Critical curves of triple gravitational microlenses

In the theory of gravitational lensing the lens caustic and its primary image, the critical curve, have fundamental importance. Knowledge of these curves greatly facilitates the interpretation and analysis of time-dependent gravitational microlensing events. A binary lens modelled by two point masses can form caustics of three different topologies, which correspond to three topologies of the critical curve. Here we analyse critical curve topologies of the triple lens. While the binary lens is characterized by two parameters, five parameters are needed to describe the triple lens. We present an example illustrating the analysis of special triple-lens models described by two parameters. We find analytical conditions for the change of critical-curve topology, which define boundaries of regions in parameter space with different critical-curve topology. For each region we present corresponding critical curves and caustics. We also include sample results for a three-parameter model describing a triple lens with equal masses in a general spatial configuration.