A Complete Set of Solutions for Caustic Crossing Binary Microlensing Events

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Abstract
We present a method to analyze binary lens microlensing light curves with one well-sampled fold caustic crossing. In general, the surface of χ2 shows extremely complicated behavior over the nine-parameter space that characterizes binary lenses. This makes it difficult to systematically search the 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 can 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 allows a systematic search for all solutions and thus identification of all local minima. We illustrate this technique using the PLANET data for MACHO 98-SMC-1, an excellent and publicly available caustic crossing data set. We show that a very broad range of parameter combinations are compatible with the PLANET data set, demonstrating that observations of binary lens light curves with a sampling of only one caustic crossing do not yield unique solutions. The corollary to this is that the time of the second caustic crossing cannot be reliably predicted on the basis of early data including the first caustic crossing alone. We investigate the requirements for determination of a unique solution and find that occasional observations of the first caustic crossing may be sufficient to derive a complete solution.
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