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.
