Cluster mass profiles from weak lensing: constraints from shear and magnification information

A massive foreground cluster lens changes the shapes (shear effect) and number density (magnification effect) of the faint background galaxy population. In this paper we investigate how the shear, magnification and combined information can be used to constrain cluster mass profiles in the weak lensing regime. We develop maximum likelihood techniques to make quantitative predictions for each of the methods, in the framework of parameterized mass profiles. Our analytic results are checked against Monte Carlo simulations. We find that the magnification method is a better discriminator of the slope of a cluster profile, provided that the unlensed number counts of background galaxies are accurately known, whereas the shear method is a better discriminator of the normalisation. Combining the shear and magnification information places the tightest constraints on the mass profile. In the absence of reliable external calibration, the shear method is superior, and little is gained by the inclusion of magnification information. For the magnification method, we discuss the effects of random and systematic uncertainties in the background galaxy counts.