Cluster mass reconstruction from weak gravitational lensing

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 with 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 find that typically the compensation factor is appreciable, 1.4 less than or similar to f less than or similar to 2.2, and varies considerably depending on the observing conditions and sample selection. We demonstrate that in all cases our method yields a compensation factor which, when used to correct the surface density estimates, produces values that are in good agreement with those of the original cluster. Thus 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.