Kavli Affiliate: Michael A. McDonald
| First 5 Authors: Nixon Hanna, Nixon Hanna, , ,
| Summary:
For any elliptical potential with an external parallel shear, Witt has proven
that the gravitational center lies on a rectangular hyperbola derived from the
image positions of a single quadruply lensed object. Moreover, it is predicted
that for an isothermal elliptical potential the source position both lies on
Witt’s Hyperbola and coincides with the center of Wynne’s Ellipse (fitted
through the four images). Thus, by fitting Witt’s Hyperbolae to several
quartets of images – ten are known in Abell 1689 – the points of intersection
provide an estimate for the center for the assumed isothermal elliptical
potential. We introduce a new figure of merit defined by the offset of the
center of Wynne’s Ellipse from Witt’s Hyperbola. This offset quantifies
deviations from an ideal elliptical isothermal potential and serves as a
discriminant to exclude poorly fitted quadruples and assign greater weight to
intersections of hyperbolae of better fitting systems. Applying the method to
10 quads (after excluding 7 poorly fitted quads) in Abell 1689, we find the
potential is centered within 11" of the BCG, X-ray center, flexion-based center
and the center found from a total strong lensing analysis. The Wynne-Witt
framework thus delivers a fast, analytic, and self-consistency-checked
estimator for centers in clusters with multiple quads.
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