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Is galaxy distribution non-extensive and non-Gaussian?

Author

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  • Nakamichi, Akika
  • Morikawa, Masahiro

Abstract

Self-gravitating systems in the Universe are generally thought to be non-extensive, and often show long-tails in various distribution functions. In principle, these non-Boltzmann properties are naturally expected from the peculiar property of gravity, long-range and unshielded. Therefore, the ordinary Boltzmann statistical mechanics would not be applicable for these self-gravitating systems in its naive form. In order to step further, we quantitatively investigate the above two properties, non-extensivity and long-tails, by explicitly introducing various models of statistical mechanics. We use the data of CfA II South redshift survey and apply the count-in-cell method. We study four statistical mechanics: (1) Boltzmann statistical mechanics, (2) Fractal statistical mechanics, (3) Rényi-entropy-based (REB) statistical mechanics, and (4) Tsallis statistical mechanics, and use Akaike information criteria (AIC) for the fair comparison. We found that both Rényi-entropy-based statistical model and Tsallis statistical model are far better than the other two models. Therefore, the long-tail in the distribution function turns out to be essential.

Suggested Citation

  • Nakamichi, Akika & Morikawa, Masahiro, 2004. "Is galaxy distribution non-extensive and non-Gaussian?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 215-233.
    • Handle: RePEc:eee:phsmap:v:341:y:2004:i:c:p:215-233
    DOI: 10.1016/j.physa.2004.04.116
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    Cited by:

    1. Chacón-Cardona, C.A. & Casas-Miranda, R.A. & Muñoz-Cuartas, J.C., 2016. "Multi-fractal analysis and lacunarity spectrum of the dark matter haloes in the SDSS-DR7," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 22-33.
    2. Shi, Leilei, 2006. "Does security transaction volume–price behavior resemble a probability wave?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 419-436.

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