1998A&A...330..399B

We present a detailed model of the absolute number counts, color and redshift distributions of gravitational arclets observed in clusters of galaxies. The framework adopted for galaxy evolution is chosen to reproduce the observed number counts and redshift distribution of field galaxies. Then, a spectrophotometric evolutionary code is coupled with an accurate modelling of the cluster-lens mass distribution. The interest in applying these calculations to arclets is to use cluster-lenses as filters to select faint distant galaxies, gravitational magnification being more efficient as the redshift of the galaxy is higher. This procedure is applied on two different cluster-lenses, Abell 2218 and Abell 370, for which the mass distribution is well constrained. We have studied the impact of the different sources of uncertainty on the predicted number counts and redshift distributions, taking into account the observational conditions for two sets of data, HST and ground-based images. We investigate in details the influence of the mass modelling on the counts and we show that simple cluster-scale potentials can no longer be used for arcs statistics. The main result is that arcs at redshifts between 0.5 and 1 are correctly predicted by the modelling as observed. Nevertheless, an important population of high redshift arclets (z≥1.0) is also revealed by the simulations, which is not observed in spectroscopic surveys of arclets. We discuss the nature of this disagreement, due to uncertainties in the evolutionary models adopted here for galaxies at high redshift and to some biases in the spectroscopic surveys. The spatial distribution of arclets in number density and the local mean redshift of the sample are also derived. These maps can be used as a tool to optimize the search for high redshift galaxies magnified by the clusters of galaxies.