Lens Models Under the Microscope: Comparison of Hubble Frontier Field
  Cluster Magnification Maps
  Using the power of gravitational lensing magnification by massive galaxy
clusters, the Hubble Frontier Fields provide deep views of six patches of the
high redshift Universe. The combination of deep Hubble imaging and exceptional
lensing strength has revealed the greatest numbers of multiply-imaged galaxies
available to constrain models of cluster mass distributions. However, even with
$\mathcal{O}(100)$ images per cluster, the uncertainties associated with the
reconstructions are not negligible. The goal of this paper is to show the
diversity of model magnification predictions. We examine 7 and 9 mass models of
Abell 2744 and MACS J0416, respectively, submitted to the Mikulski Archive for
Space Telescopes for public distribution in September 2015. The dispersion
between model predictions increases from 30% at common low magnifications
($\mu\sim2$) to 70% at rare high magnifications ($\mu\sim40$). MACS J0416
exhibits smaller dispersions than Abell 2744 for $2<\mu<10$. We show that
magnification maps based on different lens inversion techniques typically
differ from each other by more than their quoted statistical errors. This
suggests that some models underestimate the true uncertainties, which are
primarily due to various lensing degeneracies. Though the exact mass sheet
degeneracy is broken, its generalized counterpart is not broken at least in
Abell 2744. Other, local degeneracies are also present in both clusters. Our
comparison of models is complementary to the comparison of reconstructions of
known synthetic mass distributions. By focusing on observed clusters, we can
identify those that are best constrained, and therefore provide the clearest
view of the distant Universe.
