Redshift-Space Distortions of the Correlation Function in Wide-Angle Galaxy Surveys

Abstract

Using a novel two-dimensional coordinate system, we have derived a particularly simple way to express the redshift distortions in galaxy redshift surveys with arbitrary geometry in closed form. This method provides an almost ideal way to measure the value of $\beta=\Omega_0^{0.6}/b$ in wide area surveys, since all pairs in the survey can be used for the analysis. In the limit of small angles, this result straightforwardly reduces to the plane-parallel approximation. This expansion can also be used together with more sophisticated methods such as for the calculation of Karhunen-Loeve eigenvectors in redshift space for an arbitrary survey geometry. Therefore, these results should provide for more precise methods in which to measure the large scale power spectrum and the value of $\beta$ simultaneously.