Maximum entropy states and the structure of galaxies

Details Maximum entropy states and the structure of galaxies Maximum entropy states and the structure of galaxies

Nov 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987mnras.229..103w&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 229, Nov. 1, 1987, p. 103-117.

Statistics

29

Galactic Structure, Gravitational Fields, Maximum Entropy Method, Elliptical Galaxies, Mathematical Models, Quantum Statistics, Relaxation (Mechanics)

Scientific paper

The properties of maximum entropy states of isolated self-gravitating gas spheres of given mass, energy, extent, and maximum phase space density are investigated, in order to understand the structure of elliptical galaxies and of the objects formed in N-body studies of violent relaxation. If consideration is restricted to objects with power law density profiles, the maximum entropy state has a high central concentration, as found in violent relaxation experiments. However, if the form of the density profile is not constrained, the highest entropy state is a diffuse system superposed on a central spike of infinitesimal mass but finite binding energy. The appearance of this central spike is mathematically analogous to the growth of a Bose condensate in a quantum gas. Limiting the maximum phase space density of the system eliminates the central singularity but does not alter the two-component nature of the maximum entropy solutions. Thus, the near universal power-law behavior found in numerical experiments must reflect further constraints in addition to those included in this study. It is speculated that these may be related to the requirement that there be sufficient coupling between different parts of the system to permit violent relaxation to transfer energy effectively.

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