ARC STATISTICS WITH REALISTIC CLUSTER POTENTIALS - IV - CLUSTERS IN DIFFERENT COSMOLOGIES

We use numerical simulations of galaxy clusters in different cosmologi es to study their ability to form large arcs. The cosmological models are: Standard CDM (SCDM; Omega(0) = 1, Omega(lambda) = 0); tau CDM wit h reduced small-scale power (parameters as SCDM, but with a smaller sh ape parameter of the power spectrum); open CDM (OCDM; Omega(0) = 0.3, Omega(lambda) = 0); and spatially flat, low-density CDM (lambda CDM; O mega(0) = 0.3, Omega(lambda) = 0.7). All models are normalised to the local number density of rich clusters. Simulating gravitational lensin g by these clusters, we compute optical depths for the formation of la rge arcs. For large arcs with length-to-width ratio greater than or eq ual to 10, the optical depth is largest for OCDM. Relative to OCDM, th e optical depth is lower by about an order of magnitude for lambda CDM , and by about two orders of magnitude for S/tau CDM. These difference s originate from the different epochs of cluster formation across the cosmological models, and from the non-linearity of the strong lensing effect. We conclude that only the OCDM model can reproduce the observe d are abundance well, while the other models fail to do so by orders o f magnitude.