The Peak-Patch Picture of Cosmic Catalogs. III. Application to Clusters

In adjoining papers, we developed a picture of large-scale structure formation based upon the collapse and flow 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 σ_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 σ_8_ is within ~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.