Accurate modeling of the strong and weak lensing profiles for the galaxy clusters Abell 1689 and 1835

An accurate, spherically symmetric description of the mass distribution is presented for two quite virialized galaxy clusters, Abell 1689 and Abell 1835. A suitable regularization of the small eigenvalues of the covariance matrices is introduced. A stretched exponential profile is assumed for the brightest cluster galaxy. A similar stretched exponential for the dark matter and halo galaxies combined, functions well, as do thermal fermions for the dark matter and a standard profile for the halo galaxies. To discriminate between them, sensitive tests have been identified and applied. A definite verdict can follow from sharp data near the cluster centers and beyond 1 Mpc.