Modeling and measuring the anisotropic halo 3-point correlation function: a coordinated study

Abstract Apparent anisotropies in the statistical properties of the spatial distribution of galaxies encode precious cosmological information. Its extraction is commonly performed using 2-point clustering statistics. However, ongoing and future spectroscopic galaxy surveys will cover unprecedented volumes with a number of objects large enough to effectively probe clustering anisotropies through higher-order statistics. In this work, we present a novel and efficient implementation of both a model for the multipole moments of the anisotropic 3-point correlation function (3PCF) and of their estimator. To evaluate the performance of our model, we compared its predictions against 3PCF measurements obtained with our estimator from a set of 298 dark matter halo catalogs drawn from the z = 1 snapshots of N -body simulations. For the statistical analysis, we employed a covariance matrix estimated from an independent suite of 3000 mock halo catalogs at the same redshift. We then repeated the analysis by combining the 2-point correlation function (2PCF) to the 3PCF, with and without including its anisotropic part. In the 3PCF-only analysis, the addition of the anisotropic component of the 3PCF effectively breaks the degeneracy between the growth rate f and the linear bias b 1 , significantly reducing their uncertainties. It also significantly improves the precision of the Alcock-Paczynski parameter ε but does not reduce the ∼ 1 % offset we find in the estimate of the isotropic dilation parameter α . The joint 2PCF+3PCF analysis reduces, though does not fully remove, biases in the AP and isotropic dilation parameters and breaks the f - b 1 - σ 8 degeneracy, leading to tighter constraints overall. The anisotropic 3PCF adds little to the joint analysis because the tree-level 3PCF model fails to capture the anisotropic information primarily encoded on small scales and in squeezed triangle configurations. A more advanced model, e.g. based on 1-loop perturbation theory, will be required to exploit this information fully.