Arc statistics with realistic cluster potentials. IV. Clusters in different cosmologies

We use numerical simulations of galaxy clusters in different cosmologies to study their ability to form large arcs. The cosmological models are: Standard CDM (SCDM; Omega_0 =1, Omega_ Lambda =0); tau CDM with reduced small-scale power (parameters as SCDM, but with a smaller shape parameter of the power spectrum); open CDM (OCDM; Omega_0 =0.3, Omega_ Lambda =0); and spatially flat, low-density CDM (Lambda CDM; Omega_0 =0.3, Omega_ Lambda =0.7). All models are normalised to the local number density of rich clusters. Simulating gravitational lensing by these clusters, we compute optical depths for the formation of large arcs. For large arcs with length-to-width ratio >=10, the optical depth is largest for OCDM. Relative to OCDM, the 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 differences 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 observed arc abundance well, while the other models fail to do so by orders of magnitude.