Robust modeling of quadruply lensed quasars (and random quartets) using Witt's hyperbola

Understand

We develop a robust method to model quadruply lensed quasars, relying heavily on the work of Witt (1996), who showed that for elliptical potentials, the four image positions, the source, and the lensing galaxy lie on a right hyperbola.

• For the singular isothermal elliptical potential, there exists a complementary ellipse centered on the source which also maps through the four images, with the same axis ratio as the potential but perpendicular to it.
• We first solve for Witt's hyperbola, reducing the allowable space of models to three dimensions.
• We then obtain the best fitting complementary ellipse.