Gaussianizing the non-Gaussian lensing convergence field I: the performance of the Gaussianization

TL;DR

This paper introduces a Gaussianization transform for the non-Gaussian lensing convergence field, significantly reducing non-Gaussian features and improving the analysis of weak lensing data.

Contribution

The study demonstrates the effectiveness of a local monotonic Gaussianization transform in suppressing non-Gaussianity in lensing convergence fields, validated against N-body simulations.

Findings

Gaussianization suppresses skewness, kurtosis, and higher cumulants by orders of magnitude.

Significant reduction in bispectrum, with residuals near zero.

Works effectively on 2D matter density fields from weak lensing tomography.

Abstract

Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010, we proposed a Gaussianization transform to Gaussianize the non-Gaussian lensing convergence field $\kappa$. It performs a local monotonic transformation $\kappa\rightarrow y$ pixel by pixel to make the unsmoothed one-point probability distribution function of the new variable $y$ Gaussian. We tested whether the whole $y$ field is Gaussian against N-body simulations. (1) We found that the proposed Gaussianization suppresses the non-Gaussianity by orders of magnitude, in measures of the skewness, the kurtosis, the 5th- and 6th-order cumulants of the $y$ field smoothed over various angular scales relative to that of the corresponding smoothed $\kappa$ field. The residual non-Gaussianities are often consistent with zero within the statistical errors. (2) The Gaussianization significantly suppresses the bispectrum. Furthermore, the residual scatters around zero, depending on the configuration in the Fourier space. (3) The Gaussianization works with even better performance for the 2D fields of the matter density projected over $\sim 300 \mpch$ distance interval centered at $z\in(0,2)$, which can be reconstructed from the weak lensing tomography. (4) We identified imperfectness and complexities of the proposed Gaussianization. We noticed weak residual non-Gaussianity in the $y$ field. We verified the widely used logarithmic transformation as a good approximation to the Gaussianization transformation. However, we also found noticeable deviations.