Using a high resolution radio image, we successfully resolve the two fold image components B and C of the quasar lens system SDSS J1029+2623. The flux anomalies associated with these two components in the optical regime persist, albeit less strongly,
in our radio observations, suggesting that the cluster must be modeled by something more than a single central potential. We argue that placing substructure close to one of the components can account for a flux anomaly with negligible changes in the component positions. Our best fit model has a substructure mass of ~10^8 solar masses up to the mass-sheet degeneracy, located roughly 0.1 arcsecs West and 0.1 arcsecs North of component B. We demonstrate that a positional offset between the centers of the source components can explain the differences between the optical and radio flux ratios.
We develop a new approach for studying flux anomalies in quadruply-imaged fold lens systems. We show that in the absence of substructure, microlensing, or differential absorption, the expected flux ratios of a fold pair can be tightly constrained usi
ng only geometric arguments. We apply this technique to 11 known quadruple lens systems in the radio and infrared, and compare our estimates to the Monte Carlo based results of Keeton, Gaudi, and Petters. We show that a robust estimate for a flux ratio from a smoothly varying potential can be found, and at long wavelengths those lenses deviating from from this ratio almost certainly contain significant substructure.
