Weak Lensing Trispectrum and Kurt-Spectra

TL;DR

This paper introduces two kurt-spectra to analyze fourth-order statistics in weak lensing maps, compares numerical simulations with theoretical models, and develops estimators for higher-order spectra.

Contribution

It presents novel kurt-spectra for weak lensing analysis, validates the hierarchical ansatz in nonlinear regimes, and proposes estimators for beyond fourth-order spectra.

Findings

Kurt-spectra shape depends on source redshift and scale.

Hierarchical ansatz reproduces nonlinear regime trends.

New estimators for higher-order spectra are introduced.

Abstract

We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function of source redshifts and smoothing angular scales. We employ a pseudo-$C_{\ell}$ approach to estimate the spectra from realistic convergence maps in the presence of an observational mask and noise for stage-IV large-scale structure surveys. We compare these results against theoretical predictions calculated using the FFTLog formalism, and find that a simple nonlinear clustering model-the hierarchical ansatz-can reproduce the numerical trends for the kurt-spectra in the nonlinear regime. In addition, we provide estimators for beyond fourth-order spectra where no definitive analytical results are available, and present corresponding results from numerical simulations.