Arc Statistics with Realistic Cluster Potentials. II. Influence of   Cluster Asymmetry and Substructure
  We construct a sample of numerical models for clusters of galaxies and employ these to investigate their capability of imaging background sources into long arcs. Emphasis is laid on the statistics of these arcs. We study cross sections for arc length and length-to-width ratio and optical depths for these arc properties, we examine the distribution of arc widths and curvature radii among long arcs, and we compare these results to predictions based on simplified (radially symmetric) cluster models. We find that the capability of the numerically modeled clusters to produce long arcs is larger by about two orders of magnitude than that of spherically symmetric cluster models with the same observable parameters (core radii and velocity dispersions), and that they are similarly efficient as singular isothermal spheres with the same velocity-dispersion distribution. The influence of source ellipticity is also investigated; we find that the optical depth for arcs with a length-to-width ratio $\ga10$ is significantly larger for elliptical than for circular sources. Given these results, we conclude that spherically symmetric lens models for galaxy clusters, adapted to the observable parameters of these clusters, grossly underestimate the frequency of long arcs. We attribute this difference between numerically constructed and simplified analytical lens models to the abundance and the extent of intrinsic asymmetry and to substructure in galaxy clusters. 
Matthias Bartelmann, Matthias Steinmetz, and Achim Weiss