Galaxy Cluster Constraints on Extensions of Modified Gravity

Abstract Modified Newtonian dynamics (MOND) has achieved notable success in explaining galaxy-scale phenomena and has made several unexpected, a priori predictions that align with observations. However, MOND struggles to account for the dynamics of galaxy groups and clusters without invoking additional unseen mass. To address these shortcomings, various extensions to MOND have been proposed. Among these, extended MOND (EMOND) and MOND combined with a form of dark matter (DM), denoted MOND + DM, offer distinct theoretical pathways. However, these models often introduce additional degrees of freedom or mathematical complexities that limit their falsifiability. In this work, we investigate the viability of EMOND and MOND + DM in the context of galaxy clusters using both observational and theoretical constraints. We use Chandra observations of cluster temperature profiles, alongside the assumption of hydrostatic equilibrium (HSE), to evaluate the predictive power of these extensions. Our analysis reveals that HSE imposes stringent constraints on MOND-based theories, highlighting points of failure in both the EMOND and MOND + DM paradigms. We derive new theoretical bounds that MOND + DM models must satisfy to remain consistent with observed mass and temperature distributions and show that these can be tested with X-ray observatories such as XRISM. For EMOND, we demonstrate significant inconsistencies between its predictions and observed cluster profiles, suggesting that EMOND is not a viable solution at the cluster scale. Our findings emphasize the need for further theoretical development within the MOND framework to reconcile its success at galaxy scales with its shortcomings in more massive systems.