STATISTICS OF HIGHLY MAGNIFIED GRAVITATIONAL IMAGES IN CLUSTERS OF GALAXIES .1. IMPLICATIONS FOR THE CLUSTERS

The probability distribution of observing images of background galaxies gravitationally lensed by clusters of galaxies, in the form of elongated arcs, is studied as a function of the following observable properties: the arc width, the radius of curvature, and the orientation of the elongation. The calculation is performed for single lenses with a spherical component and a quadrupole component in the mass distribution, and also for two superposed lenses with the same components, as a simplified model of substructure in the projected mass distribution of the cluster. From the available observations, we obtain the following conclusions on the mass distribution in the clusters: (1) As a simple consequence of the observed arc curvatures, an upper limit is obtained on the size of the cores, in agreement with Grossman & Narayan. This upper limit is smaller than cluster core radii obtained for the ps from the X-ray surface brightness. (2) It is shown how the curvature and orientation of the arcs give additional information on the mass profile of the lensing clusters within the arcs. In the case of A963, the observed arcs imply that the mass profile is shallower than a singular isothermal sphere. In several other clusters, the observed positions, orientations, and curvatures of the arcs seem to indicate the existence of more than one mass concentration in the central parts, which approximately follow a smoothed version of the substructure indicated by the distribution of cluster galaxies. (3) We calculate the probability of observing radial arcs, produced in the cluster cores, and ''straight arcs,'' produced between two mass concentrations. (4) We argue that lensing clusters are likely to be elongated along the line of sight, with an enhanced surface density caused by projection effects.