Lensed galaxies in Abell 370 I. Modeling the number counts and redshift distribution of background sources

We present new observations of the cluster-lens Abell 370: a deep HST/WFPC2 F675W image and ESO 3.6m spectroscopy of faint galaxies. These observations shade new lights on the statistical properties of faint lensed galaxies. In particular, we spectroscopically confirm the multiple image nature of the B2--B3 gravitational pair (Kneib et al. 1993), and determine a redshift of z=0.806 which is in very good agreement with earlier predictions. A refined mass model of the cluster core (that includes cluster galaxy halos) is presented, based on a number of newly identified multiple images. Following Bezecourt et al. (1998a), we combine the new cluster mass model with a spectrophotometric prescription for galaxy evolution to predict the arclets number counts and redshift distribution in the HST image. In particular, the ellipticity distribution of background sources is taken into account, in order to properly estimate the statistical number and redshift distribution of arclets. We show that the redshift distribution of arclets, and particularly its high redshift tail can be used as a strong constraint to disentangle different galaxy evolution scenario. A hierarchical model which includes a number density evolution is favored by our analysis. Finally, we compute the depletion curves in the faint galaxies number counts and discuss its wavelength dependence.