Abstract
We consider the fractal behavior of the large scale galaxy distribution and we introduce a family of fractal cascading models based on appropriate modifications of the β model of turbulence. These models generate distributions with scale-dependent fractal properties, as observed in the analysis of real galaxy catalogs. In particular, a smooth transition from small-scale self-similarity to large-scale homogeneity is considered. The scale dependence of the fractal properties generates a ‘dressing’ of the asymptotic value of the fractal dimension to a larger effective value D ef . The physical motivations for the use of a scale-dependent β model in Cosmology are discussed. The multifractal properties of the distributions are considered and an extended version of the β model for the field of density perturbations δ ρ/ρ is introduced.
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Provenzale, A. (1991). Fractals and the Large—Scale Galaxy Distribution. In: Heck, A., Perdang, J.M. (eds) Applying Fractals in Astronomy. Lecture Notes in Physics Monographs, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47582-8_4
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DOI: https://doi.org/10.1007/978-3-540-47582-8_4
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