Simulations of Wide-Field Weak Lensing Surveys. I. Basic Statistics and Non-Gaussian Effects

We study the lensing convergence power spectrum and its covariance for a standard ΛCDM cosmology. We run 400 cosmological N -body simulations and use the outputs to perform a total of 1000 independent ray-tracing simulations. We compare the simulation results with analytic model predictions. The semianalytic model based on Smith et al. fitting formula underestimates the convergence power by ∼ 30% at arcmin angular scales. For the convergence power spectrum covariance, the halo model reproduces the simulation results remarkably well over a wide range of angular scales and source redshifts. The dominant contribution at small angular scales comes from the sample variance due to the number fluctuations of halos in a finite survey volume. The signal-to-noise ratio for the convergence power spectrum is degraded by the non-Gaussian covariances by up to a factor of 5 for a weak lensing survey to z s ∼ 1. The probability distribution of the convergence power spectrum estimators, among the realizations, is well approximated by a χ 2 distribution with broadened variance given by the non-Gaussian covariance, but has a larger positive tail. The skewness and kurtosis have non-negligible values especially for a shallow survey. We argue that a prior knowledge on the full distribution may be needed to obtain an unbiased estimate on the ensemble-averaged band power at each angular scale from a finite volume survey.