2003AJ....125.1033S

An image of a remote source microlensed by the stars of a foreground galaxy consists of a number of microimages. The motion of the stars causes their gravitational field on the line of sight to vary, resulting in positional motion of the image centroid (IC) at the microarcsecond level. This motion is the sum of the average velocity (which depends upon the mass and velocity of the stars far from the line of sight) and a fluctuating part (due to the nearest stars). Both components are potentially measurable via astrometric monitoring over some tens of years, provided that microarcsecond accuracy is achieved. We describe an algorithm that enables one to relate the statistical characteristics of such IC motions to lens shear and optical depth along the line of sight. We have carried out simulations of IC motions in the case of stochastic point microlenses having the same velocity, equal to the bulk velocity of the lensing galaxy. We present the dependencies of the rms variations of the IC velocity upon the shear and its orientation, as well as upon the microlensing optical depth and the contribution of a continuous component that may represent dark matter. For medium values of shear and optical depth, the velocity variations turn out to be on the order of the lensing galaxy's angular motion.