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 magnificat ion effect changes the observed number density. In Schneider et al. (2000) we developed likelihood techniques to compare the constraints on cluster ma ss profiles that can be obtained using the shear and magnification informat ion. This work considered circularly symmetric power-law models for cluster s at fairly low redshifts where the redshift distribution of source galaxie s could be neglected. Here this treatment is extended to encompass NFW prof iles which are a good description of clusters from cosmological N-body simu lations, and NFW clusters at higher redshifts where the influence of variou s scenarios for the knowledge of the redshift distribution are examined. Si nce in reality the overwhelming majority of clusters have ellipsoidal rathe r than spherical profiles, the singular isothermal ellipsoid (SIE) is inves tigated. We also briefly consider the impact of substructure on such a like lihood analysis. In general, we find that the shear information provides a better constraint on the NFW profile under consideration, so this becomes t he 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 t he number density of galaxies for which an ellipticity can be measured. Com bining Monte Carlo simulations with likelihood techniques is a very suitabl e way to predict whether profiles will be distinguishable, given the field of view and depth of the observations. For higher redshift NFW profiles, th ere is very little reduction (similar to1.5%) in the dispersion of paramete r estimates when spectroscopic redshifts, as opposed to photometric redshif t estimates, are available for the galaxies used in the lensing analysis.