Simple lens models

Abstract

The principal aim of GL theory is to determine which pairs, consisting of a deflecting mass distribution and a source, can lead to a given (e.g., observed) configuration of images. To approach the answer, one first chooses some simple, plausible mass distributions and studies the inversions of the corresponding lens mappings, i.e., one searches for all points ξ which solve the equation for a given source position η. As mentioned before, this is a nontrivial task in general, that has been carried out analytically only for special mass distributions of the lens. In general, one has to rely on numerical calculations; several methods are described in Chap. 10. Here, we concentrate on the simplest models which can be treated analytically. An understanding of these simple models is essential for the application of numerical methods, partly because the number of images is not known a priori for a given source position. It is therefore dangerous to use a numerical routine, e.g., for root searching, as a black box without useful estimates of the possible results.