SIMBAD references

We analyse the surface density of very faint galaxies at the limit of the sky background noise in the field of the cluster of galaxies Cl 0024+1654. The radial variation of their number density in the magnitude bins B=26-28 and I=24-26.5 displays an (anti)bias magnification effect similar to the one observed in A1689 by Broadhurst (1995) for I<24. The study of this effect provides a determination of the radial distribution of critical lines of the gravitational lens from which we infer the redshift range of the populations seen in B and I. The surface density of B galaxies drops rapidly to a well-defined inner critical line near the large triple arc. The depletion extends from R_B=30" to R_B=53" and the shape of the curve can almost be reproduced with two redshift populations selected by the two filters. With our data 60%±10% of the B-selected galaxies are between z=0.9 and z=1.1 while most of the remaining 40% galaxies should be at a redshift close to z=3. The I selected population observed with the lens has a broader depletion with a minimum extending from the B inner critical line to R_I=60". Whatever the cosmological model, the very faint I-selected galaxies spread up to a larger redshift with about 20% above z>4. The fact that many faint I selected galaxies are not detected in B also favour the existence of a more distant population with a redshift range between z=3 and z=4.5. Using a model for the gravitational potential derived from a study of the large triple arc seen around the cluster, the locations of the two extreme critical lines for the B and I selected galaxies seems to favour {OMEGA}_{LAMBDA}-dominated flat universes with a cosmological constant ranging from 0.6 to 0.9. The result is confirmed by a preliminary investigation of the Broadhurst's effect in A 370. However, ultra-deep detection of faint distant galaxies down to the noise level are technically very difficult. In this first paper we mainly discuss the method to search the so-called "last critical line" and several possible effects which may bias the results on cosmological parameters. We conclude that the systematic measurement of this outer critical line of the faint I selected galaxies population around many clusters with gravitational arcs of known (low) redshift may help to count the number of faint galaxies at very large redshifts beyond the possibility of any spectroscopic survey, and eventually to settle the issue of the existence of the cosmological constant.