A linear-filter approach to extracting the Rees-Sciama effect in merging clusters of galaxies

We discuss the prospects for detecting the Rees-Sciama (RS) effect associated with merging clusters of galaxies in millimetric observations. Using the extended Press-Schechter formalism, we characterize the distribution of the parameters describing the mergers, and use these results to generate a mock catalogue of cluster mergers. We use realistic N-body simulations to confirm the reliability of the mock catalogue, and build a new filter that attempts to optimize the extraction of the RS signal. This is an extension of the spatial-filtering method described in Haehnelt & Tegmark (1996, MNRAS, 279, 545), that has a general definition and hence can be applied in other contexts, such as gravitational lensing of the CMB or lensing of background galaxies. When applied to our mock cluster merger catalogue, we show that with the announced sensitivities of future experiments like the Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT), or the Atacama Large Millimeter Array (ALMA), a detection of the signal will be possible if we consider roughly 1000 cluster mergers.