Optical depth from realistic microlensing models of M31

We provide a set of microlensing optical depth maps for M31. Optical depths toward Andromeda were calculated on the basis of a four-component model of the lens and source populations: disk and bulge sources lensed by bulge, M 31 halo, and Galactic halo lenses. We confirm the high optical depth and th e strong optical depth gradient along the M31 minor axis due to a dark halo of lenses and also discuss the magnitude of the self-lensing due to the bu lge. We explore how the shape of the optical depth maps to M31 vary with th e halo parameters core radius and flattening.