Hydrodynamical simulations of the Sunyaev-Zel'dovich effect

With detections of the Sunyaev-Zel'dovich (SZ) effect induced by galaxy clusters becoming routine, it is crucial to establish accurate theoretical predictions. We use a hydrodynamical N-body code to generate simulated maps, of size 1 deg(2), of the thermal SZ effect. This is done for three different cosmologies: the currently favoured low-density model with a cosmological constant, a critical-density model and a low-density open model. We stack simulation boxes corresponding to different redshifts in order to include contributions to the Compton y-parameter out to the highest necessary redshifts. Our main results are as follows. (i) The mean y-distortion is around 4x10(-6) for low-density cosmologies, and 1x10(-6) for critical density. These are below current limits, but not by a wide margin in the former case. (ii) In low-density cosmologies, the mean y-distortion is contributed across a broad range of redshifts, with the bulk coming from z less than or similar to 2 and a tail out to z similar to 5. For critical-density models, most of the contribution comes from z < 1. (iii) The number of SZ sources above a given y depends strongly on instrument resolution. For a 1-arcmin beam, there are around 0.1 sources per deg(2) with y > 10(-5) in a critical-density Universe, and around 8 such sources per deg(2) in low-density models. Low-density models with and without a cosmological constant give very similar results. (iv) We estimate that the Planck satellite will be able to see of order 25 000 SZ sources if the Universe has a low density, or around 10 000 if it has critical density.