An extra-solar 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 extra-solar 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 \Delta \mbox { \boldmath$ \delta$ } ) and the correlations of \Delta \mbox { \boldmath$ \delta$ } with the photometric deviations .
For this , we construct vector field maps of \Delta \mbox { \boldmath$ \delta$ } , 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 , due 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 each other .
For systems with u _ { p } > 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 u _ { p } < 1.0 .
The major deviation region is surrounded by the region of moderate deviations , within which the orientation of \Delta \mbox { \boldmath$ \delta$ } is reversed compared to 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 \Delta \mbox { \boldmath$ \delta$ } 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 \Delta \mbox { \boldmath$ \delta$ } with these parameters .