Dark matter halos are fundamental structures in the Universe and serve as crucial cosmological probes. Key properties of halos—such as their concentration, ellipticity, and mass centroid—encode valuable information about their formation and evolutionary history. In particular, halo concentration reflects the collapse time and internal structure of halos, while measurements of ellipticity and centroid positions provide insights into the shape and dynamical state of halos. Moreover, accurately characterizing these properties is essential for improving mass estimates and for testing models of dark matter. Gravitational lensing, which directly probes the projected mass distribution without relying on assumptions about the dynamical state, has emerged as a powerful observational tool to constrain these halo properties with high precision. We aim to derive precise constraints on key structural properties of galaxy clusters—including halo concentration, ellipticity, and the position of mass centroids—by directly fitting observed two-dimensional (2D) weak-lensing shear maps with elliptical Navarro–Frenk–White (NFW) models. These measurements help to reveal the internal structure of massive clusters and to quantify systematic uncertainties in stacked lensing analyses. We performed a 2D weak-lensing analysis of 299 massive clusters selected from the redMaPPer catalog, using shear measurements from the first-year data release of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). Elliptical NFW profiles were fit to the shear maps with Gaussian priors on the halo mass calibrated from the redMaPPer cluster richness–mass relation. These priors serve to break the mass–concentration degeneracy in the statistical modeling and, to some extent, tighten the constraints on the other parameters of primary interest. The derived concentration–mass relation exhibits a slightly steeper slope than traditional weak-lensing power-law or upturn models, and agrees more closely with the results from strong lensing selected halos. More massive and lower-redshift clusters tend to have lower concentrations and appear more spherical. The halo ellipticity distribution is characterized by e = 1 - b/a = 0.530 ± 0.168, with a mean of łangle e ̊angle = 0.505 ± 0.007. We also detect a bimodal distribution in the offsets between optical centers and mass centroids: some halos are well aligned with their brightest cluster galaxy (BCG), while others show significant displacements. These results highlight the power of 2D weak-lensing modeling in probing halo morphology and in providing key inputs for understanding and modeling systematic effects in stacked lensing analyses.
Cui et al. (Thu,) studied this question.