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There is a variety of cosmological models for dark matter and dark energy in which a possible interaction is considered between these two significant components of the Universe. We focus on five suggested models of interacting dark matter and dark energy and derive the modified virial theorem for them by developing a previous approach. It provides an opportunity to study the evolution of this modified virial theorem with time and interacting constants for different interacting models. Then, we use this obtained virial condition to investigate the modified mass-temperature relation in galaxy clusters via three various methods. It reveals that the effect of interaction between dark matter and dark energy merely appears in the normalization factor of MâT32. This relation also leads to a new constraint on the constants of interacting models, which only depends on the concentration parameter and density profile of the cluster. Then, we use five observational datasets to check some proposed figures for the constants of interaction which have resulted from other observational constraints. Finally, by fitting the observational results to the modified mass-temperature relation, we obtain values for interacting constants of three models and four specific cases of the two remaining models. In agreement with many other observational outcomes, we find that, according to observational data for masses and temperatures of the galaxy clusters, energy transfer occurs from dark matter to dark energy in the seven investigated models.
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