Kavli Affiliate: Paul L. Schechter

| First 5 Authors: Paul L. Schechter, Raymond A. Wynne, , ,

| Summary:

Witt (1996) has shown that for an elliptical potential, the four images of a

quadruply lensed quasar lie on a rectangular hyperbola that passes through the

unlensed quasar position and the center of the potential as well. Wynne and

Schechter (2018) have shown that, for the singular isothermal elliptical

potential (SIEP), the four images also lie on an `amplitude’ ellipse centered

on the quasar position with axes parallel to the hyperbola’s asymptotes. Witt’s

hyperbola arises from equating the directions of both sides of the lens

equation. The amplitude ellipse derives from equating the magnitudes. One can

model any four points as an SIEP in three steps. 1. Find the rectangular

hyperbola that passes through the points. 2. Find the aligned ellipse that also

passes through them. 3. Find the hyperbola with asymptotes parallel to those of

the first that passes through the center of the ellipse and the pair of images

closest to each other. The second hyperbola and the ellipse give an SIEP that

predicts the positions of the two remaining images where the curves intersect.

Pinning the model to the closest pair guarantees a four image model. Such

models permit rapid discrimination between gravitationally lensed quasars and

random quartets of stars.

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