RedMaPPer Cluster Properties from Two-Dimensional Lensing Shear Maps in the HSC-SSP Survey

Abstract

Dark matter halos are fundamental cosmological structures whose properties-such as concentration, ellipticity, and mass centroid-encode information about their formation and evolution. Concentration traces collapse time and internal structure, while ellipticity and centroid offsets reflect halo shape and dynamical state. Accurate characterization of these properties improves mass estimates and tests dark matter models. Gravitational lensing, which directly probes projected mass distributions, provides a powerful means to constrain halo structure. We present a 2D weak-lensing analysis of 299 RedMaPPer clusters using shear measurements from the HSC-SSP first-year data release. By fitting elliptical NFW models with mass priors from the RedMaPPer cluster richness-mass relation, considering the priors helps us break the mass-concentration degeneracy and tighten constraints on other parameters. 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 <e>=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.

Figures (8)

• Figure 1: Normalized distribution of spectroscopic redshifts for the lens sample (purple dashed) and photometric redshifts for the source sample (blue solid).
• Figure 2: Upper panels: The left panel shows the observed 2D shear map for an illustrative RedMaPPer cluster ($M\simeq10^{14.73} h^{-1}M_{\odot}$), while the right panel displays the corresponding best-fitting shear field predicted by the elliptical NFW model. Each map covers an area of 18$'$$\times$18$'$. In both maps, the orientation and length of the sticks within each 1$'$$\times$1$'$ pixel indicate the local tangential direction and amplitude of the distortion, respectively. For visualization purposes, both shear fields have been smoothed with a Gaussian kernel with a full width at half maximum (FWHM) of $\approx2'$33. The blue dot marks the weak-lensing-derived center, and the red pentagram denotes the observed center. Lower panel: Posterior constraints on structural parameters of the cluster, including the halo concentration, ellipticity, and projected offsets of the mass centroid. The contours represent the $1\sigma$ and $2\sigma$ confidence levels.
• Figure 3: The concentration–mass (c–M) relation. Light gray points represent the best-fitting concentration and mass for individual clusters, while black points show the weighted average values in each mass bin, with error bars indicating the standard deviation. For comparison, the results on strong-lensing selected halos from Meneghetti_SL are shown as orange solid line. Weak-lensing-based results from 19 (upturn model) are plotted as blue dot-dashed line, and the power-law model from 2008Duffy derived from dark-matter-only numerical simulations, is plotted as red dashed line, respectively.
• Figure 4: The concentration–mass–redshift (c–M–z) relation. Gray points indicate the positions of individual clusters in the mass–redshift plane. Colored diamonds represent the weighted mean concentration within each bin. Bins containing fewer than 10 clusters are excluded from the analysis. Colored contour lines trace surfaces of constant concentration across the plane, and the color bar (labelled "concentration") gives their numerical values.
• Figure 5: Upper panel: Probability distribution function (PDF) of the projected offset between the BCG position and the weak-lensing-determined halo center. Red data points show the observed BCG offsets in our sample, with error bars estimated via 1000 bootstrap resamplings. The blue and black solid lines represent the best-fitting single- and two-component 2D Gaussian models, respectively. The purple and orange dashed lines correspond to the well-centered and miscentered components of the two-component model. All offset scale parameters, including $\sigma$, $\sigma_1$, and $\sigma_2$, are expressed in units of $h^{-1} \mathrm{kpc}$. Lower panels: Fitting results for the two-component (left) and single-component (right) 2D Gaussian models. Contours indicate $1\sigma$ and $2\sigma$ confidence levels, with best-fitting values and 68% confidence intervals shown above each 1D marginalized distribution.