The implications of lenses for galaxy structure

The 12 possible cases of lensing by isolated galaxies are inverted using a set of five simple models. The set includes five lenses with four images, four with two images, and three radio rings. The image positions for all of the point image lenses are satisfied to within observational errors by any of five simple models: fits to the image positions cannot distinguish between a galaxy which is a point mass or a singular isothermal sphere, or a quadrupole moment generated entirely inside or entirely outside the area containing the images. The four image lenses and the rings tightly constrain the mass inside the ring of images, and the ellipticities, orientations, and positions to a lesser extent. The greatest systematic effects are associated with the radial structure of the quadrupole moment of the lens; models with the same quadrupole tend to require the same ellipticities, orientations, and positions even after drastic changes in the structure of the monopole. The variations of the results can be dominated by either observational errors or systematic errors associated with the choice of a model potential, depending on the morphology of the images.