Hydrodynamical simulations of the Sunyaev--Zel'dovich effect

We use a hydrodynamical N-body code to generate simulated maps, of size one square degree, of the thermal SZ effect. We study 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: 1. The mean y-distortion is around $4 \times 10^{-6}$ for low-density cosmologies, and $1 \times 10^{-6}$ for critical density. These are below current limits, but not by a wide margin in the former case. 2. In low-density cosmologies, the mean y-distortion comes from a broad range of redshifts, the bulk coming from $z < 2$ and a tail out to $z \sim 5$. For critical-density models, most of the contribution comes from $z < 1$. 3. 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 $y > 10^{-5}$ 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. 4. We estimate that the {\sc 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.