Cluster cosmology, as investigated by the number counts method, is deeply linked to the constituent properties of our Universe and small-scale astrophysical phenomena. In the number counts method, a key challenge is relating observations of cluster galaxy members or the gas component to the total mass of the system. This dissertation aims to address this challenge by developing a better understanding of mass--observables relation, with a subsequent goal of enhancing the interpretation of cluster samples that have emerged from large-scale multi-wavelength surveys. These surveys include the XMM-XXL project, the Local Cluster Substructure Survey (LoCuSS), and eventually the Dark Energy Survey data (DES). The results of this work support the science goal of understanding the content and evolution of the Universe;;s most massive systems, thereby improving cosmological constraints leading to a better understanding of the constituents of our Universe. In this dissertation, I propose a novel method for cluster mass estimation based on member galaxy kinematics. I demonstrate a percent-level accuracy for the expected conditional log-mass, which implies that this algorithm is one of the most accurate algorithms available in the literature. The accuracy of this algorithm is extensively evaluated on a set of large-scale simulations. Next, all key systematics are identified and calibrated. With this method, we then estimate dynamical masses of a large, optically-selected cluster sample derived from the Sloan Digital Sky Survey (SDSS) and an X-ray-selected cluster sample derived from the XXL Survey. The multi-wavelength scaling behavior of cluster observables is driven by the astrophysical evolution of the baryonic components within the potential well of massive halos. To facilitate the multi-wavelength scaling modeling, I study the stellar and gas content of dark matter halos extracted from the BAHAMAS simulations, a set of large-scale, full-physics hydrodynamical simulations. The results verify the popular log-normal model of the halo population, but deviate from the power-law approximation. With these simulations, I establish a new set of predictions, most importantly an intrinsic anti-correlation between gas mass and stellar content of these systems. This anti-correlation is a key prediction that we continue to strive to confirm through a subset of the LoCuSS cluster sample. I implement a robust hierarchical Bayesian inference algorithm, which models the effects of sample selection and the measurement error covariance, to examine the gas and stellar contents of the underlying dark matter halos. To study the relation between the mass of dark matter halos and the multi-wavelength cluster observables, I apply this model to a subset of the LoCuSS cluster sample. Most importantly, this model enables us to examine the predicted anti-correlation between gas and stellar content of these systems. Finally, the results of this study establish the first empirical evidence for this anti-correlation, which has a profound implication for how the Universe;;s most massive structures formed and evolved.
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