PERTURBATIONS OF CLUSTER CUSPS BY GALAXIES - THE TRIPLE ARC IN CL 0024 + 1654

Triple images formed by a source near the tip of a cusp should satisfy the length theorem, according to which the length of the middle image equals the sum of the lengths of the other two. If, however, a cusp is perturbed by a smaller lens component, both the topology of the time delay surface and the image multiplicity can change significantly. While it is still possible to have a triple image, the length theorem does not apply. We offer a simple method of analysis for perturbed cusps, which does not require detailed numerical modeling. We then apply this method to the triple arc in Cl 0024 + 1654, in which the three segments visibly violate the length theorem. The perturbation of the cluster cusp appears to be caused by a clump of galaxies near the middle segment of the arc. To check this hypothesis we need only the relative positions of the ends of the three segments. Our analysis leads to the conclusion that, if this arc is indeed created by a single source, it should be formed by a perturbed right-handed cusp; each of the segments should be a single image, and the middle segment should be inverted with respect to the two outer segments. We then perform a numerical search for a model of the triple arc, subject to the constraints imposed by the geometry of the segments. The results of this search confirm the predictions of our qualitative analysis. The numerical model we find provides a rough picture of the lens potential and predicts that the perturbed cusp is naked and no counterarc is formed. Finally, we report the most recent high-resolution images of the cluster 0024 + 1654, obtained at CFHT with a seeing of 0.5" for the B and I filters. They reveal significant substructure in each segment of the triple arc and show that the source is multicomponent: there are two main source galaxies imaged approximately on each edge of the segments. The overall geometry supports our qualitative and numerical inferences. The positions of the six nuclei and the ratios of their fluxes impose stricter constraints on the gravitational lens. We performed a numerical search subject to these constraints and found models of the lens potential that are more accurate, but not very different from our first crude model.