The area of isodensity contours as a measure of large-scale structure

Mathematics – Probability

Scientific paper

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Cosmology, Galactic Clusters, Interstellar Matter, Probability Distribution Functions, Red Shift, Statistical Analysis, Astronomical Models, Density Distribution, Sky Surveys (Astronomy), Universe

Scientific paper

One statistic which describes the large-scale structure of a density field is the mean area per unit volume of isodensity contour surfaces, computed as a function of threshold density. In a homogeneous, isotropic field, this quantity is equal to twice the mean number of isodensity contour crossings along a line of unit length drawn through the field. When the density and its gradients are independent variables, the number of contour crossings, as a function of threshold density, is proportional to the probability distribution function for the density. Thus, this statistic can distinguish between Gaussian and non-Gaussian distributions of large-scale structure.

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