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Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton, Gaudi & Petters, this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies. [ABSTRACT FROM AUTHOR]

Flux ratio ‘anomalies’ in quadruply imaged gravitational lenses can be explained with galactic substructure of the sort predicted by ΛCDM, but the strength and uniqueness of that hypothesis need 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 a toy model to study finite source effects in substructure lensing. Treating substructure as a singular isothermal sphere allows us to compute the images of a finite source analytically, and then to explore how the image configurations and magnifications depend on source position and size. Although simplified, our model yields instructive general principles: 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; and, most importantly, there is a tremendous amount to be learned from 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, the evidence for a radio flux ratio anomaly is marginal, but if the anomaly is real then image C is probably the culprit. In B1422+231, the anomaly is in image A. Interestingly, B2045+265 and B1555+375 both appear to have two anomalous images. Coincidentally, in each system one of the anomalies is in image C, and the other is in either image A or image B (both possibilities lead to acceptable models). It remains to be seen whether ΛCDM predicts enough substructure to explain multiple anomalies in multiple lenses. When we finally join our modelling 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 ΛCDM. 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. [ABSTRACT FROM AUTHOR]

We study the impact of lens galaxy environments on the image separation distribution of lensed quasars. We account for both environmental convergence and shear, using a joint distribution derived from galaxy formation models calibrated by galaxy–galaxy lensing data and number counts of massive elliptical galaxies. We find that the external field enhances lensing probabilities, particularly, at large image separations; the increase is ∼30 per cent at and ∼200 per cent at , when we adopt a power-law source luminosity function . The enhancement is mainly driven by convergence, which boosts both the image separation and magnification bias (for a fixed lens galaxy mass). These effects have been neglected in previous studies of lens statistics. Turning the problem around, we derive the posterior convergence and shear distributions and point out that they are strong functions of image separation; lens systems with larger image separations are more likely to lie in dense environments. [ABSTRACT FROM AUTHOR]