The Influence of Core Radius on Gravitational Lensing by Elliptical Lenses

We model a galaxy lens by means of a simple analytical potential with three parameters: velocity dispersion, ellipticity, and core radius. We compute lensing cross sections for a wide range of these parameters and integrate over the distributions of velocity dispersion and ellipticity appropriate to galaxies. The model predictions are in good agreement with the observations. The number of lensed quasars as a function of apparent magnitude and the relative numbers of doubly imaged and quadruply imaged quasars are predicted satisfactorily. Magnification bias is found to be extremely large at bright magnitudes, particularly for quadruply imaged configurations. The presence of an even number of images in nearly all examples of multiply imaged quasars discovered so far, despite the odd number expected theoretically, can be explained through demagnification of an image in the core of the lens. This requires lens core radii to be smaller than about 200 pc.