Generalizing MOND to explain the missing mass in galaxy clusters

Modified Newtonian Dynamics (MOND) is a gravitational framework designed to explain the astronomical observations in the Universe without the inclusion of particle dark matter. Modified Newtonian Dynamics, in its current form, cannot explain the missing mass in galaxy clusters without the inclusion of some extra mass, be it in the form of neutrinos or non-luminous baryonic matter. We investigate whether the MOND framework can be generalized to account for the missing mass in galaxy clusters by boosting gravity in high gravitational potential regions. We examine and review Extended MOND (EMOND), which was designed to increase the MOND scale acceleration in high potential regions, thereby boosting the gravity in clusters. We seek to investigate galaxy cluster mass profiles in the context of MOND with the primary aim at explaining the missing mass problem fully without the need for dark matter. Using the assumption that the clusters are in hydrostatic equilibrium, we can compute the dynamical mass of each cluster and compare the result to the predicted mass of the EMOND formalism. We find that EMOND has some success in fitting some clusters, but overall has issues when trying to explain the mass deficit fully. We also investigate an empirical relation to solve the cluster problem, which is found by analysing the cluster data and is based on the MOND paradigm. We discuss the limitations in the text.