Annu. Rev. Astron. Astrophys. 1992. 30: 311-358 Copyright © 1992 by Annual Reviews. All rights reserved

5.3 Clusters of Galaxies

The possibility that galaxy clusters and superclusters may produce gravitational lensing has been considered by several authors (Noonan 1971, Dyer & Roeder 1976, Narayan et al. 1984, Sanders et al. 1984, Webster 1985, Hammer & Nottale 1986b, Crawford et al. 1986, Blandford et al. 1987, Kovner 1987f). The discovery of long arcs in a handful of clusters and the subsequent discovery of smaller arcs in these and several other clusters (Section 2.2) has now opened up this exciting field. Compared to lensing by individual galaxies, clusters offer several advantages. (a) Rich clusters cover a substantially larger angular area of the sky, thus increasing the cross section for lensing. (b) The lensed sources in this case, faint galaxies, are much more numerous than quasars, particularly at the low brightness levels achievable today. (c) Since the sources are resolved, image distortions may be directly measured, and one can study even modest effects due to lensing. (d) Since the mass distribution of clusters is considerably less relaxed and ordered than galaxy halos, there is potentially much more new information to be obtained through gravitational lensing.

Several groups have attempted to model the clusters with the longest arcs using a variety of mass models (Hammer 1987, Fort et al. 1988, Kovner 1988, 1989a, Grossman & Narayan 1988, 1989, Narasimha & Chitre 1988, Hammer & Rigaut 1989, Wambsganss et al. 1989, Nemiroff & Dekel 1989, Bergmann et al. 1990, Mellier et al. 1990, Hammer 1991, Kassiola et al. 1992). Parameters such as the velocity dispersion of the cluster, the mass-to-light ratio M / L, core radius, and ellipticity have been estimated. Since long arcs arise as a result of extreme tangential elongation of the image, usually by a cusp caustic, the radius of curvature of such an arc is roughly of order the Einstein radius [but not always, e.g. the ``straight arc'' in Abell 2390 (Pello et al. 1991)]. This can be used to estimate and M / L of the lens (cf Section 3.2). Derived values of these parameters are generally quite high ( 1000 km s^-1, M / L 100 solar units), but consistent with measured cluster velocity dispersions where available (Mellier et al. 1988). Almost all studies indicate that the lensing clusters must have smaller core radii (< 100 kpc) than indicated by either their optical or X-ray images (e.g. Bahcall 1977). Abell 370 shows the clearest evidence for noncircularity, with a strong indication that the projected mass distribution is elongated along the axis defined by the two central cD galaxies and not traced by the observed galaxies (e.g. Grossman & Narayan 1989, Soucail 1991). In other cases (e.g. Cl 2244-02) it is possible to associate all the mass with the visible cluster galaxies (e.g. Bergmann et al. 1990, Mellier et al. 1991).

The longest and most luminous arcs are rare since they are due to high redshift bright galaxies that happen to be close to caustics. Images of the sky down to a level of B = 29 per square arcsecond reveal a population of faint blue galaxies with a number density as high as ~ 100 per square arcminute (Tyson 1988). It now appears that up to B = 27 (corresponding to a surface brightness of B = 29 per square arcsecond with 0.8 arcsecond seeing), ~ 80% of the galaxies have redshifts in the range 0.7-1.4 (Fort 1992), consistent with extrapolations of redshift surveys of 24^m galaxies (e.g. Colless et al. 1990, Lilly et al. 1991), and with other observations (Grossman 1990, Guhathakurta et al. 1990). These galaxies are therefore ideal for studying the gravitational lensing influence of clusters at redshifts 0.5.

The tangentially elongated arclets observed in the fields of several moderate redshift rich clusters, notably Abell 1689 with 50 arclets (Tyson et al. 1990) and Abell 370 with 60 (Fort 1992), give two-dimensional maps of a distortion measure which approximately reflect the cluster mass distribution. It is found that the dark matter is reasonably correlated with the cluster red light. This promising technique to trace the mass in clusters is unfortunately limited by lack of knowledge of the individual redshifts and intrinsic ellipticities of the background sources (Kochanek 1990b, Miralda-Escudé 1991a, Knieb et al. 1992).

Individual galaxies in a rich cluster can have an exaggerated influence on images of background sources because of the enhancement of their lensing action by the overall mass distribution of the cluster. Particularly interesting are the optical rings seen around a few cluster galaxies. If these are due to gravitational lensing, then their analysis leads to interesting constraints on the mass of the galaxy as well as the surface density and shear of the cluster. However, there are alternative explanations of these features (Kochanek & Blandford 1991, Petrosian 1992).