Identifying lenses with small-scale structure. I. Cusp lenses

The inability of standard models to explain the flux ratios in many four-image gravitational lens systems has been presented as evidence for significant small-scale structure in lens galaxies. That claim has generally relied on detailed lens modeling, so it is both model dependent and somewhat difficult to interpret. We present a more robust and generic method for identifying lenses with small-scale structure. For a close triplet of images created when the source lies near an ideal cusp catastrophe, the sum of the signed magnifications should exactly vanish, independent of any global properties of the lens potential. For realistic cusps, the magnification sum vanishes only approximately, but we show that it is possible to place strong upper bounds on the degree to which the magnification sum can deviate from zero. Lenses with flux ratio anomalies, or fluxes that significantly violate the upper bounds, can be said with high confidence to have structure in the lens potential on scales of the image separation or smaller. Five observed lenses have such flux ratio anomalies: B2045+265 has a strong anomaly at both radio and optical/near-IR wavelengths; B0712+472 has a strong anomaly at optical/near-IR wavelengths and a marginal anomaly at radio wavelengths; 1RXS J1131-1231 has a strong anomaly at optical wavelengths; RXJ0911+0551 appears to have an anomaly at optical/near-IR wavelengths, although the conclusion in this particular lens is subject to uncertainties in the typical strength of octopole density perturbations in early-type galaxies; and finally, SDSS J0924+0219 has a strong anomaly at optical wavelengths. Interestingly, analysis of the cusp relation does not reveal a significant anomaly in B1422+231, even though this lens is known to be anomalous from detailed modeling. Methods that are more sophisticated (and less generic) than the cusp relation may therefore be necessary to uncover flux ratio anomalies in some systems. Although these flux ratio anomalies might represent either millilensing or microlensing, we cannot identify the cause of the anomalies using only broadband flux ratios in individual lenses. Rather, the conclusion we can draw is that the lenses have significant structure in the lens potential on scales comparable to or smaller than the separation between the images. Additional arguments must be invoked to specify the nature of this small-scale structure.