Order-disorder phase transition in black-hole star clusters. II. A scale-free cluster

Abstract

The supermassive black holes found at the centers of galaxies are often surrounded by dense star clusters. The ages of these clusters are generally longer than the resonant-relaxation time and shorter than the two-body relaxation time over a wide range of radii. We explore the thermodynamic equilibria of such clusters using a simple self-similar model. We find that the cluster exhibits a phase transition between a high-temperature spherical equilibrium and a low-temperature equilibrium in which the stars are on high-eccentricity orbits with nearly the same orientation. In the absence of relativistic precession, the spherical equilibrium is metastable below the critical temperature and the phase transition is first-order. When relativistic effects are important, the spherical equilibrium is linearly unstable below the critical temperature and the phase transition is continuous. A similar phase transition has recently been found in a model cluster composed of stars with a single semimajor axis. The presence of the same phenomenon in two quite different cluster models suggests that lopsided equilibria may form naturally in a wide variety of black-hole star clusters.

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References in corpus (8)

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Cited by in corpus (7)

• Nuclear Star Clusters
• The Thermodynamics of Rotating Black-Hole Star Clusters
• Orbital alignment and mass segregation in galactic nuclei via vector resonant relaxation
• Order-disorder phase transition in black-hole star clusters -- III. A mono-energetic cluster
• Black Hole Discs and Spheres in Galactic Nuclei -- Exploring the Landscape of Vector Resonant Relaxation Equilibria
• Apsidal Clustering following the Inclination Instability
• On the Missing Red Giants near the Galactic Center