Since a few years, a new application of gravitational lensing in clusters of galaxies has started to be explored, namely the depletion effect of number counts of background galaxies in cluster centers. This effect results from the competition between the gravitational magnification that increases the detection of individual objects (at least for flux limited data and marginally resolved objects) and the deviation of light beam that spatially magnifies the observed area and thus decreases the apparent number density of sources.
This effect was pointed out as a possible application of the magnification bias by Broadhurst et al. (1995) where they suggested a new method for measuring the projected mass distribution of galaxy clusters, based solely on gravitational magnification of background populations by the cluster gravitational potential. In addition, they suggested that the mass-sheet degeneracy, initially pointed out by Schneider & Seitz (1995) and observed in mass reconstruction with weak lensing measures, could be broken by using gravitational magnification information which is directly provided by the depletion curves. This method has been used by Fort et al. (1997) and by Taylor et al. (1998) to reconstruct a two-dimensional mass map of Abell 1689 in the innermost 27 arcmin2, taking into account the nonlinear clustering of the background population and shot noise. The results are consistent with those inferred from weak shear measurements and from strong lensing. However, the surface mass density cannot be obtained from magnification alone since magnification also depends on the shear caused by matter outside the data field (Young, 1981; Bartelmann & Schneider, 2000). But in practice, if the data field is sufficiently large and no mass concentration lies close to but outside the data field, the mass reconstruction obtained from magnification can be quite accurate (Schneider et al., 2000).
This method is an attractive alternative to weak lensing because it is only based on galaxy counts and does not require the measure of shape parameters of very faint galaxies. In addition, it is still valid in the intermediate lensing regime, close to the cluster center, without any strong modifications of the formalism. Meanwhile, it is more sensitive to Poisson noise which increases when the number density decreases in the depletion area. Another weak point identified by Schneider et al. (2000) is that it may significantly depend on the galaxy clustering of background objects which can have large fluctuations from one cluster to another.
A second application of the magnification bias that has been suggested is to use the shape and the width of depletion curves to reveal the redshift distribution of the background populations. This technique was first used by Fort et al. (1997) in the cluster Cl0024+1654 to study the redshift distribution of background sources in the range and . They found that of the population in the B band is located between and while the remaining galaxies are broadly distributed around . The population in the I band shows a similar redshift distribution but it extends to larger redshift of objects at .
The last application of the magnification bias that has been explored is the search for constraints on cosmological parameters. This method is based on the fact that the ratio of the two extreme radii which delimit the depletion area depends on the ratio of the angular distances lens-source and observer-source. Consequently it depends on the cosmological parameters, as soon as all the redshifts are fixed, and mainly on the cosmological constant. This method was first used by Fort et al. (1997) in Cl0024+1654 and in Abell 370. Their results favor a flat cosmology with and are consistent with those obtained from other independent methods (see White (1998)). This technique requires a good modeling of the lens and could be improved by being extended to a large number of cluster lenses and by using an independent estimate of the redshift distribution (for example from photometric redshifts). However, this method was disputed by Asada (1997) who claimed that it is difficult to determine by this method without the assumption of a spatially flat universe. He also mentioned the uncertainty of the lens model as one of the most serious problems in this test and concluded that this method cannot be taken as a clear cosmological test to determine .
In order to better understand the formation of depletion curves and their dependence with the main characteristics of the lenses and the sources, we developed a detailed modeling of the curves in various conditions. In Sect. 2 we present the lens and counts models used in our simulations. In Sect. 3 we study the influence of the lens mass profile, with several sets of analytical mass distributions. In Sect. 4 we explore the influence of background sources distribution, selected through different filters. An application on real data is presented in Sect. 5, in the cluster MS 1008-1224, observed with the VLT. We compare these observations with the simulations in order to derive some constraints on the mass profile and the ellipticity of the cluster, as well as on the background sources distribution. Some prospects about the future of this method are given as a conclusion in Sect. 6. Throughout the paper, we adopt a Hubble constant of H0=50 km s-1 Mpc-1, with and .
© European Southern Observatory (ESO) 2000
Online publication: October 2, 2000