2011ApJ...729..127U

We directly construct model-independent mass profiles of galaxy clusters from combined weak-lensing distortion and magnification measurements within a Bayesian statistical framework, which allows for a full parameter-space extraction of the underlying signal. This method applies to the full range of radius outside the Einstein radius, and recovers the absolute mass normalization. We apply our method to deep Subaru imaging of five high-mass (>10¹⁵ M_☉) clusters, A1689, A1703, A370, Cl0024+17, and RXJ1347-11, to obtain accurate profiles beyond the virial radius (r_vir). For each cluster, the lens distortion and magnification data are shown to be consistent with each other, and the total signal-to-noise ratio of the combined measurements ranges from 13 to 24 per cluster. We form a model-independent mass profile from stacking the clusters, which is detected at 37σ out to R ~ 1.7r_vir. The projected logarithmic slope γ_2D(R) ≡ dln Σ/dln R steepens from γ_2D= -1.01±0.09 at R ~ 0.1r_vir to γ_2D= -1.92±0.51 at R ~ 0.9r_vir. We also derive for each cluster inner strong-lensing-based mass profiles from deep Advanced Camera for Surveys observations with the Hubble Space Telescope, which we show overlap well with the outer Subaru-based profiles and together are well described by a generalized form of the Navarro-Frenk-White profile, except for the ongoing merger RXJ1347-11, with modest variations in the central cusp slope (-dln ρ/dln r ≲ 0.9). The improvement here from adding the magnification measurements is significant, ∼30% in terms of cluster mass profile measurements, compared with the lensing distortion signal.