Ray-tracing Simulations of Weak Lensing by Large-Scale Structure

We investigate weak lensing by large-scale structure using ray tracing through N-body simulations. Photon trajectories are followed through high-resolution simulations of structure formation to make simulated maps of shear and convergence on the sky. Tests with varying numerical parameters are used to calibrate the accuracy of computed lensing statistics on angular scales from ~1' to a few degrees. Various aspects of the weak-lensing approximation are also tested. We show that the nonscalar component of the shear generated by the multiple deflections is small. For fields a few degrees on a side, the shear power spectrum is almost entirely in the nonlinear regime and agrees well with nonlinear analytical predictions. Sampling fluctuations in power-spectrum estimates are investigated by comparing several ray-tracing realizations of a given model. For survey areas smaller than 1° on a side, the main source of scatter is nonlinear coupling to modes larger than the survey. We develop a method that uses this effect to estimate Ω_m from the scatter in power-spectrum estimates for subregions of a larger survey. We show that the power spectrum can be measured accurately on scales corresponding to 1-10 h^-1 Mpc with realistic number densities of source galaxies with large intrinsic ellipticities. Non-Gaussian features in the one-point distribution function of the weak-lensing convergence (reconstructed from the shear) are also sensitive to Ω_m. We suggest several techniques for estimating Ω_m in the presence of noise and compare their statistical power, robustness, and simplicity. With realistic number densities of source galaxies, Ω_m can be determined to within 0.1-0.2 from a deep survey of several square degrees.