Isothermal elliptical gravitational lens models

Details Isothermal elliptical gravitational lens models Isothermal elliptical gravitational lens models

Apr 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...284..285k&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 284, no. 1, p. 285-299

Other

177

Astronomical Models, Ellipsoids, Gravitational Lenses, Isothermal Processes, Mass Distribution, Critical Velocity, Distortion, Finite Difference Theory, Vector Analysis

Scientific paper

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 mass follows light. Elliptical mass distributions are also expected on theoretical grounds. On the other hand, since elliptical matter distributions are in general more difficult to handle, quasi-elliptical lens models, in which the isopotential curves are ellipses or in which an external shear component is added onto a spherical deflector, are often used for model fitting or for statistical lens studies. However, elliptical 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 'isothermal' ellipsoids. Their mattter distribution forms a natural generalization 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 particularly easy. We derive the critical curves and caustics of these isothermal elliptical lens models and obtain a complete classification of the topologies of the critical curves and the caustics. Cross sections for multiple imaging are derived. Especially the singular isothermal ellipsoid provides a very convenient lens model, which is not much more complicated to handle than quasi-elliptical models, and we expect that the explicit equations derived here will be useful for future work.

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