The Maximum Optical Depth toward Bulge Stars from Axisymmetric Models of the Milky Way

It has been known that recent microlensing results toward the bulge imply mass densities that are surprisingly high, given dynamical constraints on the Milky Way mass distribution. We derive the maximum optical depth toward the bulge that may be generated by axisymmetric structures in the Milky Way, and we show that observations are close to surpassing these limits. This result argues in favor of a bar as a source of significantly enhanced microlensing. Several of the bar models in the literature are discussed.