Statistics of arcs in clusters of galaxies

Samples of gravitational lens events in clusters show many large arcs compared to arclets, relative to what can be obtained by idealized singular lens models. We describe the probability of image magnification for point sources and for simple but more realistic gravitational lensing models that include a finite core size and an ellipticity. In addition, we explore the changes in the probability distribution of image magnifications, distortions, and angular extents for sources of different sizes as the parameters of the lenses are varied. A finite core in spherically symmetric lens models introduces a discontinuity in the probability distribution at which the relative number of highly magnified images is increased. In elliptical lenses, this discontinuity and its effect are replaced by a continuous increase in the probability of obtaining high-magnification images relative to singular spherically symmetric models. We also find that the finite size of the source causes a further increase in the expected number of images just below the maximum possible magnification.