We outline our methods for obtaining high precision mass profiles , combining independent weak-lensing distortion , magnification , and strong-lensing measurements .
For massive clusters the strong and weak lensing regimes contribute equal logarithmic coverage of the radial profile .
The utility of high-quality data is limited by the cosmic noise from large scale structure along the line of sight .
This noise is overcome when stacking clusters , as too are the effects of cluster asphericity and substructure , permitting a stringent test of theoretical models .
We derive a mean radial mass profile of four similar mass clusters of high-quality Hubble Space Telescope and Subaru images , in the range R = 40 kpc h ^ { -1 } to 2800 kpc h ^ { -1 } , where the inner radial boundary is sufficiently large to avoid smoothing from miscentering effects .
The stacked mass profile is detected at 58 \sigma significance over the entire radial range , with the contribution from the cosmic noise included .
We show that the projected mass profile has a continuously steepening gradient out to beyond the virial radius , in remarkably good agreement with the standard Navarro-Frenk-White form predicted for the family of CDM-dominated halos in gravitational equilibrium .
The central slope is constrained to lie in the range , - d \ln \rho / d \ln { r } = 0.89 ^ { +0.27 } _ { -0.39 } .
The mean concentration is c _ { vir } = 7.68 ^ { +0.42 } _ { -0.40 } ( at M _ { vir } = 1.54 ^ { +0.11 } _ { -0.10 } \times 10 ^ { 15 } M _ { \odot } h ^ { -1 } ) , which is high for relaxed , high-mass clusters , but consistent with \Lambda CDM when a sizable projection bias estimated from N -body simulations is considered .
This possible tension will be more definitively explored with new cluster surveys , such as CLASH , LoCuSS , Subaru HSC , and XXM-XXL , to construct the c _ { vir } – M _ { vir } relation over a wider mass range .