Sunyaev-Zeldovich Fluctuations from Spatial Correlations between Clusters of Galaxies

We present angular power spectra of the cosmic microwave background radiation anisotropy due to fluctuations of the Sunyaev-Zeldovich (SZ) effect through clusters of galaxies. A contribution from the correlation among clusters, which has been neglected in previous analyses, is especially focused on. Employing the evolving linear bias factor based on the Press-Schechter formalism, we find that the clustering contribution amounts to 20%-30% of the Poissonian contribution at degree angular scales. If we exclude clusters in the local universe, it even exceeds the Poissonian noise and makes the dominant contribution to the angular power spectrum. As a concrete example, we demonstrate the subtraction of the ROSAT X-ray and Planck SZ flux-limited cluster samples. It indicates that we should include the clustering effect in the analysis of the SZ fluctuations. We further find that the degree scale spectra essentially depend upon the normalization of the density fluctuations, i.e., sigma8, and the gas mass fraction of the cluster, rather than the density parameter of the universe and details of cluster evolution models. Our results show that the SZ fluctuations at the degree scale will provide a possible measure of sigma8, while the arcminute spectra will provide a probe of the cluster evolution. In addition, the clustering spectrum will give us valuable information on the bias at high redshift, if we can detect it by removing X-ray or SZ luminous clusters.