Improving the line of sight for the anisotropic 3-point correlation function of galaxies: Centroid and Unit-Vector-Average methods scaling as 𝒪 (N2)

Abstract

ABSTRACT The 3-point correlation function (3PCF) is a powerful tool for the current era of high-data volume, high-precision cosmology. It goes beyond the Gaussian cosmological perturbations probed by the 2-point correlation function, including late-time non-Gaussianities, and encodes information about peculiar velocities, which distort observed positions of galaxies along the line of sight away from their true positions. To access this information, we must track the 3PCF’s dependence not only on each triangle’s shape, but also on its orientation with respect to the line of sight. Consequently, different choices for the line of sight will affect the measured 3PCF. Up to now, the line of sight has been taken as the direction to a single triplet member, but which triplet member is used impacts the 3PCF by ∼20 per cent of the statistical error for a BOSS-like survey. For DESI (5× more precise) this would translate to ∼100 per cent of the statistical error. We propose a new method that is fully symmetric between the triplet members, and uses either the average of the three galaxy position vectors, or the average of their unit vectors. We prove that these methods are equivalent to $\mathcal {O}(\theta ^2)$, where θ is the angle subtended at the observer by any triangle side. By harnessing the solid harmonic shift theorem, we show how these methods can be evaluated scaling as N2, with N the number of objects. We expect that they can be used to make a robust, systematics-free measurement of the anisotropic 3PCF of upcoming redshift surveys such as DESI.