A generalisation of the mass-sheet degeneracy producing ring-like artefacts in the lens mass distribution

TL;DR

This paper generalizes the mass-sheet degeneracy in gravitational lensing, showing how circularly symmetric mass distributions can produce ring-like artifacts, complicating the unique reconstruction of lens mass profiles.

Contribution

It introduces a broader class of degeneracies involving circularly symmetric mass distributions, revealing the need for additional constraints to accurately determine lens mass.

Findings

Circularly symmetric mass distributions can mimic mass-sheet effects.

Ring-shaped features can arise from degeneracies in lens mass reconstructions.

Many observational constraints are necessary to break this degeneracy.

Abstract

The inversion of a gravitational lens system is, as is well known, plagued by the so-called mass-sheet degeneracy: one can always rescale the density distribution of the lens and add a constant-density mass-sheet such that the, also properly rescaled, source plane is projected onto the same observed images. For strong lensing systems, it is often claimed that this degeneracy is broken as soon as two or more sources at different redshifts are available. This is definitely true in the strict sense that it is then impossible to add a constant-density mass-sheet to the rescaled density of the lens without affecting the resulting images. However, often one can easily construct a more general mass distribution -- instead of a constant-density sheet of mass -- which gives rise to the same effect: a uniform scaling of the sources involved without affecting the observed images. We show that this can be achieved by adding one or more circularly symmetric mass distributions, each with its own center of symmetry, to the rescaled mass distribution of the original lens. As it uses circularly symmetric distributions, this procedure can lead to the introduction of ring shaped features in the mass distribution of the lens. In this paper, we show explicitly how degenerate inversions for a given strong lensing system can be constructed. It then becomes clear that many constraints are needed to effectively break this degeneracy.