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

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 $\kappa \to y$ 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.

13 pages, 15 figures, accepted by PRD

References in corpus (8)

• Cosmology with Weak Lensing Surveys
• Cosmic variance of weak lensing surveys in the non-Gaussian regime
• Rejuvenating Power Spectra II: the Gaussianized galaxy density field
• Re-capturing cosmic information
• Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak Lensing Analysis
• Copula Cosmology: Constructing a Likelihood Function
• Precise Estimation of Cosmological Parameters Using a More Accurate Likelihood Function
• Increasing the Fisher Information Content in the Matter Power Spectrum by Non-linear Wavelet Weiner Filtering