A new look at lines of sight: using Fourier methods for the wide-angle anisotropic 2-point correlation function

Abstract

The anisotropic 2-point correlation function (2PCF) of galaxies measures pairwise clustering as a function of the pair separation's angle to the line of sight. The latter is often defined as either the angle bisector of the observer-galaxy-pair triangle or the vector from the observer to the separation midpoint. Here we show how to accelerate either of these measurements with Fourier Transforms, using a slight generalization of the Yamamoto et al. (2006) estimator in which each member of the pair is used successively as the line of sight. We also present perturbation theory predictions for our generalized estimator including wide-angle corrections.