Cluster mass profiles from weak lensing II

When a cluster gravitationally lenses faint background galaxies, its tidal gravitational field distorts their shapes (shear effect) and its magnification effect changes the observed number density. In Schneider et al. (2000) we developed likelihood techniques to compare the constraints on cluster mass profiles that can be obtained using the shear and magnification information. This work considered circularly symmetric power-law models for clusters at fairly low redshifts where the redshift distribution of source galaxies could be neglected. Here this treatment is extended to encompass NFW profiles which are a good description of clusters from cosmological N-body simulations, and NFW clusters at higher redshifts where the influence of various scenarios for the knowledge of the redshift distribution are examined. Since in reality the overwhelming majority of clusters have ellipsoidal rather than spherical profiles, the singular isothermal ellipsoid (SIE) is investigated. We also briefly consider the impact of substructure on such a likelihood analysis. In general, we find that the shear information provides a better constraint on the NFW profile under consideration, so this becomes the focus of what follows. The ability to differentiate between the NFW and power-law profiles strongly depends on the size of the data field, and on the number density of galaxies for which an ellipticity can be measured. Combining Monte Carlo simulations with likelihood techniques is a very suitable way to predict whether profiles will be distinguishable, given the field of view and depth of the observations. For higher redshift NFW profiles, there is very little reduction (similar to1.5%) in the dispersion of parameter estimates when spectroscopic redshifts, as opposed to photometric redshift estimates, are available for the galaxies used in the lensing analysis.