GRAVITATIONAL LENSING BY CLUSTERS OF GALAXIES - CONSTRAINING THE MASS-DISTRIBUTION

Clusters of galaxies can deflect the light of background, high-redshift galaxies, producing distorted images of them. Recently, Tyson, Valdes, and Wenk reported the discovery of a preferential tangential alignment of the galaxies behind two clusters. Motivated by the discovery, we investigate the possibility of constraining the mass distribution of a cluster by observing the shapes of the lensed galaxies in the limit of weak distortion. The accuracy with which the mass distribution can be determined has a fundamental limit due to the random ellipticities intrinsic to the background galaxies. From this fundamental limit, we calculate the expected accuracy in the determination of the following parameters: the center of the cluster, its velocity dispersion, the density profile in the outer parts, and the projected ellipticity of the cluster potential. We also consider the possibility of constraining the redshift distribution of the background sources and the value of the cosmological constant. Our results indicate that clusters with line-of-sight velocity dispersions higher than about 500 km s-1 should produce a detectable distortion on the background galaxies. The velocity dispersion can be measured with increasing accuracy as it increases. The center of the cluster can be determined with an accuracy which is of the order of the average separation between background galaxies. The quadrupole moment of the cluster potential can also be measured to about 20% of the total potential for a velocity dispersion of 1000 km s-1, and the accuracy improves with velocity dispersion. The power law describing the density profile in the outer parts of the cluster can, in principle, be determined, if background galaxies in a sufficiently large area in the sky around the cluster are observed. However, other density fluctuations in the line of sight will dominate over the cluster at some radius. The accuracy of the measurement of these quantities can be severely degraded by several systematic observational errors: poor resolution of the lensed galaxies (essentially due to seeing), uncorrected guiding errors, and confusion of background galaxies with cluster galaxies.