Gravitational lensing and galaxy clusters
Kaiser & Squires have proposed a technique for mapping the dark matter in galaxy clusters using the coherent weak distortion of background galaxy images caused by gravitational lensing. We investigate the effectiveness of this technique under controlled conditions by creating simulated CCD frames containing galaxies lensed by a model cluster, measuring the resulting galaxy shapes, and comparing the reconstructed mass distribution with the original. Typically, the reconstructed surface density is diminished in magnitude when compared to the original. The main cause of this reduced signal is the blurring of galaxy images by atmospheric seeing, but the overall factor by which the reconstructed surface density is reduced depends also on the signal-to-noise ratio in the CCD frame and on both the sizes of galaxy images and the magnitude limit of the sample that is analysed. We propose a method for estimating a multiplicative compensation factor, f, directly from a CCD frame which can then be used to correct the surface density estimates given by the Kaiser & Squires formalism. We test our technique using a lensing cluster drawn from a cosmological N-body simulation with a variety of realistic background galaxy populations and observing conditions. We conclude that weak lensing observations when calibrated using this method yield not only accurate maps of the cluster morphology but also quantitative estimates of the cluster mass distribution. We then show that weak lensing simulations by rich clusters can be used to constrain the likely range of values of the cosmological constant Ω(_0). Again employing the Kaiser & Squires mass density estimator, we model the lensing induced by a number of simulated clusters from three different cosmologies. We introduce new statistics which are independent of any uncertainties in the surface density mentioned above. We conclude that lensing observations of a small number of clusters should be sufficient to place broad constraints on Ω(_0) and certainly distinguish between the extreme values of 0.2 and 1.We also present deep two-colour photometry of two rich clusters at z = 0.18; A1689 and A665. We use the data to construct number counts as a function of magnitude. To the magnitude depth we were able to probe, we conclude that there is no strong evidence for a steep faint end slope to the galaxy luminosity functioning moderate-redshift clusters.