Finite source effects in strong lensing: implications for the substructure mass scale

Flux ratio `anomalies' in quadruply-imaged gravitational lenses can be explained with galactic substructure of the sort predicted by CDM, but the strength and uniqueness of that hypothesis needs to be further assessed. A good way to do that is to use the physical scale associated with the size of the source quasar, and its dependence on wavelength. We develop an analytic toy model to study finite source effects in substructure lensing and identify general principles. We find that image positions and magnifications are basically independent of source size until the source is large enough to intersect a substructure caustic. Even sources that are much larger than the substructure Einstein radius can be perturbed at a detectable level. A tremendous amount could be learned by comparing image positions and magnifications at wavelengths that correspond to different source sizes. In a separate analysis, we carefully study four observed radio lenses to determine which of the images are anomalous. In B0712+472, if the flux ratio anomaly is real it is probably in image C. In B1422+231, the anomaly is in image A. Interestingly, B2045+265 and B1555+375 both appear to have two anomalous images. It remains to be seen whether CDM predicts enough substructure to explain multiple anomalies in multiple lenses. When we join our modeling results and substructure theory, we obtain lower bounds on the masses of the substructures responsible for the observed anomalies. The mass bounds are broadly consistent with expectations for CDM. Perhaps more importantly, we outline various systematic effects in the mass bounds; poor knowledge of whether the substructure lies within the main lens galaxy or elsewhere along the line of sight appears to be the dominant systematic. [Abridged]