CONSEQUENCES OF CLUSTER EVOLUTION FOR THE STATISTICS OF GIANT LUMINOUS ARCS

Richstone et al. (1992) have recently discussed cluster-formation time scales in FLRW universes. They conclude that the epoch of cluster form ation is shifted towards small redshifts for OMEGA0 --> 1, and togethe r with indications that clusters are ''young'' entities, they derive a lower limit for OMEGA0, OMEGA0 greater than or similar to 0.5. If the cluster population is dominated by low-redshift clusters, this should have significant consequences for its lensing capabilities, because l enses close to the observer are inefficient. On the basis of a theoret ically derived cluster redshift distribution in an Einstein-deSitter u niverse, I investigate the optical depth for the formation of large ar cs. I find that, on the account of cluster evolution, the optical dept h is reduced by a factor of congruent-to 5 for moderate- and high-reds hift sources relative to the case of non-evolving clusters, and that t he mean redshift and the rms width of the redshift distribution of lar ge-arc clusters is significantly lowered.