Thermodynamics of Self-Gravitating Systems with Softened Potentials

Details Thermodynamics of Self-Gravitating Systems with Softened Potentials Thermodynamics of Self-Gravitating Systems with Softened Potentials

1999-11-08

arxiv.org/abs/cond-mat/9911107v2

Phys.Rev.E61:6270,2000

Physics

Condensed Matter

Statistical Mechanics

16 pages, 1 table, 4 figures, REVTEX. Partially rewritten, 5 references added

Scientific paper

10.1103/PhysRevE.61.6270

The 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.

Affiliated with

Also associated with

No associations

Rating

Thermodynamics of Self-Gravitating Systems with Softened Potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Thermodynamics of Self-Gravitating Systems with Softened Potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Thermodynamics of Self-Gravitating Systems with Softened Potentials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-61362