New constraints on modified Newtonian dynamics from galaxy clusters

We revisit the application of modified Newtonian dynamics (MOND) to galaxy clusters. We confront the high-quality X-ray data for eight clusters of galaxies observed by the XMM-Newton satellite with the predictions of MOND. We obtain a ratio of the MOND dynamical mass to the baryonic mass of M_m/M_b= 4.94 +/- 0.50 in the outer parts (i.e. r~ 0.5R_vir), in the concordance cosmological model where the predicted asymptotic ratio, if any baryons are present, is 7.7^+1.4_-1.1 (at r>= 0.3R_vir). We confirm that the MOND paradigm lowers the discrepancy between the binding mass and the baryonic mass in clusters by a factor of ~1.6 at about half the virial radius. However, at this radius about 80 per cent of the mass is still missing, and as pointed out by Sanders, this necessitates a component of dark baryons or neutrinos in the cluster core. Concerning the neutrino hypothesis, application of the new data requires a minimum neutrino mass of m_ν > 1.74 +/- 0.34 eV to fill this gap. The corresponding 2σ lower limit of m_ν > 1.06 eV is marginally inconsistent with the current constraints from the cluster number counts, and from the cosmic microwave background and large-scale structure data. MOND must invoke neutrinos to represent the main component that account for the missing mass problem in clusters.