On the estimation and detection of the Rees–Sciama effect

Maps of the Rees–Sciama (RS) effect are simulated using the parallel N-body code, hydra, and a run-time ray-tracing procedure. A method designed for the analysis of small, square cosmic microwave background (CMB) maps is applied to our RS maps. Each of these techniques has been tested and successfully applied in previous papers. Within a range of angular scales, our estimate of the RS angular power spectrum due to variations in the peculiar gravitational potential on scales smaller than 42/h megaparsecs is shown to be robust. An exhaustive study of the redshifts and spatial scales relevant for the production of RS anisotropy is developed for the first time. Results from this study demonstrate that (i) to estimate the full integrated RS effect, the initial redshift for the calculations (integration) must be greater than 25, (ii) the effect produced by strongly non-linear structures is very small and peaks at angular scales close to 4.3 arcmin, and (iii) the RS anisotropy cannot be detected either directly—in temperature CMB maps—or by looking for cross-correlations between these maps and tracers of the dark matter distribution. To estimate the RS effect produced by scales larger than 42/h megaparsecs, where the density contrast is not strongly non-linear, high accuracy N-body simulations appear unnecessary. Simulations based on approximations such as the Zel'dovich approximation and adhesion prescriptions, for example, may be adequate. These results can be used to guide the design of future RS simulations.