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

A massive foreground cluster lens changes the shapes (shear effect) and num ber density (magnification effect) of the faint background galaxy populatio n. In this paper we investigate how the shear, magnification and combined i nformation can be used to constrain cluster mass profiles in the weak lensi ng regime. We develop maximum likelihood techniques to make quantitative pr edictions for each of the methods, in the framework of parameterized mass p rofiles. Our analytic results are checked against Monte Carlo simulations. We find that the magnification method is a better discriminator of the slop e of a cluster profile, provided that the unlensed number counts of backgro und galaxies are accurately known, whereas the shear method is a better dis criminator of the normalisation. Combining the shear and magnification info rmation 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 magnifica tion method, we discuss the effects of random and systematic uncertainties in the background galaxy counts.