Weak Lensing Mass Calibration of the ACT DR5 Galaxy Clusters with the DES Year 3 Weak Lensing Data

TL;DR

We calibrate the masses of SZ-selected ACT DR5 clusters using weak-lensing measurements from DES Year 3 within a hierarchical Bayesian framework, enabling a measurement of the hydrostatic mass bias $1-b$ and a forward model for the mass–SZ observable relation. The analysis employs a three-component halo model (1-halo baryons + dark matter plus the 2-halo term) with marginalization over key systematics (photo-$z$ bias, shear calibration, boost factor, and miscentering) and incorporates per-cluster redshifts and SZ measurements, allowing redshift and mass evolution of the bias. We find $1-b=0.75^{+0.04}_{-0.06}$ for the full sample with no evolution and detect strong redshift evolution, $\zeta=2.0^{+0.4}_{-0.7}$ (99.95% confidence), while mass evolution is not significant; a broken-power-law redshift model suggests possible flattening at $z\lesssim0.25$. The results are broadly consistent with independent cross-correlation studies and previous WL analyses, providing a robust mass calibration for ACT clusters and enabling their use as astrophysical and cosmological probes.

Abstract

We use weak gravitational lensing measurements from Year 3 Dark Energy Survey data to calibrate the masses of 443 galaxy clusters selected via the Sunyaev-Zel'dovich effect from Atacama Cosmology Telescope Data Release 5 maps of the cosmic microwave background. We incorporate redshift and SZ measurements for individual clusters into a hierarchical model for the stacked lensing signals and perform Bayesian analyses to constrain the hydrostatic mass bias of the clusters. Our treatment of systematic uncertainties includes a prescription for measuring and accounting for the weak lensing boost factor, consideration of a miscentering effect, as well as marginalization over uncertainties in the source galaxy photometric redshift distributions and shear calibration. The resultant constraints on the normalization of the mass-observable relation have a precision of approximately 7\%, with the mean WL halo mass of $M_{\rm 500c} = 5.4 \times 10^{14} M_{\odot}$. We measure the bias between the true cluster mass and the mass estimated from the SZ signal based on an X-ray--calibrated scaling relation assuming hydrostatic equilibrium, to be $1-b = 0.75^{+0.04}_{-0.06}$ over the full sample. When splitting the clusters into high ($z$=0.43-0.70) and low ($z$=0.15-0.43) redshift bins, we measure $1-b = 0.58^{+0.06}_{-0.05}$ and $0.82^{+0.07}_{-0.07}$, respectively. When introducing additional freedom in redshift and mass to the hydrostatic bias model, we find that $1-b$ decreases with redshift (with the power law of $-2.0^{+0.7}_{-0.4}$, 99.95\% confidence), consistent with findings from other recent studies, while we do not find any significant trend in mass. We also demonstrate that our result is robust against various systematics. The weak-lensing mass calibration presented in this study will be a useful tool for using the ACT clusters as probes of astrophysics and cosmology.

Figures (8)

• Figure 1: The distribution of the 443 Compton-y parameters ($y_{2.4}$) and the redshifts of the cluster sample used in this study. The red lines demarcate our binning of the cluster sample.
• Figure 2: The redshift distributions of the galaxy clusters (gray) and source galaxies (other curves) considered in this work. The vertical gray line at $z=0.43$ shows the location where we split the clusters into two redshift bins. We exclude the first two source redshift bins (dashed) as majority of the galaxies within those bins are at or in front of our cluster sample, having no lensing signal.
• Figure 3: The tangential shear measurements around our cluster sample are shown with the black points with errorbars. The correlation of the same cluster sample with the cross-component of the shear is shown with the grey points with errorbars; the cross-shear component is expected to be consistent with zero in the absence of systematics. The green bands represent the 68% confidence range on the model fit to the data. The left (right) two columns correspond to the low (high) redshift cluster sample, while the top (bottom) panels correspond to the low (high) Compton-y cluster sample.
• Figure 4: The normalized covariance matrix (correlation matrix) for the tangential shear of the cluster bin $y=[0.00,1.05]$ and $z=[0.15,0.43]$. The first six bins represent the tangential shear from the source bin 3, and the last six represents that from the source bin 4.
• Figure 5: The measured boost factors (black points with errorbars) and the corresponding 68% confidence intervals (green bands) from the model fitting. The top (bottom) panels correspond to the low (high) Compton-$y$ bins. The left two (right two) columns correspond to the low (high) redshift bins, as indicated in the title.