Microlensing by a wide-separation planet: Detectability and boundness

The microlensing technique has proven sensitive to Earth-like and/or wide-separation extrasolar planets. The unbiased spatial distribution of extrasolar planets with respect to host stars is crucial in studying the planet formation processes. If one can characterize the planetary microlensing light curves whether they are produced by a wide-separation planet or a freefloating planet, it will greatly help to establish the spatial distribution of extrasolar planets without contamination by free-floating planets. Previous studies have shown that the effect of the host star on the microlensing by the accompanying wide-separation planet can be significant enough to be detected by the high-frequency microlensing experiments for typical microlensing parameters. Here, we further explore the detection condition of a wide-separation planet through the perturbation induced by the planetary caustic for various microlensing parameters, especially for the size of the source stars. By constructing the fractional deviation maps at various positions in the space of microlensing parameters, we find that the pattern of the fractional deviation depends on the ratio of the source radius to the caustic size, and the ratio satisfying the observational threshold varies with the star-planet separation. We have also obtained the upper limits of the source size that allow the detection of the signature of the host star as a function of the separation for given observational threshold. It is shown that this relation further leads one to a simple analytic condition for the star-planet separation to detect the boundness of wide-separation planets as a function of the mass ratio and the source radius. For example, when 5 per cent of the detection threshold is assumed, for a source star with the radius of ~1Rȯ, an Earth-mass planet and a Jupiter-mass planet can be recognized of its boundness when it is within the separation range of ~10 and ~30 au, respectively. We also compare the separation ranges of detection by the planetary caustic with those by the central caustic. It is found that when the microlensing light curve caused by the planetary caustic happens to be analysed, one may afford to support the boundness of the wide-separation planet farther than when that caused by the central caustic is analysed. Finally, we conclude by briefly discussing the implication of our findings on the next-generation microlensing experiments.