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Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation
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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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Identifying multiple images of gravitational-wave sources lensed by elliptical lensing potentials
For singular isothermal ellipsoid lenses that produce four gravitational-wave images, three-image search templates reduce waveform mismatch by roughly a factor of two to five relative to two-image templates, and geome...
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