Witt's hyperbola is both predicted and observed to pass close to the lensing galaxies in quadruple quasars

Abstract

When a rectangular hyperbola is constructed from the image positions of a quadruply lensed quasar, as proposed by Witt (1996), it passes very close to the the lensing galaxy. The median measured perpendicular offset between the observed light center of the lens and Witt's hyperbola is 0.013" for a sample for 39 systems lensed by a relatively isolated galaxy. The family of lens models adopted by Witt predicts that the lens lies on the hyperbola, but its position in not used for its construction. The median offset corresponds to roughly 1% of the Einstein ring radius, and suggests that the centers of the lensing potential are close to the light centers of the lens. By putting a restrictive prior on the perpendicular distance to Witt's hyperbola (or on the distance between the galaxy and the potential), one reduces by one the dimensionality of a model space when fitting data. Taking the brightest pixel of a lensing galaxy as its center avoids a shortcoming of using the average light center for a constraint.