Galaxies as gravitational lenses: Realistic models

Abstract

The gravitational lens effects associated with a transparent mass distribution are quite different from those of the well-known opaque sphere. We have shown that any spherical galaxy whose mass distribution, when projected onto the plane of the sky, decreases outward from the center of the galaxy and diverges less rapidly than 1/h ash→0, must always produce an odd number of images, usually one or three, of a source located behind the galaxy. Using optical scalar techniques, the amplification of each image can readily be obtained. For a given source and galaxy, we can define a dimensionless focal length, a function of impact parameter, and a dimensionless distance factor, depending on lens parameters and source distance. The central value of the ratio of these quantities determines the multiplicity of the images. The mass distribution of the galaxy is a crucial function, and we show in some detail how this affects the various focal lengths.