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We present a stacked lensing analysis of 96 galaxy clusters selected by the thermal Sunyaev-Zel'dovich (SZ) effect in maps of the cosmic microwave background (CMB). We select foreground galaxy clusters with a $5\sigma$-level SZ threshold in CMB observations from the Atacama Cosmology Telescope, while we define background source galaxies for the lensing analysis with secure photometric redshift cuts in Year 3 data of the Subaru Hyper Suprime Cam survey. We detect the stacked lensing signal in the range of $0.1 < R\, [h^{-1}\mathrm{Mpc}] < 100$ in each of three cluster redshift bins, $0.092

We present an investigation into a hitherto unexplored systematic that affects the accuracy of galaxy cluster mass estimates with weak gravitational lensing. Specifically, we study the covariance between the weak lensing signal, $\Delta\Sigma$, and the "true" cluster galaxy number count, $N_{\rm gal}$, as measured within a spherical volume that is void of projection effects. By quantifying the impact of this covariance on mass calibration, this work reveals a significant source of systematic uncertainty. Using the MDPL2 simulation with galaxies traced by the SAGE semi-analytic model, we measure the intrinsic property covariance between these observables within the 3D vicinity of the cluster, spanning a range of dynamical mass and redshift values relevant for optical cluster surveys. Our results reveal a negative covariance at small radial scales ($R \lesssim R_{\rm 200c}$) and a null covariance at large scales ($R \gtrsim R_{\rm 200c}$) across most mass and redshift bins. We also find that this covariance results in a $2-3\%$ bias in the halo mass estimates in most bins. Furthermore, by modeling $N_{\rm gal}$ and $\Delta\Sigma$ as multi-(log)-linear equations of secondary halo properties, we provide a quantitative explanation for the physical origin of the negative covariance at small scales. Specifically, we demonstrate that the $N_{\rm gal}$-$\Delta\Sigma$ covariance can be explained by the secondary properties of halos that probe their formation history. We attribute the difference between our results and the positive bias seen in other works with (mock)-cluster finders to projection effects. These findings highlight the importance of accounting for the covariance between observables in cluster mass estimation, which is crucial for obtaining accurate constraints on cosmological parameters.

Cosmological constraints from current and upcoming galaxy cluster surveys are limited by the accuracy of cluster mass calibration. In particular, optically identified galaxy clusters are prone to selection effects that can bias the weak lensing mass calibration. We investigate the selection bias of the stacked cluster lensing signal associated with optically selected clusters, using clusters identified by the redMaPPer algorithm in the Buzzard simulations as a case study. We find that at a given cluster halo mass, the residuals of redMaPPer richness and weak lensing signal are positively correlated. As a result, for a given richness selection, the stacked lensing signal is biased high compared with what we would expect from the underlying halo mass probability distribution. The cluster lensing selection bias can thus lead to overestimated mean cluster mass and biased cosmology results. We show that the lensing selection bias exhibits a strong scale-dependence and is approximately 20 to 60 percent for $\Delta\Sigma$ at large scales. This selection bias largely originates from spurious member galaxies within +/- 20 to 60 Mpc/h along the line of sight, highlighting the importance of quantifying projection effects associated with the broad redshift distribution of member galaxies in photometric cluster surveys. While our results qualitatively agree with those in the literature, accurate quantitative modelling of the selection bias is needed to achieve the goals of cluster lensing cosmology and will require synthetic catalogues covering a wide range of galaxy-halo connection models., Comment: 16 pages, 16 figures; replaced to match published version

Counts of galaxy clusters offer a high-precision probe of cosmology, but control of systematic errors will determine the accuracy of this measurement. Using Buzzard simulations, we quantify one such systematic, the triaxiality distribution of clusters identified with the redMaPPer optical cluster finding algorithm, which was used in the Dark Energy Survey Year-1 (DES Y1) cluster cosmology analysis. We test whether redMaPPer selection biases the clusters' shape and orientation and find that it only biases orientation, preferentially selecting clusters with their major axes oriented along the line of sight. Modeling the richness-mass relation as a log-linear relation, we find that the log-richness amplitude $\ln(A)$ is boosted from the lowest to highest orientation bin with a significance of $14\sigma$, while the orientation dependence of the richness-mass slope and intrinsic scatter is minimal. We also find that the weak lensing shear-profile ratios of cluster-associated dark halos in different orientation bins resemble a "bottleneck" shape that can be quantified with a Cauchy function. We test the correlation of orientation with two other leading systematics in cluster cosmology -- miscentering and projection -- and find a null correlation. Analytic templates for the triaxiality bias of observed-richness and lensing profiles are mapped as corrections to the observable of richness-binned lensing profiles for redMaPPer clusters. The resulting mass bias confirms the DES Y1 finding that triaxiality is a leading source of bias in cluster cosmology. However, the richness-dependence of the bias confirms that triaxiality does not fully resolve the tension at low-richness between DES Y1 cluster cosmology and other probes. Our model can be used for quantifying the impact of triaxiality bias on cosmological constraints for upcoming weak lensing surveys of galaxy clusters.

We perform a joint analysis of the counts and weak lensing signal of redMaPPer clusters selected from the Dark Energy Survey (DES) Year 1 dataset. Our analysis uses the same shear and source photometric redshifts estimates as were used in the DES combined probes analysis. Our analysis results in surprisingly low values for $S_8 =\sigma_8(\Omega_{\rm m}/0.3)^{0.5}= 0.65\pm 0.04$, driven by a low matter density parameter, $\Omega_{\rm m}=0.179^{+0.031}_{-0.038}$, with $\sigma_8-\Omega_{\rm m}$ posteriors in $2.4\sigma$ tension with the DES Y1 3x2pt results, and in $5.6\sigma$ with the Planck CMB analysis. These results include the impact of post-unblinding changes to the analysis, which did not improve the level of consistency with other data sets compared to the results obtained at the unblinding. The fact that multiple cosmological probes (supernovae, baryon acoustic oscillations, cosmic shear, galaxy clustering and CMB anisotropies), and other galaxy cluster analyses all favor significantly higher matter densities suggests the presence of systematic errors in the data or an incomplete modeling of the relevant physics. Cross checks with X-ray and microwave data, as well as independent constraints on the observable--mass relation from SZ selected clusters, suggest that the discrepancy resides in our modeling of the weak lensing signal rather than the cluster abundance. Repeating our analysis using a higher richness threshold ($\lambda \ge 30$) significantly reduces the tension with other probes, and points to one or more richness-dependent effects not captured by our model., Comment: 35 pages, 20 figures, submitted to Physical Review D