On the Number Density of Sunyaev-Zeldovich Clusters of Galaxies

If the mean properties of clusters of galaxies are well described by the entropy-driven model, the distortion induced by the cluster population on the blackbody spectrum of the cosmic microwave background radiation is proportional to the total amount of intracluster gas, while temperature anisotropies are dominated by the contribution of 1014 M⊙ clusters. This result depends marginally on cluster parameters, and it can be used to estimate the number density of clusters with enough hot gas to produce a detectable Sunyaev-Zeldovich effect. Comparing different cosmological models, the relation depends mainly on the density parameter Ωm. If the number density of clusters could be estimated by a different method, then this dependence could be used to constrain Ωm.