Gravitational lensing of distant field galaxies by rich clusters - I. Faint galaxy redshift distributions.

From deep optical images of three clusters, selected by virtue of their X-ray luminosity and/or optical richness (1455 + 22, z = 0.26; 0016+16, z = 0.55; 1603 + 43, z = 0.89), we construct statistically complete samples of faint field galaxies (I <= 25) that are suitable for probing the effects of gravitational lensing. By selecting clusters across a wide redshift range, we separate the effects of the mean redshift of the faint field population well beyond spectroscopic limits and the distribution of dark matter in the lensing clusters. A significant lensing signature is seen in the two lower redshift clusters, whose X-ray properties are well constrained. Based on these and dynamical data, it is straightforward to rule out field redshift distributions for I <= 25, which have a significant low-redshift excess compared to the no-evolution prediction, such as would be expected if the number counts at faint limits were dominated by low-z dwarf systems. The degree to which we can constrain any high-redshift tail to the no-evolution redshift distribution depends on the distribution of mass in the most distant lensing cluster. In the second paper in this series, we demonstrate that the mass distributions in our lensing clusters are well understood, by reconstructing the full two-dimensional distributions from the lensing signal. The principal result is therefore the absence of a dominant low-z dwarf population to I <= 25.