Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005tsra.conf..380n&link_type=abstract
Proceedings of the 22nd Texas Symposium on Relativistic Astrophysics at Stanford, Stanford California, December 13-17, 2004. Ed
Astronomy and Astrophysics
Astrophysics
Scientific paper
The long-range force gravity produces all unique structures in the universe. Such structures, called self gravitating systems (SGS), are thought to represent the basic nature of gravity. Since the gravity is long-range and unshielded, we cannot expect a naïve Boltzmann statistical mechanics, which is fully based on the additivity of conserved quatities such as energy and angular momentum. Therefore in this paper, we return to the very basic stand point and try to find out what kind of statistical mechanics is applicable for SGS. We especially emphasize the two properties often appear in SGS systems: the non-extensive property and the long-tails in various distribution functions. In order to determine which property is essential in statistical description of SGS, we study four kinds of statistical mechanics, possessing all the combinations of these two properties: (1) Boltzmann, (2) Fractal matter, (3) Renyi, and (4) Tsallis statistical mechanics. We use Akaike Information Criteria for their fair comparison. We use the data of SDSS DR3 spectroscopic survey and apply the count-in-cell method. We conclude that only the Tsallis statistical mechanics properly describe the system. That is, both non-extensive and long-tail in distribution function are essential for SGS.
Morikawa Masahiro
Nakamichi Akika
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