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The positions of multiple images in galaxy lenses are related to the galaxymass distribution. Smooth elliptical mass profiles were previously shown to beinadequate in reproducing the quad population. In this paper, we explore thedeviations from such smooth elliptical mass distributions. Unlike most otherwork, we use a model-free approach based on the relative polar image angles ofquads, and their position in 3D space with respect to the Fundamental Surfaceof Quads. The FSQ is defined by quads produced by elliptical lenses. We havegenerated thousands of quads from synthetic populations of lenses withsubstructure consistent with $\Lambda$CDM simulations, and found that suchperturbations are not sufficient to match the observed distribution of quadsrelative to the FSQ. The result is unchanged even when subhalo masses areincreased by a factor of ten, and the most optimistic lensing selection bias isapplied. We then produce quads from galaxies created using two components,representing baryons and dark matter. The transition from the mass beingdominated by baryons in inner radii to being dominated by dark matter in outerradii can carry with it asymmetries, which would affect relative image angles.We run preliminary experiments using lenses with two elliptical mass componentswith nonidentical axis ratios and position angles, perturbations fromellipticity in the form of nonzero Fourier coefficients $a_4$ and $a_6$, andartificially offset ellipse centers as a proxy for asymmetry at image radii. Weshow that combination of these effects is a promising way of accounting forquad population properties. We conclude that the quad population provides aunique and sensitive tool for constraining detailed mass distribution in thecenters of galaxies.

The impact of $\Lambda$CDM substructure and baryon-dark matter transition on the image positions of quad galaxy lenses