Testing the density field with the muenster redshift program

New expressions are given for the gravitational magnification and the ratio between source and image sizes, which apply to the giant thin and luminous arcs found in distant cluster cores, and for any number of lenses in the cluster. Source properties are strongly dependent on the a priori choice of the lensing mass density profile. The new formulae provide the first attempt to disentangle the properties of the lensing clusters from the arc source properties. Available observations - spectroscopy, imagery and photometry - are used to constrain the nature of the sources, which are probably spiral galaxies, and hence, to derive new and independent conditions on the mass density profile of the dark matter inside the lensing clusters. Most of the lensing clusters should be much more compact than inferred from their X-ray density profiles and even more compact than inferred from their visible luminosity profiles, except if there was an enormous evolution of the entire luminosity function of galaxies from z <= 0.4 to z approx 0.8. Indeed lensing clusters should have mass density profiles more compact than isothermal spheres with small core radii (r_c <= 100 h_50^-1 kpc where H_0 = 50 h_50 km/s/Mpc). Mass estimations derived from giant luminous arcs are also discussed. It is finally argued that the sources of the small and faint arclets found in deep images of distant clusters, could be dwarf galaxies at moderate redshift (z <= 1). The new test presented here to derive lensing mass distribution is finally compared with the method using arclets.