From Weak Lensing to non-Gaussianity via Minkowski Functionals

TL;DR

This paper introduces a harmonic-domain method to extract Minkowski Functionals from weak lensing maps, enabling better analysis of non-Gaussian features and separation of late-time and primordial non-Gaussianity.

Contribution

It develops a novel harmonic-based approach for Minkowski Functional estimation, extending skewness parameters to skew-spectra, and compares different bispectrum models for weak lensing.

Findings

Harmonic approach effectively handles masks and noise.

Skew-spectra provide more information than one-point statistics.

Separation of late-time and primordial non-Gaussianity depends on redshift and scale.

Abstract

We present a new harmonic-domain approach for extracting morphological information, in the form of Minkowski Functionals (MFs), from weak lensing (WL) convergence maps. Using a perturbative expansion of the MFs, which is expected to be valid for the range of angular scales probed by most current weak-lensing surveys, we show that the study of three generalized skewness parameters is equivalent to the study of the three MFs defined in two dimensions. We then extend these skewness parameters to three associated skew-spectra which carry more information about the convergence bispectrum than their one-point counterparts. We discuss various issues such as noise and incomplete sky coverage in the context of estimation of these skew-spectra from realistic data. Our technique provides an alternative to the pixel-space approaches typically used in the estimation of MFs, and it can be particularly useful in the presence of masks with non-trivial topology. Analytical modeling of weak lensing statistics relies on an accurate modeling of the statistics of underlying density distribution. We apply three different formalisms to model the underlying dark-matter bispectrum: the hierarchical ansatz, halo model and a fitting function based on numerical simulations; MFs resulting from each of these formalisms are computed and compared. We investigate the extent to witch late-time gravity-induced non-Gaussianity (to which weak lensing is primarily sensitive) can be separated from primordial non-Gaussianity and how this separation depends on source redshift and angular scale.