Cosmology in two dimensions: the concentration-mass relation for galaxy clusters

Our aim in this paper is to perform a systematic study of the measures of mass and concentration estimated by fitting the convergence profile of a large sample of mock galaxy-cluster-sized lenses, created with the publicly available code moka. We have found that the first main contribution to the bias in mass and in concentration is the halo triaxiality; the second contribution is the presence of substructures within the host halo virial radius. We show that knowledge of the cluster elongation along the line of sight helps when correcting the mass bias, but it still retains a small negative bias for the concentration. If these mass and concentration biases can characterize the galaxy cluster sample of a wide field survey, it will be difficult to recover well within 1s the cosmological parameters that mainly influence the cM relation, using as a reference the three-dimensional cM relation measured in cosmological N-body simulations. In this paper, we propose a method for correcting the cM relation for projection effects and for adiabatic contraction. We suggest using these as references for real observed data. Correcting the mass and concentration estimates, as we propose, gives a measurement of the cosmological parameter within 1s confidence contours.