Probing galactic dark matter in dense environments: on the strong lensing efficiency of galaxies in rich clusters

The recent detection by Limousin et al. of five new strong lensing events dominated by galaxy cluster members in Abell 1689, and outside the critical regime of the cluster itself, offers a way to obtain constraints on the cluster mass distribution in a region inaccessible to standard lensing analysis. In addition, modelling such systems will provide another window on the dark matter haloes of galaxies in very dense environments. Here, it is shown that the boost in image separation due to the external shear and convergence from a smooth cluster component means that more numerous, less massive galaxies have the potential to create multiple images with detectable separations, relative to isolated field galaxies. This comes in addition to a potential increase in their lensing (source plane) cross-section. To gain insight into the factors involved and as a precursor to a numerical study using N-body simulations, a simple analytic model of a cluster at z = 0.3 lensing background galaxies at z = 2 is considered here. The fiducial model has cluster members with isothermal density profiles and luminosities L, distributed in a Schechter function (faint-end slope v = -1.25), related to their velocity dispersions sigma via the Faber-Jackson scaling L proportional to sigma(4). Just outside the critical regime of the cluster, the scale of galaxy- dominated image separations is significantly increased. Folding in the fact that less massive galaxies present a lower lensing cross- section, and that the cross- section can itself be enhanced in an external field leads to a factor of a few times more detected events relative to field galaxies. These values will be higher closer to the critical curve. Given that the events in Abell 1689 were detected over a very small region of the cluster where ACS data were available, this motivates the search for such events in other clusters.