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ABSTRACT 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. 

ABSTRACT 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. 

ABSTRACT The Hubble Frontier Fields data, along with multiple data sets obtained by other telescopes, have provided some of the most extensive constraints on cluster lenses to date. Multiple lens modelling teams analyzed the fields and made public a number of deliverables. By comparing these results, we can then undertake a unique and vital test of the state of cluster lens modelling. Specifically, we see how well the different teams can reproduce similar magnifications and mass profiles. We find that the circularly averaged mass profiles of the fields are remarkably constrained (scatter $\lt 5{{\ \rm per\ cent}}$) at distances of 1 arcmin from the cluster core, yet magnifications can vary significantly. Averaged across the six fields, we find a bias of −6 per  cent (−17 per cent) and a scatter of ∼40 per cent (∼65 per cent) at a modest magnification of 3 (10). Statistical errors reported by individual teams are often significantly smaller than the differences among all the teams, indicating the importance of continued systematics studies in cluster lensing.