The Area of Isodensity Contours in Cosmological Models and Galaxy Surveys. Ryden, B., S. *The Astrophysical Journal*, 340:647-660, 1989. Paper abstract bibtex The large-scale structure of a smoothed density field can be quantified by measuring various properties of its isodensity contour surfaces. One such property is the contour crossing statistic, defined as the mean number of times per unit length that a straight line drawn through the field crosses a given contour. This statistic is proportional to the area of the contour surface. We appy the contour crossing statistic to model density fields and to smoothed samples of galaxies. Models in which the matter is in a bubble structure, in a filamentary net, or in clusters can be distinguished from Gaussian density distributions. The shape of the contour crossing curve in the initially Gaussian fields we consider remains Gaussian after gragitational evolution and biasing, as long as the smoothing length is longer than the mass corrlation length. With a smoothing length of 5h^-1 Mpc, models containing cosmic strongs are indistinguishable from Gaussian distributions. Cosmic explosion models are significantly non-Gaussian, having abubbly structure. Samples from the CfA survey and the Haynes and Giovanelli survey are more strongly non-Gaussian at a smoothing length of 6h^-1 Mpc than any of the models examined. At a smoothing length of 12h^-1 Mpc, the Haynes and Giovanelli sample appears Gaussian.

@article{
title = {The Area of Isodensity Contours in Cosmological Models and Galaxy Surveys},
type = {article},
year = {1989},
keywords = {cosmology -- dark metter -- galaxies: clustering},
pages = {647-660},
volume = {340},
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abstract = {The large-scale structure of a smoothed density field can be quantified by measuring various properties of its isodensity contour surfaces. One such property is the contour crossing statistic, defined as the mean number of times per unit length that a straight line drawn through the field crosses a given contour. This statistic is proportional to the area of the contour surface. We appy the contour crossing statistic to model density fields and to smoothed samples of galaxies. Models in which the matter is in a bubble structure, in a filamentary net, or in clusters can be distinguished from Gaussian density distributions. The shape of the contour crossing curve in the initially Gaussian fields we consider remains Gaussian after gragitational evolution and biasing, as long as the smoothing length is longer than the mass corrlation length. With a smoothing length of 5h^-1 Mpc, models containing cosmic strongs are indistinguishable from Gaussian distributions. Cosmic explosion models are significantly non-Gaussian, having abubbly structure. Samples from the CfA survey and the Haynes and Giovanelli survey are more strongly non-Gaussian at a smoothing length of 6h^-1 Mpc than any of the models examined. At a smoothing length of 12h^-1 Mpc, the Haynes and Giovanelli sample appears Gaussian.},
bibtype = {article},
author = {Ryden, Barbara S.},
journal = {The Astrophysical Journal}
}