A practical computational method for the anisotropic redshift-space three-point correlation function

Abstract

Here, we present an algorithm enabling computation of the anisotropic redshift-space galaxy threepoint correlation function ( 3 PCF) scaling as N 2 , with N the number of galaxies. Our previous work showed how to compute the isotropic 3 PCF with this scaling by expanding the radially binned density field around each galaxy in the survey into spherical harmonics and combining these coefficients to form multipole moments. The N 2 scaling occurred because this approach never explicitly required the relative angle between a galaxy pair about the primary galaxy. Here, we generalize this work, demonstrating that in the presence of azimuthally symmetric anisotropy produced by redshift-space distortions (RSD), the 3 PCF can be described by two triangle side lengths, two independent total angular momenta, and a spin. This basis for the anisotropic 3 PCF allows its computation with negligible additional work over the isotropic 3 PCF. We also present the covariance matrix of the anisotropic 3 PCF measured in this basis. Our algorithm tracks the full 5 D redshift-space 3 PCF, uses an accurate line of sight to each triplet, is exact in angle, and easily handles edge correction. It will enable use of the anisotropic large-scale 3 PCF as a probe of RSD in current and upcoming large-scale redshift surveys.