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arXiv · astro-ph/0211389

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

Hideki Asada·Takashi Hamana·Masumi Kasai
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Abstract

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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Hideki Asada, Takashi Hamana, Masumi Kasai. 2002-11-18. Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation. https://doi.org/10.1051/0004-6361%3A20021599

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