The MACHO Project: Microlensing Optical Depth toward the Galactic Bulge from Difference Image Analysis

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Abstract
We present the microlensing optical depth toward the Galactic bulge based on the detection of 99 events found in our Difference Image Analysis (DIA) survey. This analysis encompasses 3 yr of data, covering ~17 million stars in ~4 deg2, to a source-star baseline magnitude limit of V = 23. The DIA technique improves the quality of photometry in crowded fields, and allows us to detect more microlensing events with faint source stars. We find that this method increases the number of detection events by 85% compared with the standard analysis technique. DIA light curves of the events are presented, and the microlensing fit parameters are given. The total microlensing optical depth is estimated to be τtotal = 2.43 × 10-6, averaged over eight fields centered at l = 268 and b = -335. For the bulge component, we find τbulge = 3.23 × 10-6, assuming a 25% stellar contribution from disk sources. These optical depths are in good agreement with the past determinations of the MACHO and OGLE groups, and are higher than predicted by contemporary Galactic models. We show that our observed event timescale distribution is consistent with the distribution expected from normal mass stars, if we adopt the Scalo stellar mass function as our lens mass function. However, we note that since there is still disagreement about the exact form of the stellar mass function, there is uncertainty in this conclusion. Based on our event timescale distribution, we find no evidence for the existence of a large population of brown dwarfs in the direction of the Galactic bulge.