ISOTHERMAL ELLIPTIC GRAVITATIONAL LENS MODELS

Gravitational lens models for observed lensing systems are often based on quasi-elliptical lenses. The use of elliptical mass distributions is motivated by observations of galaxies and by the assumption that ma ss follows light. Elliptical mass distributions are also expected on t heoretical grounds. On the other hand, since elliptical matter distrib utions are in general more difficult to handle, quasi-elliptical lens models, in which the isopotential curves are ellipses or in which an e xternal shear component is added onto a spherical deflector, are often used for model fitting or for statistical lens studies. However, elli ptical potentials correspond to unphysical matter distributions if the ellipticity is large. In this paper we derive explicit lens equations for a special type of elliptical matter distributions, the 'isotherma l' ellipsoids. Their matter distribution forms a natural generalizatio n of isothermal spheres, one of the most commonly used models in lens theory. We consider the singular and the non-singular case. For both, the deflection angle is derived in closed form, and it is particularly simple for the singular case. The lens equation in the singular case can be reduced to a one-dimensional equation, making its solution part icularly easy. We derive the critical curves and caustics of these iso thermal elliptical lens models and obtain a complete classification of the topologies of the critical curves and the caustics. Cross section s for multiple imaging are derived. Especially the singular isothermal ellipsoid provides a very convenient lens model, which is not much mo re complicated to handle than quasi-elliptical models, and we expect t hat the explicit equations derived here will be useful for future work .