Caustics, critical curves and cross-sections for gravitational lensing by disc galaxies

We study strong gravitational lensing by spiral galaxies, modelling them as infinitely thin uniform discs embedded in singular isothermal spheres. We derive general properties of the critical curves and caustics analytically. The multiple-image cross-section is a sensitive function of the inclination angle of the disc relative to the observer. We compute the inclination-averaged cross-section for several sets of lensing parameters. For realistic disc mass and size parameters, we find that the cross-section for multiple imaging is increased by only a modest factor, and that no dramatic increase in the optical depth for strong lensing of QSOs would be expected. However, the cross-section for high magnifications is significantly increased due to the inclusion of a disc, especially for nearly edge-on configurations; due to the strong observational selection effects favouring high magnifications, there might be significant consequences for lensing statistics.