Mass-sheet degeneracy: Fundamental limit on the cluster mass reconstruction from statistical (weak) lensing

Weak gravitational lensing is considered to be one of the most powerful tools to study the mass and the mass distribution of galaxy clusters. However, weak lensing mass reconstructions are plagued by the so-called mass-sheet degeneracy - the surface mass density κ of the cluster can be determined only up to a degeneracy transformation κ -> κ' = λ κ + (1 - λ), where λ is an arbitrary constant. This transformation fundamentally limits the accuracy of cluster mass determinations if no further assumptions are made. We describe here a method to break the mass-sheet degeneracy in weak lensing mass maps using the distortion and redshift information of background galaxies and illustrate this by two simple toy models. Compared to other techniques proposed in the past, it does not rely on any assumptions on cluster potential; it can be easily applied to non-parametric mass-reconstructions and no assumptions on boundary conditions have to be made. In addition it does not make use of weakly constrained information (such as the source number counts, used in the magnification effect). Our simulations show that we are effectively able to break the mass-sheet degeneracy for supercritical lenses, but that for undercritical lenses the mass-sheet degeneracy is very difficult to break, even under idealised conditions.