Depletion curves in cluster lenses: simulations and application to the cluster MS1008-1224

Abstract

When the logarithmic slope of the galaxy counts is lower than 0.4 (this is the case in all filters at large magnitude), the magnification bias due to the lens makes the number density of objects decrease, and consequently, the radial distribution shows a typical depletion curve. In this paper, we present simulations of depletion curves obtained in different filters for a variety of different lens models - e.g., a singular isothermal sphere, an isothermal sphere with a core, a power-law density profile, a singular isothermal ellipsoid and a NFW profile. The different model parameters give rise to different effects, and we show how the filters, model parameters and redshift distributions of the background populations affect the depletion curves. We then compare our simulations to deep VLT observations of the cluster MS1008--1224 and propose to constrain the mass profile of the cluster as well as the ellipticity and the orientation of the mass distribution. This application is based solely on deep photometry of the faint background galaxies. We finally give some possible applications of this method, useful for cluster lenses.