Clustering in Redshift Space: Linear Theory

Abstract

The clustering in redshift space is studied here to first order within the framework of gravitational instability. The distortion introduced by the peculiar velocities of galaxies results in anisotropy in the galaxy distribution and mode-mode coupling when analyzed in Fourier space. An exact linear calculation of the full covariance matrix in both the real and Fourier space is presented here. The explicit dependence on $\Omeg$ and the biasing parameter is calculated and its potential use as a probe of these parameters is analyzed. It is shown that Kaiser's formalism can be applied only to a data set that subtends a small solid angle on the sky, and therefore cannot be used in the case of all sky surveys. The covariance matrix in the real space is calculated explicitly for {\it CDM} model, where the behavior along and perpendicular to the line of sight is shown.