreted as a sequence of scattering events. We refer to this behavior as scattering-type vZLK oscillations. The rotation of the SMBH also modifies the oscillation profiles, although its effect is less significant than the dependence on the initial orbital parameters. These results suggest a unified picture of periapsis-driven tidal dynamics in galactic nuclei.