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 24m
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).
