Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation

Details Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation

2002-11-18

arxiv.org/abs/astro-ph/0211389v1

Astron.Astrophys. 397 (2003) 825

Astronomy and Astrophysics

Astrophysics

5 pages; accepted for publication in A&A

Scientific paper

10.1051/0004-6361:20021599

We present explicit expressions for the lens equation for a cored isothermal ellipsoidal gravitational lens as a single real sixth-order algebraic equation in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar ones. We find a condition for physical solutions which correspond to at most five images. For a singular isothermal ellipsoid, the sixth-order equation is reduced to fourth-order one for which analytic solutions are well-known. Furthermore, we derive analytic criteria for determining the number of images for the singular lens, which give us simple expressions for the caustics and critical curves. The present formulation offers a useful way for studying galaxy lenses frequently modeled as isothermal ellipsoids.

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