Morphology of weak lensing convergence maps

Abstract

We study the morphology of convergence maps by perturbatively reconstructing their Minkowski functionals (MFs). We present a systematic study using a set of three generalized skew spectra as a function of source redshift and smoothing angular scale. These spectra denote the leading-order corrections to the Gaussian MFs in the quasi-linear regime. They can also be used as independent statistics to probe the bispectrum. Using an approach based on pseudo-Sℓs, we show how these spectra will allow the 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 ℓ and source redshift zs, 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 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.