Density profiles of a self-gravitating lattice gas in one, two, and three dimensions

Physical Review. E
Benaoumeur BakhtiGerhard Müller

Abstract

We consider a lattice gas in spaces of dimensionality D=1,2,3. The particles are subject to a hardcore exclusion interaction and an attractive pair interaction that satisfies Gauss' law as do Newtonian gravity in D=3, a logarithmic potential in D=2, and a distance-independent force in D=1. Under mild additional assumptions regarding symmetry and fluctuations we investigate equilibrium states of self-gravitating material clusters, in particular radial density profiles for closed and open systems. We present exact analytic results in several instances and high-precision numerical data in others. The density profile of a cluster with finite mass is found to exhibit exponential decay in D=1 and power-law decay in D=2 with temperature-dependent exponents in both cases. In D=2 the gas evaporates in a continuous transition at a nonzero critical temperature. We describe clusters of infinite mass in D=3 with a density profile consisting of three layers (core, shell, halo) and an algebraic large-distance asymptotic decay. In D=3 a cluster of finite mass can be stabilized at T>0 via confinement to a sphere of finite radius. In some parameter regime, the gas thus enclosed undergoes a discontinuous transition between distinct density profil...Continue Reading

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Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Benaoumeur BakhtiGerhard Müller

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Citations

Apr 18, 2021·Physical Review. E·Benaoumeur Bakhti, Gerhard Müller

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