Cluster mass estimation from lens magnification

The surface mass density of a cluster of galaxies, and thus its total mass, can be estimated from its lens magnification. The magnification can be det ermined from the variation in number counts of its background galaxies. In the weak lensing approximation the surface mass density is a linear functio n of the magnification. However, most observational data are concentrated i n the central parts of clusters, so one needs to go beyond the weak lensing approximation and consider the lens shear as well. which is unknown from t he variation in number counts alone. Our approach is to look for approximat e relations between the lens shear and other lens properties in this strong lensing regime. Such relations exist for simple analytical cluster models, like the isother mal sphere, but are not generally a good description of observed or simulat ed galaxy clusters. We therefore study the lensing properties of a catalogu e of numerical cluster models in order to find the best possible approximat ion for the shear that still allows straightforward determination of the su rface mass density. We show that by using such an approximation one can fai rly well reconstruct the surface mass distribution from the magnification a lone. The approximations are tested using clean magnification maps obtained directly from simulated clusters, and also using lensed mock background ga laxy distributions in order to estimate the intrinsic uncertainties of the method. We demonstrate that the mass estimated using the weak lens magnific ation approximation is usually at least twice the true mass. We illustrate our technique on existing data, and show that the resulting masses compare well with other estimates.