Steepestdescent technique and stellar equilibrium statistical mechanics. I. Newtonian clusters in a box.
Abstract
A microcanonical statisticalmechanics formulation which produces an exact functional integral expression for entropy is used to study a model of star clusters in which the addition of certain constraints makes possible the existence of thermodynamic equilibrium configurations corresponding to slowly evolving stages of a real star cluster. In the analysis, stellar evaporation is eliminated by confining the stars to a finite volume, and tightly bound subclustering is eliminated by adopting an appropriate shortdistance cutoff for the gravitational interaction between particles. The Gibbs microcanonical entropy of a confined cluster is transformed to a functional integral, this integral is evaluated by steepestdescent methods, and the mean field entropy is determined from the saddlepoint value. Thermodynamic and localfluctuation stability conditions are obtained by analyzing quadratic fluctuations. An evaluation of the stability conditions for spherically symmetric clusters in a rigid sphere relative to arbitrary fluctuations about the mean field shows that only clusters with almost uniform density are thermodynamically stable.
 Publication:

The Astrophysical Journal
 Pub Date:
 January 1977
 DOI:
 10.1086/154924
 Bibcode:
 1977ApJ...211..226H
 Keywords:

 Globular Clusters;
 Steepest Descent Method;
 Stellar Evolution;
 Thermodynamic Equilibrium;
 Canonical Forms;
 Convergence;
 Eigenvalues;
 Entropy;
 Functionals;
 Integral Equations;
 Statistical Mechanics;
 Astrophysics