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

Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010, we proposed a Gaussian transformation to Gaussianize the non-Gaussian lensing convergence field κ. It performs a local monotonic transformation κ→y pixel by pixel to make the fine-scale one-point probability distribution function of the new variable y Gaussian. We tested whether the whole y field is Gaussian through 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 κ 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 about 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 ∼300h^-1Mpc distance interval centered at z∈(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 Gaussian transformation. However, we also found noticeable deviations.