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Fig. 13.

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Linear dimensions and areas of caustics of the ellipsoidal NFW lens for five values of the convergence parameter κs indicated at the left side. Plotted as a function of ellipticity (bottom axis) and eccentricity (top axis) in the left column are: tangential-caustic horizontal (solid green) and vertical (dashed green) radii; radial-caustic horizontal (solid purple) and vertical (dashed purple) radii; convergence−1/2 ellipse semi-major axis (solid black). The intersection of the purple and green dashed curves marks the hyperbolic umbilic; the intersection of the purple and green solid curves marks the cusp-piercing transition. The middle column shows the areas enclosed by the tangential (green) and radial (purple) caustics and the total area inside the caustics (gray), which is equal to the radial-caustic area at eccentricities lower than the cusp piercing and equal to the tangential-caustic area at eccentricities higher than the hyperbolic umbilic. The right column includes similar plots showing the caustic areas yielding three (blue), five (magenta), and at least three (gray) point-source images.

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