Journal Article

Fluid-like entropy and equilibrium statistical mechanics of self-gravitating systems

Dong-Biao Kang and Ping He

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 416, issue 1, pages 32-37
Published in print September 2011 | ISSN: 0035-8711
Published online August 2011 | e-ISSN: 1365-2966 | DOI:
Fluid-like entropy and equilibrium statistical mechanics of self-gravitating systems

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The statistical mechanics of self-gravitating systems has not been well understood, and still remains an open question so far. In a previous study by Kang & He, we showed that the fluid approximation may give a clue to investigate this problem further. In fact, there are indeed many dynamical similarities between self-gravitating and fluid systems. Based on a fluid-like entropy, that work explained successfully the outer density profiles of dark matter haloes, but there remain some drawbacks with the calculation concerning the extremizing process of the entropy. In the current paper, with the improved extremizing calculation – including an additional differential constraint of dynamical equilibrium and without any other assumptions, we confirm that statistical-mechanical methods can give a density profile with finite mass and finite energy. Moreover, this density profile is also consistent with the observational surface brightness of the elliptical galaxy NGC 3379. In our methods, the density profile is derived from the equation of state, which is obtained from the entropy principle but does not correspond to the maximum entropy of the system. Finally, we suggest an alternative entropy form, a hybrid of Boltzmann–Gibbs and Tsallis entropy, whose global maximum may give rise to this equation of state.

Keywords: equation of state; methods: analytical; galaxies: kinematics and dynamics; galaxies: structure

Journal Article.  4080 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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