Fast modeling of the shear three-point correlation function

TL;DR

This paper introduces a fast, efficient method for computing the shear three-point correlation function using multipole expansion, enabling better cosmological analysis with weak lensing data.

Contribution

The authors develop a new multipole-based technique that significantly accelerates the calculation of the shear 3PCF from bispectrum models, improving accuracy and computational speed.

Findings

Achieves 5% accuracy in 10 seconds for single redshift bin

Computes shear 3PCF efficiently for multiple redshift bins

Enables rapid calculation of third-order aperture mass statistics

Abstract

The three-point correlation function (3PCF) of a weak lensing shear field contains information that is complementary to that in the two-point correlation function (2PCF), which can help improve the cosmological parameters and calibrate astrophysical and observational systematics parameters. However, the application of the 3PCF to observed data has been limited due to the computational challenges of calculating theoretical predictions of the 3PCF from a bispectrum model. In this paper, we present a new method to compute the shear 3PCF efficiently and accurately. We employ the multipole expansion of the bispectrum to compute the shear 3PCF, and show that the method is substantially more efficient than direct numerical integration. We found that the multipole-based method can compute the shear 3PCF with 5% accuracy in 10 (40) seconds for the single (four) source redshift bin setup. The multipole-based method can be also used to compute the third-order aperture mass statistics quickly and accurately, accounting for the bin-averaging effect on the shear 3PCF. Our method provides a fast and robust tool for probing the underlying cosmological model with third-order statistics of weak lensing shear.