Modified Newtonian Dynamics and galaxy clusters

First proposed by Milgrom in 1983 as an alternative to the standard Cold Dark Matter (CDM) paradigm, Modified Newtonian Dynamics (MOND) has gained renewed momentum in light of persistent nondetections of exotic dark matter particles and growing tensions facing CDM on galactic scales. While MOND perfectly reproduces galactic rotation curves, it encounters notable challenges in explaining the equilibrium of galaxy clusters. Although it reduces the overall dark matter budget in these massive systems, an unidentified mass component remains required. This paper investigates the hypothesis that this missing mass is baryonic: composed of nonradiating ordinary matter such as stellar remnants, gas too diffuse to initiate star formation, or compact, ultra-dense clouds of cold molecular gas with low volume filling factors. Using a sample of 106 clusters mapped in X-rays, emitted by the hot intracluster medium composing most of the visible mass, we derive first the total mass within the Newtonian dynamics, assuming hydrostatic equilibrium and spherical symmetry. Then, with the modified Poisson equation, we reconstruct the spatial distribution of the invisible missing matter within the MOND framework. In the sample, the relaxed systems harboring cooling flows, known as cool-core clusters, have the highest peaks of dark missing mass. Its density profile reveals a pronounced central concentration bounded by a steep truncation immediately beyond a core radius of 20 to 30 kpc, confirming previous studies. MOND reduces the necessary dynamical mass by a factor of 4 to 10. The residual missing mass is proportional to the total gas mass, being roughly twice lower.