Properties of planet-induced deviations in the astrometric microlensing centroid shift trajectory

An extrasolar planet can be detected by microlensing because it can distort the smooth lensing light curve created by the primary lens. As a new method to search for and characterize extrasolar planets, Safizadeh, Dalal & Griest proposed to detect the planet-induced distortions in the trajectory of the microlensed source star's centroid motion (astrometric curve), which is observable by using the next generation of high-precision interferometers. In this paper we investigate the properties of the planet-induced deviations in the astrometric curves (excess centroid shifts Deltadelta) and the correlations of Deltadelta with the photometric deviations. For this, we construct vector field maps of Deltadelta, which represent the difference of the centroid shift from that expected in the absence of the planet as a function of source positions. From this investigation, we find that significant astrometric deviations occur not only in the region near the caustics but also in the region close to the planet-primary axis between the caustics. However, owing to the difference in the locations of the caustics between the two types of systems with the planet-primary separations (normalized by the angular Einstein ring radius) u(p) > 1.0 and u(p) < 1.0, the locations of the major deviation regions of the two systems are different from each other. For systems with up > 1.0, the major deviation vectors have orientations, in most cases, pointing towards the planet, while they point away from the planet for systems with lip < 1.0. The major deviation region is surrounded by the region of moderate deviations, within which the orientation of &UDelta;δ is reversed compared with the orientation in the major deviation region. We also find that the astrometric deviation is closely correlated with the photometric one, as discussed by Safizadeh et al. The astrometric deviation increases as the photometric deviation increases, and &UDelta;δ is directed towards the planet when the light curve has positive deviation, and vice versa. We also present excess centroid shift maps for lens systems with various values of the planetary separation, planet/primary mass ratio, and source size to show the changes in the pattern of &UDelta;δ with these parameters.