Cluster Mass Prooles from Weak Lensing: Shear vs. Magniication Information

A massive foreground cluster lens changes the shapes (shear eeect) and number density (magniication eeect) of the faint background galaxy population. In this paper we investigate how the shear, magniication and combined information can be used to constrain cluster mass prooles in the weak lensing regime. We develop maximum likelihood techniques to make quantitative predictions for each of the methods. Our analytic results are checked against Monte Carlo simulations. In general, we nd that the shear method is superior to the magniication method. However, the magniication information complements the shear information if the former has accurate external calibration. For the magniication method, we discuss the eeects of random and systematic uncertainties in the background galaxy counts.