Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices

Abstract

We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form that can be used to obtain general results about the dynamics of the system without being required to solve the Smoluchowski-Poisson system explicitly. We also develop the analogy between self-gravitating systems and two-dimensional point vortices and derive a Virial-like relation for the vortex system.

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Cited by in corpus (4)

• Gravitational phase transitions with an exclusion constraint in position space
• Statistical mechanics of two-dimensional point vortices: relaxation equations and strong mixing limit
• Self-gravitating clusters of Fermi-Dirac gas with planar, cylindrical, or spherical symmetry: evolution of density profiles with temperature
• Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: gaseous density profiles and onset of condensation