Direct Measurements of the magnification produced by galaxy clusters as gravitational lenses

Weak lensing is one of the best available diagnostic tools to measure the total density profiles of distant clusters of galaxies. Unfortunately, it suffers from the well-known mass-sheet degeneracy, so that weak lensing analyses cannot lead to fully reliable determinations of the total mass of the clusters. One possible way to set the relevant scale of the density profile would be to make a direct measurement of the magnification produced by the clusters as gravitational lenses. In this paper we revisit a suggestion made a few years ago for this general purpose, based on the use of the Fundamental Plane as a standard rod for early-type galaxies. Here we move one step further, beyond the simple outline of the idea given earlier, and quantify some statistical properties of this innovative diagnostic tool, with the final goal of identifying clear guidelines for a future observational test on concrete cases, which turns out to be well within the current instrument capabilities. The study is carried out by discussing the statistical properties of Fundamental Plane measurements for a sample of early-type source galaxies behind a massive cluster, for which a weak lensing analysis is assumed to be available. We proceed to study the best strategy to use Fundamental Plane measurements to determine the mass scale of a given cluster and find that the optimal choice is that of a sample of early-type galaxies behind the cluster distributed approximately uniformly in the sky. We also show that substructures do not contribute much to the magnification signal that we are looking for, but only add a modest amount of scatter. We find that for a massive cluster (M > 10^15 M_Sun) located at redshift 0.3 +/- 0.1, a set of about 20 Fundamental Plane measurements, combined with a good weak lensing analysis, should be able to lead to a mass determination with a precision of 20% or better.