Usefulness of multi-fractal analysis for galaxy distributions

Mathematics

Scientific paper

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Analysis (Mathematics), Cosmology, Fractals, Galactic Clusters, Galaxies, Many Body Problem, Spatial Distribution, Universe, Computerized Simulation, Dark Matter, Geometry, Partitions (Mathematics)

Scientific paper

When characterizing galaxy distribution, the usefulness of multi-fractal analysis was investigated by examining the results of cosmological N-body simulations which started with different initial spectra. We adopted a low-density cold dark-matter model and power-law models for the galaxy distributions, and applied multi-fractal analyses to these models. We found that the partition-function behavior is a good measure to distinguish the galaxy distribution pattern. This trend did not strongly depend on the geometry of the samples. The nearest-neighbor method, which is used for multi-fractal analysis, was not useful. We also applied a multi-fractal analysis to the CfA 2 survey and compare the partition function of this to a low-density cold dark-matter model and power-law models. However, we could not derive any clear conclusions, because this map dose not contain a sufficient number of galaxies for a multi-fractal analysis.

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