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When we first got into this business we used the distortion of background galaxies to set limits on the putative dark matter halos of individual foreground galaxies. 11 But with individual galaxies doing the lensing, the image distortions were painfully small whenever the source and lens were separated by more than a few arcseconds.

In 1981 Arthur Hoag of Lowell Observatory pointed out a peculiar blue arc near a bright galaxy in the cluster Abell 370, captured on a photographic plate. 12 Definitive evidence of more such bright blue arcs was reported five years later. 13 The idea that foreground clusters might lens quasars had been around for some time, but theoretical work on the lensing of background galaxies began in earnest in 1986. 14 A large arc implies that a distant galaxy is located on the sky very close to a point of infinite magnification on a foreground lens. In optics this is called a caustic projection. Soon observers began to find more than one arc associated with a single foreground cluster of galaxies. 15

In effect, this lensing distortion magnifies the background galaxies. A few of them even become bright enough to be studied spectroscopically. Redshift measurements of nine such bright blue arcs, from background galaxies that would be quite faint (25th magnitude) in the absence of gravitational magnification, yielded values of z ranging from 0.5 to 2.2. Unfortunately these caustic projections of background galaxies are rare. The required alignment of source and lens is very restrictive.

If the angle phi between the center of the lens and the true source position is larger than upsilonE, one doesn't get multiple images. But any source of resolvable width will be distorted as well as displaced, because each point of its image is displaced radially outward from the center of the lens. Because the faint blue background galaxies appear nice and fat, despite their great distances, a foreground lens will elongate them into concentric arcs, as shown in figure 2. The great masses associated with rich clusters of galaxies affect background galaxy images over large patches of sky behind them. They distort all the faint background galaxies within several arcminutes of the cluster. Foreground galaxy clusters with redshifts from 0.2 to 0.5 and line-of-sight velocity dispersions exceeding 700 km/sec have mass densities high enough to significantly distort background galaxies that are at least twice as far away. (Note that lensing displacement is proportional to the lever arm DLS.) Lensing preserves the surface brightness (per unit apparent area) and spectrum of the source, so that most arcs have the very faint surface brightness and characteristic blue color of the unlensed background galaxies.

We searched for distorted background images in several rich clusters, employing very sensitive CCD detectors to do deep, multiband imaging at the 4-meter telescope on Cerro Tololo and at the 3.6-meter Canada-France-Hawaii telescope on the island of Hawaii. Centered on several of the more massive galaxy clusters we found dozens of distorted background galaxy images. Their systematic, concentric alignment around the lensing foreground cluster was unambiguous. 16

We select the background galaxy population by its extreme blue color relative to the red cluster galaxies of the foreground. In our deep, three-hour-long CCD exposures at large telescopes we find 30 to 100 background galaxies per square arcminute wherever we look. That's an adequate background population for the task of mapping the dark matter in a foreground cluster anywhere in the sky.

The high-redshift background galaxies falling within the central square arcminute of a foreground compact cluster of galaxies are strongly lensed. Typically they are distorted into faint circular arcs up to 30 arcseconds long. These are not the relatively rare caustic alignments we occasionally find when single galaxies are doing the lensing. Around large foreground clusters every background galaxy appears stretched along a circle centered on the lens. It is the ubiquitous high density of faint background galaxies revealed by our sensitive imaging detectors that provides us with enough statistics to construct an approximate map of the dark matter distributions in the foreground lensing systems.

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