Observational evidence for the effect of amplification bias in gravitational microlensing experiments

Recently Alard, Mao, & Guibert and Alard proposed to detect the shift of a star's image centroid, delta x, as a method to identify the lensed source among blended stars. Goldberg & Wozniak actually applied this method to the OGLE-1 database and found that seven of 15 events showed significant centroid shifts of delta x greater than or similar to 0." 2. The amount of centroid shift has been estimated theoretically by Goldberg; however, he treated the problem in general and did not apply it to a particular survey or field and therefore based his estimate on simple toy model luminosity functions (i.e., power laws). In this paper, we construct the expected distribution of delta x for Galactic bulge events based on the precise stellar luminosity function observed by Holtzman et al. using the Hubble Space Telescope. Their luminosity function is complete up to M-I similar to 9.0 (M-V similar to 12), which corresponds to faint M-type stars. In our analysis we find that regular blending cannot produce a large fraction of events with measurable centroid shifts. By contrast, a significant fraction of events would have measurable centroid shifts if they are affected by amplification-bias blending. Therefore, the measurements of large centroid shifts for an important fraction of microlensing events of Goldberg & Wozniak confirm the prediction of Han & Alard that a large fraction of Galactic bulge events are affected by amplification-bias blending.