Galaxy Cluster Constraints on Extensions of Modified Gravity

Modified Newtonian Dynamics (MOND) has successfully matched observations on galaxy scales; however, the paradigm fails to match observations on larger scales, specifically in groups and clusters of galaxies. To rectify these tensions, various MOND extensions have emerged; however, many of these introduce mathematical abstractions or additional free parameters which make these extensions difficult to refute or confirm. In this work two such branches, EMOND and MOND + Dark Matter, are challenged using observational and theoretical constraints which emerge from galaxy clusters. CHANDRA observations of a collection of galaxy clusters are used to constrain the asymptotic behavior of the cluster temperature profiles in each MOND branch. The assumption of hydrostatic equilibrium implies very tight constraints on the MOND phenomenology and introduces some non-trivial points of failure in both branches. We demonstrate that the MOND + DM paradigm may constrained by the imposition of hydrostatic equilibrium in galaxy clusters and several results are derived to that effect. We show that these constraints could be tested with upcoming X-ray missions, including XRISM. Furthermore, we illustrate significant inconsistencies in the EMOND paradigm which suggest that extension to be non-viable in clusters of galaxies. These findings place considerable pressure on further development of MOND in the cluster regime.