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

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.