Thermodynamics of Self-Gravitating Systems with Softened Potentials

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dc.creatorFollana, Eduardo
dc.creatorLaliena, Victor
dc.date1999-11-08
dc.date2000-04-03
dc.date.accessioned2026-07-07T11:29:50Z
dc.date.available2026-07-07T11:29:50Z
dc.descriptionThe microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is achieved by truncating to N terms an expansion of the Newtonian potential in spherical Bessel functions. The order N is related to the softening at short distances. This regularization has the remarkable property that it allows for an exact solution of the mean field equation. It is found that for N not too large the absolute maximum of the entropy coincides to high accuracy with the solution of the Lane-Emden equation, which determines the mean field mass distribution for the Newtonian potential for energies larger than $E_c\approx -0.335 G M^2/R$. Below this energy a collapsing phase transition, with negative specific heat, takes place. The dependence of this result on the regularizing parameter N is discussed.
dc.description16 pages, 1 table, 4 figures, REVTEX. Partially rewritten, 5 references added
dc.identifierhttps://arxiv.org/abs/cond-mat/9911107
dc.identifierhttp://arxiv.org/abs/cond-mat/9911107
dc.identifierPhys.Rev.E61:6270,2000
dc.identifierdoi:10.1103/PhysRevE.61.6270
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/196839
dc.subjectStatistical Mechanics
dc.subjectAstrophysics
dc.titleThermodynamics of Self-Gravitating Systems with Softened Potentials
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