CHEX-MATE: Cluster multi-probes in three dimensions (CLUMP-3D): II. Combined gas and dark matter analysis from X-ray, SZE, and WL

Under the standard model of hierarchical structure formation, the overall geometry of galaxy clusters is better described by a triaxial ellipse than by a sphere. As a result, the application of spherically symmetric models can result in significant biases, with masses derived from weak-lensing observations being particularly sensitive. These biases can be mitigated by fitting a triaxial model, but this requires deep multi-probe data along with a set of physically motivated models to describe them. We present a multi-probe triaxial analysis method based on the data available for galaxy clusters in the Cluster Heritage project with XMM-Newton - Mass Assembly and Thermodynamics at Endpoint of structure formation (CHEX-MATE), which includes X-ray data from XMM-Newton, Sunyaev-Zel'dovich effect maps from Planck and ACT, and weak-lensing data from Subaru. This work builds upon our previous development of a gas-only X-ray and Sunyaev-Zel'dovich triaxial fitting formalism in Paper I. After verifying our approach using mock observations of model clusters with known properties, we applied it to the CHEX-MATE galaxy cluster PSZ2 G313.33+61.13 (Abell 1689). We found that the cluster is elongated along the line of sight relative to the plane of sky by a factor of & Rscr;(LP) = 1.20 +/- 0.04. As a result, the weak-lensing mass obtained from our triaxial fit, M-200c = (13.88(-1.43)(+1.73)) & times; 10(14)M(circle dot ) , is significantly lower than the value of (17.77(-1.75)(+2.00))& times;10(14)M(circle dot )obtained from a spherically symmetric fit that otherwise employed the same method. Our triaxial fit finds a concentration ofc(200c)=8.66(-1.70)(+2.08), consistent with the spherically symmetric value of 9.99+2.26-1.78, which suggests that the unexpectedly high concentration in Abell 1689 is not due to triaxiality and orientation. We also measured the nonthermal pressure fraction at radii between 0.18-1.37 Mpc and found a minimum of approximately 20% at intermediate radii, increasing to near 30% at the smallest and largest radii, and with a typical measurement precision of +/- 5%.