A complete set of solutions for caustic crossing binary microlensing events

We present a method to analyze binary lens microlensing light curves with o ne well-sampled fold caustic crossing. In general, the surface of chi(2) sh ows extremely complicated behavior over the nine-parameter space that chara cterizes binary lenses. This makes it difficult to systematically search th e space and verify that a given local minimum is a global minimum. We show that for events with well-monitored caustics, the caustic crossing region c an be isolated from the rest of the light curve and easily fitted to a five -parameter function. Four of these caustic crossing parameters can then be used to constrain the search in the larger nine-parameter space. This allow s a systematic search for all solutions and thus identification of all loca l minima. We illustrate this technique using the PLANET data for MACHO 98-S MC-1, an excellent and publicly available caustic crossing data set. We sho w that a very broad range of parameter combinations are compatible with the PLANET data set, demonstrating that observations of binary lens light curv es with a sampling of only one caustic crossing do not yield unique solutio ns. The corollary to this is that the time of the second caustic crossing c annot be reliably predicted on the basis of early data including the first caustic crossing alone. We investigate the requirements for determination o f a unique solution and find that occasional observations of the first caus tic crossing may be sufficient to derive a complete solution.