Extraction of the mean radial mass distribution in clusters of galaxies by observations of weak gravitational imaging

The gravitational fields of clusters of galaxies cause systematic distortions of the images of background galaxies. Recently, the lens inversion problem, reconstruction of the mean surface density distribution in the lens from the pattern of systematic distortions, has been the object of several studies. In this paper, a new and simple method is proposed to derive the mean radial distribution of mass in clusters of galaxies. The density distribution in the cluster is assumed to be a simple power law, characterized by 2 free parameters: an exponent and a normalization. It is demonstrated that observations of more than about 200 background galaxies may constrain the exponent with an accuracy of +/- 0.30 and the total mass within 35% if the sources have sizes of the order of 1.0 arcsecond. However if the mean intrinsic source size is significantly smaller than 1.0 arcsecond then the atmospheric seeing renders an estimation of the exponent of the mass distribution impossible, although given the mass distribution the total mass can still be derived within a factor of 2.