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4.6 Occurrence of Arcs and Evolution of Clusters

Clusters of galaxies are probably young gravitational systems and consequently the number of cluster lenses could vary rapidly with redshift. In particular, according to Henry et al. (1992) the Extended Medium Sensivity Survey (EMSS) shows a strong X-ray luminosity evolution from z = 0.6 until now. Wu (1993b) compared the number of expected arcs in non-evolution and evolution models with the observations. The predictions seem to contradict the hypothesis of a strong evolution of clusters after z approx 0.6, unless there are huge numbers of distant sources which increase the occurrence of arcs. The results inferred from the EMSS about the evolution of rich clusters may be meaningless due to the sparse sample of distant clusters we have at present, and further studies using the ROSAT sample should be pursued. Bartelmann (1993) also argued that the number of arcs should decrease significantly with redshift if cluster evolution is taken into account, if standard models of spherical collapse in a flat universe are assumed for clusters.