Source blending effects on microlensing time-histograms and optical depth determination

Abstract

Source blending in microlensing experiments is known to modify the Einstein time of the observed events. In this paper, we have conducted Monte-Carlo calculations, using analytical relationships to quantify the effect of blending on the observed event time distribution and optical depth. We show that short events are affected significantly by source blending and that, for moderately blended sources, the optical depth τ is globally overestimated, because of an underestimation of the exposure. For high blending situations, on the other hand, blending leads to an under estimation of the optical depth. Our results are in agreement with the most recent optical depth determinations toward the Galactic Center of the MACHO and OGLE-II collaborations that use clump giants (less affected by the blending effect) as sources. The blending-corrected, lower optical depth toward the Galactic Bulge is now in good agreement with the value inferred from galactic models, reconciling theoretical and observational determinations.