The microlensing optical depth of the COBE bulge

We examine the left-right asymmetry in the cleaned COBE/DIRBE near-infrared data of the inner Galaxy and show (i) that the Galactic bar is probably not seen very nearly end-on, and (ii) that, even if it is, it is not highly elongated. The assumption of constant mass-to-light ratio is used to derive simulated terminal velocity plots for the ISM from our model luminosity distributions. By comparing these plots with observed terminal velocities, we determine the mass-to-light ratio of the near-infrared bulge and disc. Assuming that all this mass contributes to gravitational microlensing, we compute optical depths tau for microlensing in Galactic Centre fields. For three models with bar major axis between 10 degrees and 25 degrees from the Sun-Galactic Centre line, the resulting optical depths in Baade's window lie in the range 0.83 x 10(-6) less than or similar to tau less than or similar to 0.89 x 10(-6) for main-sequence stars and 1.2 x 10(-6) less than or similar to tau less than or similar to 1.3 x 10(-6) for red clump giants. We discuss a number of uncertainties, including possible variations of the near-infrared mass-to-light ratio. We conclude that, although the values predicted from analysing the COBE and gas velocity data are inconsistent at the 2 -2.5 sigma level with recent observational determinations of 7, we believe that they should be taken seriously.