Detecting Sunyaev-Zel'dovich clusters with Planck -: I.: Construction of all-sky thermal and kinetic SZ maps

All-sky thermal and kinetic Sunyaev-Zel'dovich (SZ) maps are presented for assessing how well the Planck mission can find and characterize clusters of galaxies, especially in the presence of primary anisotropies of the cosmic microwave background (CMB) and various Galactic and ecliptic foregrounds. The maps have been constructed from numerical simulations of structure formation in a standard Lambda cold dark matter (Lambda CDM) cosmology and contain all clusters out to redshifts of z = 1.46 with masses exceeding 5 x 10(13) M-circle dot h(-1). By construction, the maps properly account for the evolution of cosmic structure, the halo-halo correlation function, the evolving mass function, halo substructure and adiabatic gas physics. The velocities in the kinetic map correspond to the actual density environment at the cluster positions. We characterize the SZ-cluster sample by measuring the distribution of angular sizes, the integrated thermal and kinetic Comptonizations, the source counts in the three relevant Planck channels, and give the angular power spectra of the SZ sky. While our results are broadly consistent with simple estimates based on scaling relations and spherically symmetric cluster models, some significant differences are seen which may affect the number of cluster detectable by Planck.