Sunyaev-Zel'dovich predictions for the Planck surveyor satellite using theHubble Volume simulations

We use the billion-particle Hubble Volume simulations to make statistical p redictions for the distribution of galaxy clusters that will be observed by the Planck Surveyor satellite through their effect on the cosmic microwave background - the Sunyaev-Zel'dovich (SZ) effect. We utilize the lightcone data sets for both critical density (tau CDM) and flat low-density (Lambda CDM) cosmologies: a 'full-sky' survey out to z similar to 0.5, two 'octant' data sets out to beyond z = 1, and a 100 square degree data set extending to z similar to 4. Making simple, but robust, assumptions regarding both th e thermodynamic state of the gas and the detection of objects against an un resolved background, we present the expected number of SZ sources as a func tion of redshift and angular size, and also as a function of flux (for both the thermal and kinetic effects) for three of the relevant High Frequency Instrument frequency channels. We confirm the expectation that the Planck S urveyor will detect around 5 x 10(4) clusters, though the exact number is s ensitive to the choice of several parameters including the baryon fraction, and also to the cluster density profile, so that either cosmology may pred ict more clusters. We also find that the majority of detected sources shoul d be at z < 1.5, and we estimate that around 1 per cent of clusters will be spatially resolved by the Planck Surveyor, though this has a large uncerta inty.