Angular-momentum pairs in spherical systems: applications to the Galactic Centre
Panamarev T. Ginat Y.B. Kocsis B.
1 February 2026Oxford University Press
Monthly Notices of the Royal Astronomical Society
2026#546Issue 2
Consider a system of point masses in a spherical potential. In such systems objects execute planar orbits covering two-dimensional rings or annuli, represented by the angular-momentum vectors, which slowly reorient due to the persistent weak gravitational interaction between different rings. This process, called vector resonant relaxation, is much faster than other processes which change the size/shape of the rings. The interaction is strongest between objects with closely aligned angular-momentum vectors. In this paper, we show that nearly parallel angular-momentum vectors may form stable bound pairs in angular-momentum space. We examine the stability of such pairs against an external massive perturber, and determine the critical separation analogous to the Hill radius or tidal radius in the three-body problem, where the angular-momentum pairs are marginally disrupted, as a function of the perturber’s mass, the orbital inclination, and the radial distance. Angular-momentum pairs or multiples closer than the critical inclination will remain bound and evolve together in angular-momentum-direction space under any external influence, such as anisotropic density fluctuations, or massive perturbers. This study has applications in various astrophysical contexts, including galactic nuclei, in particular the Milky Way’s Galactic Centre, globular clusters, or planetary systems. In nuclear star clusters with a central supermassive black hole, we apply this criterion to the disc of young, massive stars, and show that clusters in angular-momentum space may be used to constrain the presence of intermediate-mass black holes or the mass of the nearby gaseous torus.
galaxies: nuclei , Galaxy: centre , methods: numerical , stars: kinematics and dynamics
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Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford, OX1 3PU, United Kingdom
Fesenkov Astrophysical Institute, Observatory 23, Almaty, 050020, Kazakhstan
New College, Holywell Street, Oxford, OX1 3BN, United Kingdom
St. Hugh’s College, St. Margaret’s Road, Oxford, OX2 6LE, United Kingdom
Rudolf Peierls Centre for Theoretical Physics
Fesenkov Astrophysical Institute
New College
St. Hugh’s College
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