Weighting the Clusters of Galaxies with Weak Gravitational Lensing: The problem of the mass-sheet degeneracy

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 \kappa of the cluster can be determined only up to a degeneracy transformation \kappa \to \kappa' = \lambda \kappa + (1 -\lambda), where \lambda is an arbitrary constant. This transformation fundamentally limits the accuracy of cluster mass determinations if no further assumptions are made. We discuss here a possibility to break the mass-sheet degeneracy in weak lensing mass maps using distortion and redshift information of background galaxies. Compared to other techniques proposed in the past, it does not rely on any assumptions on cluster potential and 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 and that for undercritical lenses the mass-sheet degeneracy is very difficult to be broken, even under idealised conditions.