Marginal gravitational lenses of large separation: probing superclusters

The surface mass density (Σ) of clusters of galaxies and super-clusters is normally too low to split images^1-5, even for a large source redshift (z_s) and an optimal lens redshift (z_i). Because the distribution function of Σ decreases steeply with Σ, a cluster or supercluster found responsible for multiple imaging has a high probability of being a marginal lens⁵. Such a lens, barely able to split images of a distant source, has a subcritical surface mass density and remarkable properties unlike those of lenses with a density above critical. As I show here, these properties can easily be recognized observationally when the image separation is larger than is normal for a lens made of a galaxy: (1) there may be no prominent excess of galaxies and no microwave background inhomogeneities in the immediate area of the images, (2) there may be an enhancement of the number of observable quasars at very different redshifts in an area much larger than the image separation, (3) there may be split images in the vicinity of unsplit images of other sources of even larger redshifts. If split images of the same source separated by many arc seconds are observed and the responsible lens is a non-exotic object, for example, a cluster, a group of clusters or a collapsing protocluster seen edgewise, it is likely to be marginal. Modern techniques permit a specific search for these lenses, which could constrain theories of structure fermation in the Universe.