A generalization of the masssheet degeneracy producing ringlike artefacts in the lens mass distribution
Abstract
The inversion of a gravitational lens system is, as is well known, plagued by the socalled masssheet degeneracy: one can always rescale the density distribution of the lens and add a constantdensity mass sheet such that the, also properly rescaled, source plane is projected on to 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 constantdensity 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 constantdensity 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 centre 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 ringshaped 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.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 2008
 DOI:
 10.1111/j.13652966.2008.13026.x
 arXiv:
 arXiv:0801.4255
 Bibcode:
 2008MNRAS.386..307L
 Keywords:

 gravitational lensing;
 dark matter;
 Astrophysics
 EPrint:
 6 pages, accepted for publication by MNRAS