Mapping Cluster Mass Distributions via Gravitational Lensing of Background Galaxies

We present a new method for measuring the projected mass distributions of galaxy clusters, based solely on the gravitational lens amplification of background galaxies by the cluster potential field. The gravitational amplification is measured by comparing the joint distribution in redshift and magnitude of galaxies behind the cluster with that of the average distribution of field galaxies. Lensing shifts the magnitude distribution in a characteristic redshift-dependent way, and simultaneously dilutes the surface density of galaxies. These effects oppose, with the latter dominating at low redshift and the former at high redshift, owing to the curvature of the galaxy luminosity function. Lensing by a foreground cluster thus induces an excess of bright high-redshift galaxies, from which the lens amplification may be inferred. We show that the total amplification is directly related to the surface mass density in the weak field limit, and so it is possible to map the mass distribution of the cluster. The method is shown to be limited by discreteness noise and galaxy clustering behind the lens. Galaxy clustering sets a lower limit to the error along the redshift direction, but a clustering independent lensing signature may be obtained from the magnitude distribution at fixed redshift. Provided the luminosity function deviates from a pure power law, the lens induced brightening can be measured directly by comparison with the field. In the limit that galaxy luminosities are independent of environment, this method is only shot-noise limited. Statistical techniques are developed for estimating the surface mass density of the cluster. We extend these methods to account for any obscuration by cluster halo dust, which may be mapped independently of the dark matter. We apply the method to a series of numerical simulations and show the feasibility of the approach. We consider the use of approximate redshift information, and show how the mass estimates are degraded; finally we discuss the data required to map the dark matter in clusters from photometry alone.