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Dynamics of a binary system around a supermassive black hole: Binary scattering and eccentric von Zeipel-Lidov-Kozai oscillations

Kei-ichi Maeda1,2 and Hirotada Okawa3

  • 1Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
  • 2Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan
  • 3Faculty of Software and Information Technology, Aomori University, Seishincho, Edogawa, Tokyo 134-0087, Japan

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Phys. Rev. D 114, 084078 – Published 29 October, 2026

DOI: https://doi.org/10.1103/jddn-gbnz

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 semimajor 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 steplike 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.

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Phys. Rev. D 114, 084078– Published 29 October, 2026
  • Received 27 May 2026
  • Accepted 3 August 2026
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