The integrated angular bispectrum of weak lensing

TL;DR

This paper studies the integrated bispectrum in weak lensing convergence, proposing it as an easy-to-measure statistic that captures the squeezed limit of the bispectrum, and evaluates the accuracy of theoretical predictions versus simulations.

Contribution

It introduces the integrated bispectrum as a practical summary statistic for weak lensing and assesses the accuracy of theoretical models for its signal and covariance using simulations.

Findings

Theoretical predictions of the integrated bispectrum are slightly inaccurate.

Covariance matrix estimates show significant deviations from theory.

Simulations are necessary for reliable covariance estimation.

Abstract

We investigate three-point statistics in weak lensing convergence, through the integrated bispectrum. This statistic involves measuring power spectra in patches, and is thus easy to measure, and avoids the complexity of estimating the very large number of possible bispectrum configurations. The integrated bispectrum principally probes the squeezed limit of the bispectrum. To be useful as a set of summary statistics, accurate theoretical predictions of the signal are required, and, assuming Gaussian sampling distributions, the covariance matrix. In this paper, we investigate through simulations how accurate are theoretical formulae for both the integrated bispectrum and its covariance, finding that there a small inaccuracies in the theoretical signal, and more serious deviations in the covariance matrix, which may need to be estimated using simulations.