Cluster mass estimation from lens magnification

The mass of a cluster of galaxies can be estimated from its lens magnification, which can be determined from the variation in number counts of background galaxies. In order to derive the mass one needs to make assumptions for the lens shear, which is unknown from the variation in number counts alone. Furthermore, one needs to go beyond the weak lensing (linear) approximation as most of the observational data is concentrated in the central parts of clusters, where the lensing is strong. By studying the lensing properties of a complete catalogue of galaxy cluster models, one can find reasonable approximations about the lens shear as a function of the lens convergence. We show that using these approximations one can fairly well reconstruct the surface mass distribution from the magnification alone.