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Journal articles
Validity conditions of the hydrostatic approach for self-gravitating systems: a microcanonical analysis
Abstract : We consider a system of hard spheres with gravitational interactions in
a stationary state described in terms of the microcanonical ensemble. We
introduce a set of similar auxiliary systems with increasing sizes and numbers
of particles. The masses and radii of the hard spheres of the auxiliary systems
are rescaled in such a way that the usual extensive properties are maintained
despite the long-range nature of the gravitational interactions, while the mass
density and packing fractions are kept fixed. We show, within that scaling
limit, that a local thermalization spontaneously emerges as a consequence of
both extensive properties and the relative smallness of the fluctuations. The
resulting mass density profile for the infinite system can be determined within
a hydrostatic approach, where the gradient of the local hard-sphere pressure is
balanced by the average gravitational field. The derivation sheds light on the
mechanisms which ensure that the local equilibrium in the infinite system is
entirely controlled by hard-core interactions, while gravitational interactions
can be treated at the mean-field level. This allows us to determine the conditions
under which the hydrostatic approach is also valid for the actual finite system
of interest. We provide simple tests of such conditions for a few astrophysical
examples
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00750487
Contributor : Thierry Dauxois <>
Submitted on : Saturday, November 10, 2012 - 11:26:42 AM
Last modification on : Tuesday, January 5, 2021 - 10:54:03 AM
Contributor : Thierry Dauxois <>
Submitted on : Saturday, November 10, 2012 - 11:26:42 AM
Last modification on : Tuesday, January 5, 2021 - 10:54:03 AM
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