The Area of Isodensity Contours as a Measure of LargeScale Structure
Abstract
One statistic which describes the largescale 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; the normalization factor is proportional to the mean magnitude of the density gradient in the field. Thus, this statistic can distinguish between Gaussian and nonGaussian distributions of largescale structure. The counting of isodensity contour crossings is illustrated for realizations of Gaussian fields with spectra given by power laws. The contour crossing statistic can be applied to onedimensional and twodimensional samples of fields as readily as to threedimensional samples.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 1988
 DOI:
 10.1086/185284
 Bibcode:
 1988ApJ...333L..41R
 Keywords:

 Cosmology;
 Galactic Clusters;
 Interstellar Matter;
 Probability Distribution Functions;
 Red Shift;
 Statistical Analysis;
 Astronomical Models;
 Density Distribution;
 Sky Surveys (Astronomy);
 Universe;
 Astrophysics;
 COSMOLOGY;
 GALAXIES: CLUSTERING