Shape Degeneracies: the likely culprit for the differences between lens mass models of galaxy clusters

Sky-projected mass distributions of galaxy clusters are widely used to constrain particle properties of dark matter, to magnify in flux and angular extent high redshift background galaxies, and to construct their luminosity function down to faint absolute magnitudes that are otherwise hard or impossible to reach. Obtaining accurate and precise mass maps of clusters is therefore of central importance for these studies. Yet, a visual inspection of any two mass maps of the same cluster shows that the shapes of their isodensity contours are often dissimilar in detail on <30kpc scales, and there is no simple relation connecting the two. These differences are due to systematic uncertainties in reconstructions, which are in turn due to lensing degeneracies. However, commonly known degeneracies, like the mass sheet degeneracy or the source position transformation cannot account for most of these differences, implying that more generalized shape degeneracies are responsible. In this paper we study shape degeneracies using an analytical approach. We conclude with three main takeaways: (i) Shape degeneracies are the likely cause of differences in the mass maps of cluster lenses recovered by different techniques. (ii) Shape degeneracies are significantly suppressed in regions of the lens plane that have tight groupings of lensed images. (iii) In clusters where image numbers are high, such as MACS J0416, their effect on time delays between images from the same source are generally small, of order 1%, but can reach 10% for some multiply imaged background sources, affecting the determination of H 0.