Astrometric Microlensing of Quasars : Dependence on surface mass density and external shear

11 pages, 13 figures, accepted for publication in A&AA small fraction of all quasars are strongly lensed and multiply imaged, with usually a galaxy acting as the main lens. Some, maybe all of these quasars are also affected by microlensing, the effects of stellar mass objects in the lensing galaxy. Stellar microlensing not only has photometric effects (magnitude fluctuations of the quasar images), it also affects the observed position of the images. This astrometric effect was first explored by Lewis and Ibata (1998): the position of the quasar - i.e. the center-of-light of the many microimages - can shift by tens of microarcseconds due to the relatively sudden (dis-)appearance of a pair of microimages when a caustic is being crossed. We explore this effect quantitatively for different values of the surface mass density and external shear covering most of the known multiple quasar systems. We show examples of microlens-induced quasar motion and the corresponding light curves for different quasar sizes. We evaluate statistically the occurrence of large shifts in angular position and their correlation with apparent brightness fluctuations. We also show statistical relations between positional offsets and time from random starting points. As the amplitude of the astrometric offset depends on the source size, astrometric microlensing signatures of quasars - combined with the photometric variations - will provide very good constraints on the size of quasars as a function of wavelength. We predict that such signatures will be detectable for realistic microlensing scenarios with near future technology in the infrared/optical (Keck-Interferometry, VLTI, SIM, GAIA). Such detections will show that not even high redshift quasars define a 'fixed' coordinate system