Observational Evidence for the Effect of Amplification Bias in Gravitational Microlensing Experiments

Abstract

Recently Alard, Mao, & Guibert and Alard proposed to detect the shift of a star's image centroid, δx, as a method to identify the lensed source among blended stars. Goldberg & Woźniak actually applied this method to the OGLE-1 database and found that seven of 15 events showed significant centroid shifts of δx 02. 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 δx 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 MI ~ 9.0 (MV ~ 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 & Woźniak confirm the prediction of Han & Alard that a large fraction of Galactic bulge events are affected by amplification-bias blending.