Local behavior of caustics in different lens models

Abstract

Our investigation is based on the work of Schneider & Weiss (1986), where the symmetrical two-pointmass lens is discussed and a classification of the critical curves and caustics is given for the single lens plane approximation. Here we generalize this lens system for arbitrary mass ratios and different distances from the pointmass lenses to the observer. We use the two lens-plane approximation and end up with three lens parameters, which describe the mass ratio of the lenses, their distance perpendicular to the line of sight, and the separation of the two lens planes. With an explicit method we calculate the characteristic values of the lens parameters where the topology of the critical curves changes. We find five surfaces within the 3-dimensional parameter space separating six regions of constant topology, with a total of five different topologies. The application of catastrophe theory in Schneider, Ehlers & Falco (1991) also allows us to classify the metamorphoses of caustics at these characteristic values of parameters and we obtain again five different topologies for the caustics. The caustic structure changes qualitatively if the distances of the two deflectors from the observer are not equal. The convexity of caustics is no longer required, ‘very large caustics’ exist, and the maximum number of images is increased by one. Furthermore, elliptic umbilics occur, which cannot occur in the single lens-plane case. Several of the caustic shapes we find here are visible in the numerical results of Schneider & Weiss (1988), thus leading to a deeper understanding of these simulations.

The results are discussed in detail in Erdl (1990) and Erdl & Schneider (1991).