Using Quadruple Lenses to Probe the Structure of the Lensing Galaxy

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Abstract
We show here that quadruple lenses can be useful laboratories to probe whether the potential of the lensing galaxy is purely elliptical or whether an additional distortion is present in the deflector plane. For this test we only have to know the relative image positions of the quadruple lens system and the (relative) center of light position of the lensing galaxy. Furthermore, we introduce new methods that easily allow us to determine the location (rotation angle relative to the image positions) of the major axis of the lensing galaxy. In due course, we can determine the parity of the four images as well. We apply these methods to the eight currently known quadruple lenses and find that in the case of MG 0414+0534, CLASS 1608+656, and HST 12531-2914 it is impossible to accommodate the relative image positions and the galaxy position with any elliptical potential, whereas the other five cases can be described very well with a simple elliptical potential. This method will have important impacts for χ2 fits and the reconstruction of galaxy models for quadruple lenses.
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