Enhanced Kozai-Lidov Eccentricity Oscillations in Nuclear Star Clusters

Stellar motions in the innermost parts of galactic nuclei, where the gravity of a supermassive black hole dominates, follow Keplerian ellipses to the first order of approximation. These orbits may be subject to periodic (Kozai-Lidov) oscillations of their orbital elements if some nonspherically distributed matter (e.g., a secondary massive black hole, coherent stellar subsystem, or large-scale gaseous structure) perturbs the gravity of the central supermassive black hole. These oscillations are, however, affected by the overall potential of the host nuclear star cluster. In this paper, we show that its influence strongly depends on the properties of the particular system, as well as the considered timescale. We demonstrate that for systems with astrophysically relevant parameters, the Kozai-Lidov oscillations of eccentricity can be enhanced by the extended potential of the cluster in terms of reaching significantly higher maximal values. In a more general statistical sense, the oscillations of eccentricity are typically damped. The efficiency of the damping, however, may be small to negligible for the suitable parameters of the system. This applies, in particular, in the case when the perturbing body is on an eccentric orbit.