NUMBER COUNTS AND REDSHIFT DISTRIBUTION OF GRAVITATIONAL ARCLETS AS APROBE OF GALAXY EVOLUTION

We present a detailed model of the absolute number counts, color and r edshift distributions of gravitational arclets observed in clusters of galaxies. The framework adopted for galaxy evolution is chosen to rep roduce the observed number counts and redshift distribution of field g alaxies. Then, a spectrophotometric evolutionary code is coupled with an accurate modelling of the cluster-lens mass distribution. The inter est in applying these calculations to arclets is to use cluster-lenses as filters to select faint distant galaxies, gravitational magnificat ion 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 hav e studied the impact of the different sources of uncertainty on the pr edicted number counts and redshift distributions, taking into account the observational conditions for two sets of data, HST and ground-base d images. We investigate in details the influence of the mass modellin g on the counts and we show that simple cluster-scale potentials can n o 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 a s observed. Nevertheless, an important population of high redshift arc lets (z greater than or equal to 1.0) is also revealed by the simulati ons, which is not observed in spectroscopic surveys of arclets. We dis cuss the nature of this disagreement, due to uncertainties in the evol utionary models adopted here for galaxies at high redshift and to some biases in the spectroscopic surveys. The spatial distribution of arcl ets in number density and the local mean redshift of the sample are al so derived. These maps can be used as a tool to optimize the search fo r high redshift galaxies magnified by the clusters of galaxies.