2002/04/14 by C. Sire, Clément Sire, Pierre-Henri Chavanis +1 · 9 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #astro-ph #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.046133
published as Phys.Rev. E66 (2002) 046133
arxiv created 2002/04/14 · openalex publication_date 2002/10/24 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We address the thermodynamics and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. We study the equilibrium density profile and phase diagram of isothermal spheres and, for 2<D<10, determine the onset of instability in the series of equilibria. We also study the dynamics of self-gravitating Brownian particles in a high friction limit leading to the Smoluchowski-Poisson system. Self-similar solutions describing the collapse are investigated analytically and numerically. In the canonical ensemble (fixed temperature), we derive the analytic form of the density scaling profile which decays as f(x) approximately x(-alpha), with alpha=2. In the microcanonical ensemble (fixed energy), we show that f decays as f(x) approximately x(-alpha(max)), where alpha(max) is a nontrivial exponent. We derive exact expansions for alpha(max) and f in the limit of large D. Finally, we solve the problem in D=2, which displays rather rich and peculiar features with, in particular, the formation of a Dirac peak in the density profile.