Model-Free Multi-Probe Lensing Reconstruction of Cluster Mass Profiles
  Lens magnification by galaxy clusters induces characteristic spatial
variations in the number counts of background sources, amplifying their
observed fluxes and expanding the area of sky, the net effect of which, known
as magnification bias, depends on the intrinsic faint-end slope of the source
luminosity function. The bias is strongly negative for red galaxies, dominated
by the geometric area distortion, whereas it is mildly positive for blue
galaxies, enhancing the blue counts toward the cluster center. We generalize
the Bayesian approach of Umetsu et al. for reconstructing projected cluster
mass profiles, by incorporating multiple populations of background sources for
magnification bias measurements and combining them with complementary lens
distortion measurements, effectively breaking the mass-sheet degeneracy and
improving the statistical precision of cluster mass measurements. The approach
can be further extended to include strong-lensing projected mass estimates,
thus allowing for non-parametric absolute mass determinations in both the weak
and strong regimes. We apply this method to our recent CLASH lensing
measurements of MACS J1206.2-0847, and demonstrate how combining multi-probe
lensing constraints can improve the reconstruction of cluster mass profiles.
This method will also be useful for a stacked lensing analysis, combining all
lensing-related effects in the cluster regime, for a definitive determination
of the averaged mass profile.
