Lognormal Property of Weak Lensing Fields

摘要

The statistical property of the weak lensing fields is studied quantitativelyusing the ray-tracing simulations. Motivated by the empirical lognormal modelthat characterizes the probability distribution function(PDF) of thethree-dimensional mass distribution excellently, we critically investigate thevalidity of lognormal model in the weak lensing statistics. Assuming that theconvergence field, $\kappa$, is approximately described by the lognormaldistribution, we present analytic formulae of convergence for the one-point PDFand the Minkowski functionals. Comparing those predictions with ray-tracingsimulations in various cold dark matter models, we find that the one-pointlognormal PDF can describe the non-Gaussian tails of convergence fieldsaccurately up to $\nu\sim10$, where $\nu$ is the level threshold given by$\nu\equiv\kappa/\var^{1/2}$, although the systematic deviation from lognormalprediction becomes manifest at higher source redshift and larger smoothingscales. The lognormal formulae for Minkowski functionals also fit to thesimulation results when the source redshift is low. Accuracy of thelognormal-fit remains good even at the small angular scales, where theperturbation formulae by Edgeworth expansion break down. On the other hand,lognormal models does not provide an accurate prediction for the statisticssensitive to the rare events such as the skewness and the kurtosis ofconvergence. We therefore conclude that the empirical lognormal model of theconvergence field is safely applicable as a useful cosmological tool, as longas we are concerned with the non-Gaussianity of $\nu\simlt5$ for low sourceredshift samples.