Anisotropic mass segregation: two-component mean-field model

TL;DR

This paper develops a mean-field model to understand anisotropic mass segregation in galactic nuclei, revealing phase transitions and disk formation in two-component gravitating systems.

Contribution

It introduces a new equilibrium model for two-component systems in galactic nuclei, capturing anisotropic mass segregation and phase transitions.

Findings

Massive bodies condense into a disk above a critical mass.

Identifies smooth and discontinuous phase transitions.

Models the equilibrium distribution using entropy maximization and mean-field approximation.

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 (VRR). In this paper, we build simple models to understand the equilibrium distribution found previously in numerical simulations. Using the method of maximising 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 disk-like state and a disordered nearly spherical distribution both in the canonical and in the microcanonical ensembles for these long-range interacting systems.