SPT Clusters with DES and HST Weak Lensing. I. Cluster Lensing and Bayesian Population Modeling of Multi-Wavelength Cluster Datasets

We present a Bayesian population modeling method to analyze the abundance ofgalaxy clusters identified by the South Pole Telescope (SPT) with asimultaneous mass calibration using weak gravitational lensing data from theDark Energy Survey (DES) and the Hubble Space Telescope (HST). We discuss andvalidate the modeling choices with a particular focus on a robust,weak-lensing-based mass calibration using DES data. For the DES Year 3 data, wereport a systematic uncertainty in weak-lensing mass calibration that increasesfrom 1account for uncertainties in the impact of baryonic effects. We implement ananalysis pipeline that joins the cluster abundance likelihood with amulti-observable likelihood for the Sunyaev-Zel'dovich effect, opticalrichness, and weak-lensing measurements for each individual cluster. Wevalidate that our analysis pipeline can recover unbiased cosmologicalconstraints by analyzing mocks that closely resemble the cluster sampleextracted from the SPT-SZ, SPTpol ECS, and SPTpol 500d surveys and the DES Year3 and HST-39 weak-lensing datasets. This work represents a crucial prerequisitefor the subsequent cosmological analysis of the real dataset.