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 one square degree, of the thermal SZ effect. This is done for three different cosmologies — the currentlyfavoured 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: (i) The mean y-distortion is around 4 × 10 for low-density cosmologies, and 1 × 10 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 <∼ 2 and a tail out to z ∼ 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 one arcminute beam, there is around 0.1 sources per square degree with y > 10 in a critical-density Universe, and around 8 such sources per square degree 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 25000 SZ sources if the Universe has a low density, or around 10000 if it has critical density.