Measuring the intrinsic shape and orientation of dark matter (DM) and intracluster (IC) gas in galaxy clusters is crucial to constraining their formation and evolution, and for enhancing the use of clusters as more precise cosmological probes. Extending our previous works, we present for the first time results from a triaxial joint analysis of the galaxy cluster Abell 1835, by means of X-ray, strong lensing (SL) and Sunyaev Zeldovich (SZ) data. We parametrically reconstruct the full three-dimensional structure (triaxial shape and principal axis orientation) of both the DM and the IC gas, and the level of non-thermal pressure of the IC gas. We find that the intermediate-major and minor-major axis ratios of the DM are 0.71+/-0.08 and 0.59+/-0.05, respectively, and the major axis of the DM halo is inclined with respect to the line of sight at 18.3+/-5.2 deg. We present the first observational measurement of the non-thermal pressure out to R_{200}, which has been evaluated to be a few percent of the total energy budget in the internal regions, while reaching approximately 20% in the outer volumes. We discuss the implications of our method for the viability of the CDM scenario, focusing on the concentration parameter C and the inner slope of the DM gamma in order to test the cold dark matter (CDM) paradigm for structure formation: we measure gamma=1.01+/-0.06 and C=4.32+/-0.44, values which are close to the predictions of the CDM model. The combination of X-ray/SL data at high spatial resolution, capable of resolving the cluster core, with the SZ data, which are more sensitive to the cluster outer volume, allows us to characterize the level and the gradient of the gas entropy distribution and non-thermal pressure out to R_{200}, breaking the degeneracy among the physical models describing the thermal history of the ICM.
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