Morphology of Weak Lensing Convergence Maps

TL;DR

This paper introduces a perturbative method to reconstruct the Minkowski Functionals of weak lensing convergence maps, accounting for systematics, noise, and mask effects, and compares predictions with simulations.

Contribution

It presents a novel approach using pseudo-$S_{ ext{l}}$ spectra for unbiased reconstruction of convergence map morphology, including CMB lensing, with systematic and noise considerations.

Findings

Excellent agreement between theoretical predictions and simulations.

Reconstruction method effectively handles masks and inhomogeneous noise.

Post-Born corrections are significant at higher redshifts.

Abstract

We study the morphology of convergence maps by perturbatively reconstructing their Minkowski Functionals (MFs). We present a systematics study using a set of three generalised skew-spectra as a function of source redshift and smoothing angular scale. Using an approach based on pseudo-$S_{\ell}$s (PSL) we show how these spectra will allow reconstruction of MFs in the presence of an arbitrary mask and inhomogeneous noise in an unbiased way. Our theoretical predictions are based on a recently introduced fitting function to the bispectrum. We compare our results against state-of-the art numerical simulations and find an excellent agreement. The reconstruction can be carried out in a controlled manner as a function of angular harmonics $\ell$ and source redshift $z_s$ which allows for a greater handle on any possible sources of non-Gaussianity. Our method has the advantage of estimating the topology of convergence maps directly using shear data. We also study weak lensing convergence maps inferred from Cosmic Microwave Background (CMB) observations; and we find that, though less significant at low redshift, the post-Born corrections play an important role in any modelling of the non-Gaussianity of convergence maps at higher redshift. We also study the cross-correlations of estimates from different tomographic bins.