New Statistical Methods to Determine the Fractal Dimension of Structures Evident in the SDSS, WMAP, and 2MASS Surveys

Details New Statistical Methods to Determine the Fractal Dimension of Structures Evident in the SDSS, WMAP, and 2MASS Surveys New Statistical Methods to Determine the Fractal Dimension of Structures Evident in the SDSS, WMAP, and 2MASS Surveys

Dec 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aas...211.4705w&link_type=abstract

American Astronomical Society, AAS Meeting #211, #47.05; Bulletin of the American Astronomical Society, Vol. 39, p.804

Mathematics

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Scientific paper

The fractal dimension of the spatial distribution of galaxies can be characterized by various statistical and topological methods, such as the box counting and the two-point correlation function. Here we develop a new way to get fractal information, that is the Metric Space Technique (MST). It allows multiple measures to be simultaneously applied for quantitative analysis of any type of structure distribution. All such distributions are considered to be elements of multi-parameter space, and the analysis is based on considering a sample's output functions, which characterize the distributions in multi-parameter space. We use a dozen slices of a volume of space containing many newly measured galaxies from Sloan Digital Sky Survey Data Release 5. We compare results with that of mock samples of galaxies from N-body simulation with current best estimates of cosmological parameters and nested-pairs simulations, and random catalogs. By systematically studying those slices including hundreds of thousands of galaxies, we demonstrated that in the local universe there exists a fractal structure from MST. We also apply the method to 2MASS and WMAP surveys and get interesting results.

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