Microlensing Events: End of the Dark Halo?

I obtain an upper limit for the optical depth to microlensing toward Baade’s Window of $3\times {10}^{-6}$ by assuming that all of the mass of the Galaxy interior to the Sun (and not in the bulge) is in a disk. The exponential scale height of the disk is left as a completely arbitrary function of radius and is varied to maximize the optical depth. I take account of the relatively small corrections induced by the fact that the bulge is not axisymmetric. If initial estimates by the OGLE collaboration of an observed optical depth $\tau\sim 3.3\times 10^{-6}$ are confirmed, then essentially all of the dark matter interior to the Sun must be in a disk with a scale height of a few hundred parsecs.