Astrometric microlensing of stars

Because of dramatic improvements in the precision of astrometric measuremen ts, the observation of light centroid shifts in observed stars due to inter vening massive compact objects ("astrometric microlensing") will become pos sible in the near future. Upcoming space missions, such as SIM and GAIA, wi ll provide measurements with an accuracy of 4-60 mu as depending on the mag nitude of the observed stars, and an accuracy of similar to 1 mu as is expe cted to be achieved in the more distant future. There are two different way s in which astrometric microlensing signals can be used to infer informatio n: one possibility is to perform astrometric follow-up observations on phot ometrically detected microlensing events, and the other is to perform a sur vey based on astrometric observations alone. After the predictable effects of the Sun and the planets, stars in the Galactic disk play the dominant ro le in astrometric microlensing. The probability that the disk stars introdu ce a centroid shift larger than the threshold delta(T) at a given time for a given source in the Galactic bulge toward Baade's window reaches 100% for a threshold of delta(T) = 0.7 mu as, while this probability is similar to 2% for delta(T) = 5 mu as. However, this centroid shift does not vary much during the time in which a typical photometric microlensing event differs f rom baseline. So astrometric follow-ups (e.g., with SIM) are not expected t o be disturbed by the statistical astrometric microlensing due to disk star s, so that it is possible to infer additional information about the nature of the lens that caused the photometric event, as suggested. The probabilit y of observing astrometric microlensing events within the Galaxy turns out to be large compared to photometric microlensing events. The probability of seeing a variation by more than 5 mu as within 1 yr and reaching the close st angular approach between lens and source is similar to 10(-4) for a bulg e star toward Baade's window, while this reduces to similar to 6 x 10(-6) f or a direction perpendicular to the Galactic plane. For the upcoming missio n GAIA, we expect similar to 1000 of the observed stars to show a detectabl e astrometric microlensing signal within its 5 yr lifetime. These events ca n be used to determine accurate masses of the lenses, and to derive the mas s and the scale parameters (length and height) of the Galactic disk.