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Advances in Astronomy
Volume 2008 (2008), Article ID 870804, 14 pages
http://dx.doi.org/10.1155/2008/870804
Research Article

Entropy Maximization, Cutoff Distribution, and Finite Stellar Masses

Department of Physics, Banaras Hindu University, Varanasi 221 005, India

Received 18 April 2008; Revised 16 July 2008; Accepted 26 August 2008

Academic Editor: Giovanni Carraro

Copyright © 2008 Ritesh Kumar Dubey et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Conventional equilibrium statistical mechanics of open gravitational systems is known to be problematical. We first recall that spherical stars/galaxies acquire unbounded radii, become infinitely massive, and evaporate away continuously if one uses the standard Maxwellian distribution (which maximizes the usual Boltzmann-Shannon entropy and hence has a tail extending to infinity). Next, we show that these troubles disappear automatically if we employ the exact most probable distribution (which maximizes the combinatorial entropy and hence possesses a sharp cutoff tail). Finally, if astronomical observation is carried out on a large galaxy, then the Poisson equation together with thermal de Broglie wavelength provides useful information about the cutoff radius , cutoff energy , and the huge quantum number up to which the cluster exists. Thereby, a refinement over the empirical lowered isothermal King models, is achieved. Numerically, we find that the most probable distribution (MPD) prediction fits well the number density profile near the outer edge of globular clusters.