Modeling the 3-point correlation function of projected scalar fields on the sphere

TL;DR

This paper introduces a harmonic basis decomposition method for efficiently computing the three-point correlation function of projected scalar fields on the sphere, significantly reducing computation time for large datasets like LSST.

Contribution

It develops a new framework and estimator for three-point correlations using harmonic expansions within the Limber approximation, incorporating advanced models including halo, perturbation theory, and effective field theory.

Findings

Efficient computation of three-point correlations for over 200 million data points in under 10 minutes.

Improved modeling accuracy using effective field theory and halo models.

Feasible analysis pipeline for upcoming large-scale surveys like LSST.

Abstract

One of the main obstacles for the signal extraction of the three point correlation function using photometric surveys, such as the Rubin Observatory Legacy Survey of Space and Time (LSST), will be the prohibitive computation time required for dealing with a vast quantity of sources. Brute force algorithms, which naively scales as $O(N^3)$ with the number of objects, can be further improved with tree methods but not enough to deal with large scale correlations of Rubin's data. However, a harmonic basis decomposition of these higher order statistics reduces the time dramatically, to scale as a two-point correlation function with the number of objects, so that the signal can be extracted in a reasonable amount of time. In this work, we aim to develop the framework to use these expansions within the Limber approximation for scalar (or spin-0) fields, such as galaxy counts, weak lensing convergence or aperture masses. We develop an estimator to extract the signal from catalogs and different phenomenological and theoretical models for its description. The latter includes halo model and standard perturbation theory, to which we add a simple effective field theory prescription based on the short range of non-locality of cosmic fields, significantly improving the agreement with simulated data. In parallel to the modeling of the signal, we develop a code that can efficiently calculate three points correlations of more than 200 million data points (a full sky simulation with Nside=4096) in $\sim$40 minutes, or even less than 10 minutes using an approximation in the searching algorithm, on a single high-performance computing node, enabling a feasible analysis for the upcoming LSST data.