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

TL;DR

This paper introduces a robust geometric method for modeling quadruply lensed quasars based on Witt's hyperbola, effectively distinguishing real lenses from random quartets using a figure of merit.

Contribution

The authors develop a new modeling approach leveraging Witt's hyperbola and complementary ellipse, improving the identification and analysis of quadruply lensed quasars.

Findings

Successfully modeled 29 known lenses with the method.

Can exclude 98% of random quartets with a 20% sacrifice in known lenses.

Provides a figure of merit to evaluate lens models.

Abstract

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. The simplest models of quadruple lenses require seven parameters to reproduce the observed image configurations, while the four positions give eight constraints. This leaves us one degree of freedom to use as a figure of merit. We applied our model to 29 known lenses, and include their figures of merit. We then modeled 100 random quartets. A selection criterion that sacrifices 20% of the known lenses can exclude 98% of the random quartets.