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 amplificat ion of background galaxies by the cluster potential field. The gravita tional amplification is measured by comparing the joint distribution i n redshift and magnitude of galaxies behind the cluster with that of t he average distribution of field galaxies. Lensing shifts the magnitud e distribution in a characteristic redshift-dependent way, and simulta neously dilutes the surface density of galaxies. These effects oppose, with the latter dominating at low redshift and the former at high red shift, owing to the curvature of the galaxy luminosity function. Lensi ng by a foreground cluster thus induces an excess of bright high-redsh ift galaxies, from which the lens amplification may be inferred. We sh ow that the total amplification is directly related to the surface mas s density in the weak field limit, and so it is possible to map the ma ss distribution of the cluster. The method is shown to be limited by d iscreteness noise and galaxy clustering behind the lens. Galaxy cluste ring sets a lower limit to the error along the redshift direction, but a clustering independent lensing signature may be obtained from the m agnitude distribution at fixed redshift. Provided the luminosity funct ion deviates from a pure power law, the lens-induced brightening can b e measured directly by comparison with the field. In the limit that ga laxy luminosities are independent of environment, this method is only shot-noise limited. Statistical techniques are developed for estimatin g 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 n umerical simulations and show the feasibility of the approach. We cons ider the use of approximate redshift information, and show how the mas s estimates are degraded; finally we discuss the data required to map the dark matter in clusters from photometry alone.