Properties of Planetary Caustics in Gravitational Microlensing

Although some of the properties of the caustics in planetary microlensing have been known, our understanding of them is mostly from scattered information based on numerical approaches. In this paper, we conduct a comprehensive and analytic analysis of the properties of the planetary caustics, which are one of the two sets of caustics in planetary microlensing, those located away from the central star. Under the perturbative approximation, we derive analytic expressions for the location, size, and shape of the planetary caustic as a function of the star-planet separation and the planet/star mass ratio. Based on these expressions combined with those for the central caustic, which is the other set of caustics and is located close to the central star, we compare the similarities and differences between the planetary and central caustics. We also present the expressions for the size ratio between the two types of caustics and for the condition of the merging of the two types of caustics. These analytic expressions will be useful in understanding the dependence of the planetary lensing behavior on the planet parameters and thus in interpreting the planetary lensing signals.