Statistics of Arcs in Clusters of Galaxies
Abstract
Present samples of gravitational lens events in clusters show a high number of large arcs compared to arclets relative to what can be obtained by idealized singular lens models (e.g., the point mass or the spherically symmetric isothermal model). 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. We find that 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 highmagnification 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. We identify lensing models and parameters that are particularly favored to produce larger relative numbers of highly magnified images. We conclude that for clusters with a central density approximately twice the critical density and a small eccentricity in the lensing potential the number of small arclets (angular extent of the image as measured from the lens center between 10^deg^ and 50^deg^) found for every large arc (angular extent greater than 50^deg^) can be as low as eight.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1993
 DOI:
 10.1086/172973
 Bibcode:
 1993ApJ...413...18B
 Keywords:

 Astronomical Models;
 Galactic Clusters;
 Gravitational Lenses;
 Statistical Analysis;
 Isothermal Processes;
 Probability Theory;
 Astrophysics;
 GALAXIES: CLUSTERING;
 COSMOLOGY: GRAVITATIONAL LENSING