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Cluster lensing has become an important tool in the search for high-redshift galaxies through its ability to magnify sources. In order to determine the intrinsic properties of these galaxies, lensing mass models must be constructed to determine the magnification of the images. These models are traditionally 2D, focusing on the mass within the cluster and either ignoring or approximating any contribution from line-of-sight galaxies. In this paper, we present the first full set of 3D mass models of the six Hubble Frontier Fields and use them to test for systematic biases in magnifications due to using the traditional 2D approach. We find that omitting foreground or background galaxies causes image position offsets between 0.1 and 0.4 arcsec, a non-negligible fraction of the typical 0.3–0.7 arcsec residuals of current state-of-the-art models. We also find that median image magnifications can shift by up to 6 per cent, though it is dependent on the field. This can be alleviated in some cases by approximating the mass in the lensing plane, but a 5 per cent magnification bias still exists in other cases; image position offsets are also improved, but are still present at 0.10 arcsec. [ABSTRACT FROM AUTHOR]

ABSTRACT We investigate the properties of dark matter substructure in the gravitational lens HE 0435−1223 ( zl=0.455) via its effects on the positions and flux ratios of the quadruply imaged background quasar ( zs= 1.689). We start with a smooth mass model, add individual, truncated isothermal clumps near the lensed images and use the Bayesian evidence to compare the quality of different models. Compared with smooth models, models with at least one clump near image A are strongly favoured. The mass of this clump within its Einstein radius is log10( MAEin) = 7.65+0.87− 0.84 (in units of h−170 M⊙). The Bayesian evidence provides weaker support for a second clump near image B, with log10( MBEin) = 6.55+1.01− 1.51. We also examine models with a full population of substructure, and find the mass fraction in substructure at the Einstein radius to be fsub> rsim 0.000 77, assuming the total clump masses follow a mass function d N/d M∝ M−1.9 over the range M= 107-1010 M⊙. Few-clump and population models produce similar Bayesian evidence values, so neither type of model is objectively favoured. [ABSTRACT FROM AUTHOR]

We study microlensing of the faint images that form close to the centres of strong gravitational lens galaxies. These central images, which have finally begun to yield to observations, naturally appear in dense stellar fields and may be particularly sensitive to fine granularity in the mass distribution. The microlensing magnification maps for overfocused (i.e. demagnified) images differ strikingly from those for magnified images. In particular, the familiar ‘fold’ and ‘cusp’ features of maps for magnified images are only present for certain values of the fraction f of the surface mass density contained in stars. For central images, the dispersion in microlensing magnifications is generally larger than for normal (minimum and saddle) images, especially when the source is comparable to or larger than the stellar Einstein radius. The dispersion depends in a complicated way on f; this behaviour may hold the key to using microlensing as a probe of the relative densities of stars and dark matter in the cores of distant galaxies. Quantitatively, we predict that the central image C in PMN J1632−0033 has a magnification dispersion of 0.6 mag for , or 0.3 mag for . For comparison, the dispersions are 0.5–0.6 mag for image B and 0.05–0.1 mag for image A, if ; and just 0.1 mag for B and 0.008 mag for A if . (The dispersions can be extrapolated to larger sources sizes as .) Thus, central images are more susceptible than other lensed images to microlensing and hence good probes for measuring source sizes. [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]