Astrometric Microlensing of Stars

Due to dramatic improvements in the precision of astrometric measurements, the observation of light centroid shifts in observed stars due to intervening massive compact objects ('astrometric microlensing') will become possible in the near future.Upcoming space missions, such as SIM and GAIA, will provide measurements with an accuracy of 4-60 µas depending on the magnitude of the observed stars, and an accuracy of ∼ 1 µas is expected to be achieved in the more distant future.There are two different ways in which astrometric microlensing signals can be used to infer information: one possibility is to perform astrometric follow-up observations on photometrically detected microlensing events, and the other is to perform a survey based on astrometric observations alone.After the predictable effects of the Sun and the planets, stars in the Galactic disk play the dominant role in astrometric microlensing.The probability that the disk stars introduce a centroid shift larger than the threshold δ T at a given time for a given source in the Galactic bulge towards Baade's window reaches 100% for a threshold of δ T = 0.7 µas, while this probability is ∼ 2% for δ T = 5 µas.However, this centroid shift does not vary much during the time in which a typical photometric microlensing event differs from baseline.So astrometric followups (e.g. with SIM) are not expected to be disturbed by the statistical astrometric microlensing due to disk stars, so that it is possible to infer additional information about the nature of the lens that caused the photometric event, as suggested.The probability to observe astrometric microlensing events within the Galaxy turns out to be large compared to photometric microlensing events.The probability to see a variation by more than 5 µas within one year and to reach the closest angular approach between lens and source is ∼ 10 -4 for a bulge star towards Baade's window, while this reduces to ∼ 6 • 10 -6 for a direction perpendicular to the Galactic plane.For the upcoming mission GAIA, we expect ∼ 1000 of the observed stars to show a detectable astrometric microlensing signal within its 5 year lifetime.These events can be used to determine accurate masses of the lenses, and to derive the mass and the scale parameters (length and height) of the Galactic disk.