STATISTICS OF LENSING BY CLUSTERS OF GALAXIES .1. GIANT ARCS

The statistical properties of gravitational lensing by rich distant cl usters of galaxies are investigated. The sources of giant luminous arc s are assumed to be moderately luminous spirals similar to those found in deep blue redshift surveys. Arc properties (numbers, axis ratios, etc.) are found to depend strongly on the adopted cluster density prof iles, and hence provide sharp constraints on the models for matter dis tribution in clusters. Giant luminous arcs should be present in nearly half of the extremely rich clusters (L(x) greater-than-or-equal-to 9 x 10(44) erg s-1 or sigma(v) greater-than-or-equal-to 1300 km s-1), if described by the r1/4 law, with a lower incidence by a factor of appr oximately 4 for a modified Hubble profile. A considerably smaller numb er of giant luminous arcs, even fewer than the number of observed even ts, is predicted by an isothermal model for the cluster density profil e, unless the matter is much more concentrated (core radius 10 times l ower) than the luminous (optical/X-ray) matter. Extrapolating the curr ent observational data, we estimate that there are over 100 giant lumi nous arcs (B less-than-or-equal-to 22.5 and axis ratio greater-than-or -equal-to 10) over the whole sky. Our model also yields a distribution of the redshifts of the arc clusters peaking at z approximately 0.2-0 .3, while most of the arc sources are expected at redshifts ranging fr om 0.5 to 1.3; both these results agree with the observational data. U sing available lensing models to account for luminous arcs, we predict the existence of giant radio arcs, detectable in numbers (approximate ly 100 down to 0.01 mJy) comparable to the estimated number of giant o ptical luminous arcs. Giant radio arcs might be a new class of objects , which could provide additional information on either the mass distri bution of rich clusters or the redshift distribution of sub-mJy radio sources.