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With high-quality data from programs like the Hubble Frontier Fields, cluster lensing has reached the point that models are dominated by systematic rather than statistical uncertainties. We introduce a Bayesian framework to quantify systematic effects by determining how different lens modelling choices affect the results. Our framework includes a new two-sample test for quantifying the difference between posterior probability distributions that are sampled by methods like Monte Carlo Markov chains. We use the framework to examine choices related to the selection and treatment of cluster member galaxies in two of the Frontier Field clusters: Abell 2744 and MACS J0416.1–2403. When selecting member galaxies, choices about depth and area affect the models; we find that model results are robust for an I-band magnitude limit of mlim ≥ 22.5 mag and a radial cut of rlim ≥ 90 arcsec (from the centre of the field), although the radial limit likely depends on the spatial extent of lensed images. Mass is typically assigned to galaxies using luminosity/mass scaling relations. We find that the slopes of the scaling relations can have significant effects on lens model parameters but only modest effects on lensing magnifications. Interestingly, scatter in the scaling relations affects the two fields differently. This analysis illustrates how our framework can be used to analyse lens modelling choices and guide future cluster lensing programs.

Cluster lens models are affected by a variety of choices in the lens modelling process. We have begun a programme to develop a systematic error budget for cluster lens modelling. Here, we examine the selection of image constraints as a potential systematic effect. For constraining the mass model, we find that it is more important to have images be spatially distributed around the cluster than to have them distributed in redshift. We also find that some image sets appear to be more important than others in terms of how well they constrain the models; the ‘important’ image sets typically include an image that lies close to a lensing critical curve as well as an image that is relatively isolated from other images (providing constraints in a region that would otherwise lack lensing information). These conclusions can help guide observing programmes that seek follow-up data for candidate lensed images.

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 two-dimensional, 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 three-dimensional 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 0.1-0.4", a non-negligible fraction of the typical 0.3-0.7" residuals of current state-of-the-art models. We also find that median image magnifications can shift by up to 6%, 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% magnification bias still exists in other cases; image position offsets are also improved, but are still present at 0.10"., Comment: 26 pages, 9 figures, 14 tables. Accepted for publication in MNRAS

Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the parameter space. I study the statistical uncertainty in the evidence computed with nested sampling. I examine the uncertainty estimator from Skilling and introduce a new estimator based on a detailed analysis of the statistical properties of nested sampling. Both perform well in test cases and make it possible to obtain the statistical uncertainty in the evidence with no additional computational cost.

[Abridged] Many current and future astronomical surveys will rely on samples of strong gravitational lens systems to draw conclusions about galaxy mass distributions. We use a new strong lensing pipeline (presented in Paper I of this series) to explore selection biases that may cause the population of strong lensing systems to differ from the general galaxy population. Our focus is on point-source lensing by early-type galaxies with two mass components (stellar and dark matter) that have a variety of density profiles and shapes motivated by observational and theoretical studies of galaxy properties. We seek not only to quantify but also to understand the physics behind selection biases related to: galaxy mass, orientation and shape; dark matter profile parameters such as inner slope and concentration; and adiabatic contraction. We study how all of these properties affect the lensing Einstein radius, total cross-section, quad/double ratio, and image separation distribution. We find significant (factors of several) selection biases with mass; orientation, for a given galaxy shape at fixed mass; cusped dark matter profile inner slope and concentration; concentration of the stellar and dark matter deprojected Sersic models. Interestingly, the intrinsic shape of a galaxy does not strongly influence its lensing cross-section when we average over viewing angles. Our results are an important first step towards understanding how strong lens systems relate to the general galaxy population., 26 pages, 15 figures; paper I at arXiv:0808.2493; accepted for publication in MNRAS (minor revisions); PDF file with full resolution figures at http://www.sns.ias.edu/~rmandelb/paper2.pdf

In strong gravitational lensing, the multiple images we see correspond to light rays that leave the source in slightly different directions. If the source emission is anisotropic, the images may differ from conventional lensing predictions (which assume isotropy). To identify scales on which source anisotropy may be important, we study the angle delta between the light rays emerging from the source, for different lensing configurations. If the lens has a power law profile M propto R^gamma, the angle delta initially increases with lens redshift and then either diverges (for a steep profile gamma1) as zl approaches zs. The scaling with lens mass is roughly delta propto M^(1/(2-gamma)). The results for an NFW profile are qualitatively similar to those for a shallow power law, with delta peaking at about half the redshift of the source (not half the distance). In practice, beaming could modify the statistics of beamed sources lensed by massive clusters: for an opening angle theta_jet, there is a probability as high as P ~ 0.02-0.07 (theta_jet/{0.5} deg)^-1 that one of the lensed images may be missed (for 2 < zs < 6). Differential absorption within Active Galactic Nuclei could modify the flux ratios of AGNs lensed by clusters; a sample of AGNs lensed by clusters could provide further constraints on the sizes of absorbing regions. Source anisotropy is not likely to be a significant effect in galaxy-scale strong lensing., minor changes, accepted to MNRAS

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]

We report the discovery of a fifth image in the large separation lensed quasar system SDSS J1004+4112. A faint point source located 0.2'' from the center of the brightest galaxy in the lensing cluster is detected in images taken with the Advanced Camera for Surveys (ACS) and the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) on the Hubble Space Telescope. The flux ratio between the point source and the brightest lensed component in the ACS image is similar to that in the NICMOS image. The location and brightness of the point source are consistent with lens model predictions for a lensed image. We therefore conclude that the point source is likely to be a fifth image of the source quasar. In addition, the NICMOS image reveals the lensed host galaxy of the source quasar, which can strongly constrain the structure of the lensing critical curves and thereby the mass distribution of the lensing cluster., 5 pages, 5 figures, accepted for publication in PASJ