Microlensing Optical Depth toward the Galactic Bulge Using Bright Sources from OGLE-II

We present a measurement of the microlensing optical depth toward the Galactic bulge based on 4 years of the OGLE-II survey. We consider only bright sources in the extended red clump giant (RCG) region of the color-magnitude diagram, in 20 bulge fields covering ~5 deg² between 0° < l < 3° and -4° < b < -2°. Using a sample of 32 events we find τ = 2.55 × 10^-6 at (l, b) = (116, - 275). Taking into account the measured gradient along the Galactic latitude b, τ = [(4.48 ± 2.37) + (0.78 ± 0.84) × b] × 10^-6, this value is consistent with previous measurements using RCG sources and recent theoretical predictions. We determine the microlensing parameters and select events using a model light curve that allows for flux blending. Photometric quality delivered by difference image analysis (DIA) combined with the 13 median seeing of the OGLE-II images are sufficient to constrain and reject the majority of strong blends. We find that ~38% of the OGLE-II events that appear to have RCG sources are actually due to much fainter stars blended with a bright companion. We show explicitly that model fits without blending result in similar τ estimates through partial cancellation of contributions from higher detection efficiency, underestimated timescales, and a larger number of selected events. The near cancellation of the optical depth bias and the fact that microlensing event selection based on models without blending discriminates against blends have been utilized by previous analyses based on RCG sources. The latter approach, however, leads to biased timescale distributions and event rates. Consequently, microlensing studies should carefully consider source confusion effects even for bright stars.