The peak-patch picture of cosmic catalogs .3. Application to clusters

In adjoining papers, we developed a picture of large-scale structure formation based upon the collapse and now of regions of Lagrangian (initial condition) space surrounding peaks in the density field. To illustrate the utility of this ''Peak-Patch'' method, we construct cluster catalogues covering very large volumes of space for four inflation-inspired Gaussian structure formation theories with a critical density in clustering matter and whose sigma(8) normalizations roughly fit the COBE anisotropy measurements. We use these to make deep field X-ray and Sunyaev-Zeldovich maps. Subject to some uncertainties in the internal peak-patch physics and the X-ray data, we find that current X-ray temperature data suggest sigma(8) is within similar to 15% of 0.7 and the spectrum is flatter than CDM gives, for Einstein-de Sitter models. We also find the current X-ray luminosity data are difficult to fit over the entire range with such models. The prospect for the observation of the ambient thermal and kinetic SZ effect with a variety of experimental designs is discussed.