A MAXIMUM-ENTROPY METHOD FOR RECONSTRUCTING THE PROJECTED MASS-DISTRIBUTION OF GRAVITATIONAL LENSES

The maximum-entropy method is applied to the problem of reconstructing the projected mass density of a galaxy cluster using its gravitationa l lensing effects on background galaxies. We demonstrate the method by reconstructing the mass distribution in a model cluster using simulat ed shear and magnification data to which Gaussian noise is added. The mass distribution is reconstructed directly and the inversion is regul arized using the entropic prior for this positive additive distributio n. For realistic noise levels, we find that the method faithfully repr oduces the main features of the cluster mass distribution not only wit hin the observed field but also slightly beyond it. We estimate the un certainties in the reconstruction by calculating an analytic approxima tion to the covariance matrix of the reconstruction values of each pix el. This result is compared with error estimates derived from Monte Ca rlo simulations for different noise realizations and found to be in go od agreement.