CHEX-MATE: The impact of triaxiality and orientation on Planck SZ cluster selection and weak lensing mass measurements

Context. Galaxy cluster abundance measurements are a valuable tool for constraining cosmological parameters, such as the mass density (Ωm) and the density fluctuation amplitude (σ8). Wide-area surveys detect clusters based on observables, such as the total integrated Sunyaev-Zel'dovich effect signal (YSZ) in the case of Planck. Quantifying the survey selection function is necessary for cosmological analyses, with completeness representing the probability of detecting a cluster as a function of its intrinsic properties, such as YSZ and an angular scale θ500. Aims. We determine the completeness of the Planck-selected CHEX-MATE cluster catalog using mock observations of clusters with triaxial shapes and random orientations, with physically-motivated distributions of axial ratios. From these mocks, we derive the distribution of shapes and orientations of the detected clusters, along with any associated bias in weak-lensing-derived mass (MWL) due to this orientation-dependent selection (denoted as 1-bχ). Methods. Employing a Monte Carlo method, we injected triaxial cluster profiles into random positions within the Planck all-sky maps and subsequently determined the completeness as a function of both geometry and SZ brightness. This result was then used to generate 1000 mock CHEX-MATE cluster catalogs. We computed MWL for these mock CHEX-MATE clusters and for equal-sized samples of randomly selected clusters with similar mass and redshift distributions. Results. Cluster orientation impacts completeness, with a higher probability of detecting clusters elongated along the line of sight (LOS). This leads to 1-bχ values of 0-4% for CHEX-MATE clusters relative to a random population. The largest increase in MWL is observed in the lowest-mass objects, which are most impacted by orientation-related selection bias. Conclusions. Clusters in Planck SZ-selected catalogs are preferentially elongated along the LOS and have an average bias in MWL relative to randomly selected cluster samples. This bias is relevant for upcoming SZ surveys such as CMB-S4, and should be considered for surveys utilizing other probes for cluster detection, such as Euclid.