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Characterization of the Resonant Caustic Perturbation

Four of nine exoplanets found by microlensing were detected by the resonant caustic, which represents the merging of the planetary and central caustics at the position when the projected separation of a host star and a bounded planet is s~1. One of the resonant caustic lensing events, OGLE-2005-BLG-169, was a caustic-crossing high-magnification event with $A_{max} \sim$ 800 and the source star was much smaller than the caustic, nevertheless the perturbation was not obviously apparent on the light curve of the event. In this paper, we investigate the perturbation pattern of the resonant caustic to understand why the perturbations induced by the caustic do not leave strong traces on the light curves of high-magnification events despite a small source/caustic size ratio. From this study, we find that the regions with small-magnification-excess around the center of the resonant caustic are rather widely formed, and the event passing the small-excess region produces a high-magnification event with a weak perturbation that is small relative to the amplification caused by the star and thus does not noticeably appear on the light curve of the event. We also find that the positive excess of the inside edge of the resonant caustic and the negative excess inside the caustic become stronger and wider as $q$ increases, and thus the resonant caustic-crossing high-magnification events with the weak perturbation occur in the range of $q \leqslant 10^{-4}$. We determine the probability of the occurrence of events with the small excess $|ε| \leqslant 3 %$ in high-magnification events induced by a resonant caustic. As a result, we find that for the Earth-mass planets with a separation of ~ 2.5 AU, the resonant caustic high-magnification events with the weak perturbation can occur with a significant frequency.