Superluminal Caustics of Close, Rapidly Rotating Binary Microlenses

The two outer triangular caustics (regions of infinite magnification) of aclose binary microlens move much faster than the components of the binarythemselves, and can even exceed the speed of light. When $\epsilon > 1$, where$\epsilon c$ is the caustic speed, the usual formalism for calculating the lensmagnification breaks down. We develop a new formalism that makes use of thegravitational analog of the Li\'enard-Wiechert potential. We find that as thebinary speeds up, the caustics undergo several related changes: First, theirposition in space drifts. Second, they rotate about their own axes so that theyno longer have a cusp facing the binary center of mass. Third, they grow largerand dramatically so for $\epsilon >> 1$. Fourth, they grow weaker roughly inproportion to their increasing size. Superluminal caustic-crossing events areprobably not uncommon, but they are difficult to observe.Comment: 12 pages, 7 ps figures, submitted to Ap