We use high-quality Subaru/Suprime-Cam imaging data to conduct a detailed weak-lensing study of the distribution of dark matter in a sample of 30 X -ray luminous galaxy clusters at 0.15 \leq z \leq 0.3 .
A weak-lensing signal is detected at high statistical significance in each cluster , the total signal-to-noise ratio of the detections ranging from 5 to 13 .
Comparing spherical models to the tangential distortion profiles of the clusters individually , we are unable to discriminate statistically between singular isothermal sphere ( SIS ) and Navarro Frenk & White ( NFW ) models .
However when the tangential distortion profiles are combined and then models are fitted to the stacked profile , the SIS model is rejected at 6 \sigma and 11 \sigma , respectively , for low ( M _ { vir } < 6 \times 10 ^ { 14 } h ^ { -1 } M _ { \odot } ) and high ( M _ { vir } > 6 \times 10 ^ { 14 } h ^ { -1 } M _ { \odot } ) mass bins .
We also use the individual cluster NFW model fits to investigate the relationship between cluster mass and concentration , finding that concentration ( c _ { vir } ) decreases with increasing cluster mass ( M _ { vir } ) .
The best-fit c _ { vir } - M _ { vir } relation is : c _ { vir } ( M _ { vir } ) = 8.75 ^ { +4.13 } _ { -2.89 } \times ( M _ { vir } / 10 ^ { 14 } h ^ { -1 } M% _ { \odot } ) ^ { \alpha } with \alpha \approx - 0.40 \pm 0.19 : i.e .
a non-zero slope is detected at 2 \sigma significance .
This relation gives a concentration of c _ { vir } = 3.48 ^ { +1.65 } _ { -1.15 } for clusters with M _ { vir } = 10 ^ { 15 } h ^ { -1 } M _ { \odot } , which is inconsistent at 4 \sigma significance with the values of c _ { vir } \sim 10 reported for strong-lensing-selected clusters .
We find that the measurement error on cluster mass is smaller at higher over-densities \Delta \simeq 500 - 2000 , than at the virial over-density \Delta _ { vir } \simeq 110 ; typical fractional errors at \Delta \simeq 500 - 2000 are improved to \sigma ( M _ { \Delta } ) / M _ { \Delta } \simeq 0.1 - 0.2 compared with 0.2 – 0.3 at \Delta _ { vir } .
Furthermore , comparing the 3D spherical mass with the 2D cylinder mass , obtained from the aperture mass method at a given aperture radius \theta _ { \Delta } , reveals M _ { 2 D } ( < \theta _ { \Delta } ) / M _ { 3 D } ( < r _ { \Delta } = D _ { l } \theta _ { \Delta } ) % \simeq 1.46 and 1.32 for \Delta = 500 and \Delta _ { vir } , respectively .
The amplitude of this offset agrees well with that predicted by integrating an NFW model of cluster-scale halos along the line-of-sight .