We perform a joint analysis of X-ray and Sunyaev Zeldovich (SZ) effect data using an analytic model that describes the gas properties of galaxy clusters. The joint analysis allows the measurement of the cluster gas mass fraction profile and Hubble constant independent of cosmological parameters. Weak cosmological priors are used to calculate the overdensity radius within which the gas mass fractions are reported. Such an analysis can provide direct constraints on the evolution of the cluster gas mass fraction with redshift. We validate the model and the joint analysis on high signal-to-noise data from the Chandra X-ray Observatory and the Sunyaev-Zeldovich Array for two clusters, Abell 2631 and Abell 2204.
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