Statistics of Isodensity Contours in Redshift Space

Abstract

The peculiar velocities of galaxies distort the clustering pattern anisotropically in redshift space. This effect on the statistics of isodensity contours is examined by linear theory. The statistics considered in this paper are the three- and two-dimensional genus of isodensity contours, the area of isodensity contours, the length of isodensity contours in the 2-dimensional slice and the level crossing statistics on the line. We find that all these statistics in redshift space as functions of density threshold of contours have the same shape as in real space. The redshift space distortion affects only amplitudes of these statistics. The three-dimensional genus and the area hardly suffer from the redshift space distortion for $0 \leq \Omega b^{-5/3} \leq 1$, where $b$ is a linear bias parameter. The other statistics are defined in one- or two-dimensional slices of the sample volume and depend on the direction of these slices relative to the line of sight. This dependence on direction of these statistics provides a way to determine the density parameter of the universe.