STATISTICS OF ARCS IN CLUSTERS OF GALAXIES

Present samples of gravitational lens events in clusters show a high n umber of large arcs compared to arclets relative to what can be obtain ed by idealized singular lens models (e.g., the point mass or the sphe rically symmetric isothermal model). We describe the probability of im age magnification for point sources and for simple but more realistic gravitational lensing models that include a finite core size and an el lipticity. In addition, we explore the changes in the probability dist ribution of image magnifications, distortions, and angular extents for sources of different sizes as the parameters of the lenses are varied . We find that a finite core in spherically symmetric lens models intr oduces a discontinuity in the probability distribution at which the re lative number of highly magnified images is increased. In elliptical l enses this discontinuity and its effect are replaced by a continuous i ncrease in the probability of obtaining high-magnification images rela tive to singular spherically symmetric models. We also find that the f inite size of the source causes a further increase in the expected num ber of images just below the maximum possible magnification. We identi fy lensing models and parameters that are particularly favored to prod uce larger relative numbers of highly magnified images. We conclude th at for clusters with a central density approximately twice the critica l density and a small eccentricity in the lensing potential the number of small arclets (angular extent of the image as measured from the le ns center between 10-degrees and 50-degrees) found for every large arc (angular extent greater than 50-degrees) can be as low as eight.