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

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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 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 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 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 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.

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MLA
LIESENBORGS, J, Sven De Rijcke, Herwig Dejonghe, et al. “A Generalization of the Mass-sheet Degeneracy Producing Ring-like Artefacts in the Lens Mass Distribution.” MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 386.1 (2008): 307–312. Print.
APA
LIESENBORGS, J., De Rijcke, S., Dejonghe, H., & BEKAERT, P. (2008). A generalization of the mass-sheet degeneracy producing ring-like artefacts in the lens mass distribution. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 386(1), 307–312.
Chicago author-date
LIESENBORGS, J, Sven De Rijcke, Herwig Dejonghe, and P BEKAERT. 2008. “A Generalization of the Mass-sheet Degeneracy Producing Ring-like Artefacts in the Lens Mass Distribution.” Monthly Notices of the Royal Astronomical Society 386 (1): 307–312.
Chicago author-date (all authors)
LIESENBORGS, J, Sven De Rijcke, Herwig Dejonghe, and P BEKAERT. 2008. “A Generalization of the Mass-sheet Degeneracy Producing Ring-like Artefacts in the Lens Mass Distribution.” Monthly Notices of the Royal Astronomical Society 386 (1): 307–312.
Vancouver
1.
LIESENBORGS J, De Rijcke S, Dejonghe H, BEKAERT P. A generalization of the mass-sheet degeneracy producing ring-like artefacts in the lens mass distribution. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY. 2008;386(1):307–12.
IEEE
[1]
J. LIESENBORGS, S. De Rijcke, H. Dejonghe, and P. BEKAERT, “A generalization of the mass-sheet degeneracy producing ring-like artefacts in the lens mass distribution,” MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, vol. 386, no. 1, pp. 307–312, 2008.
@article{426385,
  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 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 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 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 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.},
  author       = {LIESENBORGS, J and De Rijcke, Sven and Dejonghe, Herwig and BEKAERT, P},
  issn         = {0035-8711},
  journal      = {MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY},
  language     = {eng},
  number       = {1},
  pages        = {307--312},
  title        = {A generalization of the mass-sheet degeneracy producing ring-like artefacts in the lens mass distribution},
  url          = {http://dx.doi.org/10.1111/j.1365-2966.2008.13026.x},
  volume       = {386},
  year         = {2008},
}

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