Figure 1.14 .b shows the ratio of the expected X-ray brightness to the SZ brightness at mm, which decreases strongly with z for different central temperatures of cluster. Therefore, the SZ effect provides a powerful tool with which to study the evolution of clusters, as described in further detail below. This is illustrated in figure 1.15 which shows X-ray brightness and y profiles for typical rich clusters at two different redshifts. The SZ effect is thus sensitive enough to observe the temperature drop which defines the limit of virialization. The EPIC instrument, on the XMM observatory, in a 20-hour observation, will be able to map the same cluster up to about .
Differential number counts versus redshift for different flux limits and .
The integrated value is , where y 0 stands for the central value and is expressed in arcmin. This dependence on is a consequence of the earlier formation of clusters of galaxies in a low density universe. Figure 1.16 .a shows the corresponding redshift distribution. Since these estimations are strongly model dependent, measurements of the SZ effect will provide sensitive tests of theories of structure formation. The observed counts of clusters will provide a powerful test of models of structure formation and evolution.