The Global Sunyaev-Zel'dovich Effect of the Cluster Population and Its Detectability in Cosmic Microwave Background Maps

Clusters of galaxies can distort the cosmological signal in the cosmic microwave background (CMB) temperature fluctuations maps through the Sunyaev-Zel'dovich (SZ) effect. The analysis of this effect, which depends on the properties of the cluster population and its spatial distribution, could therefore be used to constrain the cluster mass function and its evolution. We present the global SZ effect expected for a cluster population extending to z = 0.2, z = 0.5, and z = 0.8, for random and nonrandom spatial distributions. The local population (up to z = 0.2) was built according to current results and in agreement with the XBACs data for the high-mass fraction of the cluster mass distribution. The resulting signal from the global SZ effect is well under the noise level of the Wilkinson Microwave Anisotropy Probe (WMAP) data for both distributions. The extension of the population to higher redshifts was done keeping the same mass distribution (without evolution). For the Poissonian distribution only at multipoles l ≥ 300 in the z = 0.8 case, the effects are over the noise level of the WMAP data. However, for the more realistic, nonrandom distribution case that signal would be detectable in the WMAP maps for multipoles higher than l = 100 at z = 0.5 and for nearly all multipoles at z = 0.8, in clear conflict with the data. The analysis of high-quality CMB data, as those expected from the Planck mission, will allow us to determine the contribution from the cluster population and to determine the evolution of clusters even at low redshift.