Bence Kocsis

Abstract:

Galactic nuclei, the densest stellar environments in the Universe, exhibit a complex geometrical structure. The stars orbiting the central supermassive black hole follow a mass segregated distribution both in the radial distance from the center and in the inclination angle of the orbital planes. The latter distribution may represent the equilibrium state of vector resonant relaxation. In this paper, we build simple models to understand the equilibrium distribution found previously in numerical simulations. Using the method of maximizing the total entropy and the quadrupole mean-field approximation, we determine the equilibrium distribution of axisymmetric two-component gravitating systems with two distinct masses, semimajor axes, and eccentricities. We also examine the limiting case when one of the components dominates over the total energy and angular momentum, approximately acting as a heat bath, which may represent the surrounding astrophysical environment such as the tidal perturbation from the galaxy, a massive perturber, a gas torus, or a nearby stellar system. Remarkably, the bodies above a critical mass in the subdominant component condense into a disk in a ubiquitous way. We identify the system parameters where the transition is smooth and where it is discontinuous. The latter cases exhibit a phase transition between an ordered disklike state and a disordered nearly spherical distribution both in the canonical and in the microcanonical ensembles for these long-range interacting systems.

Abstract:

We derive an analytical model for the so-called phenomenon of resonant dynamical friction, where a disc of stars around a supermassive black hole interacts with a massive perturber, so as to align its inclination with the disc’s orientation. We show that it stems from a singular behaviour of the orbit-averaged equations of motion, which leads to a rapid alignment of the argument of the ascending node of each of the disc stars, with that of the perturber, p, with a phase difference of 90◦. This phenomenon occurs for all stars whose maximum possible ˙ (maximized over all values of for all the disc stars) is greater than ˙ p; this corresponds approximately to all stars whose semi-major axes are less than twice that of the perturber. The rate at which the perturber’s inclination decreases with time is proportional to its mass and is shown to be much faster than Chandrasekhar’s dynamical friction. We find that the total alignment time is inversely proportional to the root of the perturber’s mass. This persists until the perturber enters the disc. The predictions of this model agree with a suite of numerical N-body simulations, which we perform to explore this phenomenon, for a wide range of initial conditions, masses, etc., and are an instance of a general phenomenon. Similar effects could occur in the context of planetary systems, too.