Solvable model of a self-gravitating system

Abstract

We introduce and discuss an effective model of a self-gravitating system whose equilibrium thermodynamics can be solved in both the microcanonical and the canonical ensemble, up to a maximization with respect to a single variable. Such a model can be derived from a model of self-gravitating particles confined on a ring, referred to as the self-gravitating ring (SGR) model, allowing a quantitative comparison between the thermodynamics of the two models. Despite the rather crude approximations involved in its derivation, the effective model compares quite well with the SGR model. Moreover, we discuss the relation between the effective model presented here and another model introduced by Thirring forty years ago. The two models are very similar and can be considered as examples of a class of minimal models of self-gravitating systems.

21 pages, 6 figures; submitted to JSTAT for the special issue on long-range interactions

References in corpus (11)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models
• Statistical Mechanics of the Self-Gravitating Gas: I. Thermodynamic Limit and Phase Diagram
• Thermodynamics of the self-gravitating ring model
• Partial equivalence of statistical ensembles and kinetic energy
• Origin of scaling structure and non-gaussian velocity distribution in self-gravitating ring model
• Phase diagram of self-attracting systems
• On the mean-field spherical model
• Energy landscape and phase transitions in the self-gravitating ring model
• The Vlasov continuum limit for the classical microcanonical ensemble
• A one-dimensional toy model of globular clusters

Cited by in corpus (10)

• Velocity filtration and temperature inversion in a system with long-range interactions
• Caloric curve of star clusters
• On the origin of power-laws in equilibrium
• Phase transitions in simplified models with long-range interactions
• Phase transitions in Thirring's model
• Geometry of the energy landscape of the self-gravitating ring
• Coarse-grained collisionless dynamics with long-range interactions
• Multiple metastable states in an off-lattice Potts model
• Thermodynamics of gravitational clustering phenomena: $N$-body self-gravitating gas on the sphere ${\mathbb{S}}^3\subset {\mathbb{R}}^4$
• Crossover in densities of confined particles with finite range of interaction