THE GRAVITATIONAL LENS HYPOTHESIS FOR THE RING IN A2218

We examine the gravitational lens hypothesis for the nearly Perfect ring around the elliptical galaxy 373 in cluster A2218. We first investigate analytically the variation of the mean radius and thickness along the circumference of a ring formed around a galaxy in a cluster. If the velocity dispersion of G373 is the one inferred from its luminosity (less than or similar 220 km s-1), variations can be small only if the shear induced by the gravitational field of the cluster in the area of the ring is very small. This constrains the cluster to a relatively large core and small ellipticity. In addition, the cluster should contain a small clump of matter not traced by isophotes. Numerical modeling confirms the results of the analytical investigation. We present a lens model which reproduces a ring similar to the observed one. This model includes the smoothed mass of the, cluster, the galaxy 373, the undetected clump, and three perturbing galaxies in the vicinity of the ring. The undetected clump is necessary for the formation of a nearly perfect ring. The core of the cluster is approximately 100 h-1 kpc, and its axes ratio is almost-equal-to 0.96. The shape of the ring is rather unstable with respect to perturbations by relatively minor masses. This instability implies that the ring must be a result of a coincidental alignment of the masses in the cluster. Stability is improved if the galaxy 373 is more massive than what can be inferred from its luminosity. It is also possible that the undetected clump is at a higher redshift. We present a second lens model which includes these two variations. Our conclusion is that although the ring can be produced by gravitational lensing, the lens must necessarily involve a coincidental alignment of its components.