Equilibrium configurations of 11 eV sterile neutrinos in MONDian galaxy clusters

Modified Newtonian dynamics (MOND) can fit a broad range of galaxy kinematic data, but struggles with clusters of galaxies. MONDian clusters need dark matter (DM), and here we test the 11 eVc^-2 sterile neutrino (SN) - used to fit the first three acoustic peaks of the cosmic microwave background (CMB) - by investigating their equilibrium distributions in 30 groups and clusters over a wide range of temperatures. We do this by first taking the known SN density, necessary for hydrostatic equilibrium of the intracluster medium (or to produce the observed lensing map). Then, we solve for the SN velocity dispersion (VD), needed for their own hydrostatic equilibrium, through the equation of state for a partially degenerate neutrino gas. The VD is a unique, continuous function of radius determined by the density and mass of the SN particles. Knowing both the SN density and VD tells us the Tremaine-Gunn phase-space limit at all radii. We find that all 30 systems serendipitously reach the Tremaine-Gunn limit by the centre, which means a portion of the dynamical mass must always be covered by the brightest cluster galaxy. Interestingly, the typical fitted K-band mass-to-light ratio is unity and at most 1.2, which is very consistent - although leaving no margin for error - with stellar population synthesis models. Amidst the sample there are several special cases including the Coma cluster (for which DM was first proposed), NGC 720 (where geometrical evidence for DM was found) and the bullet cluster (where DM - of some kind - in clusters was directly proven to exist). We demonstrate that 11 eVc^-2 SNs are unlikely to influence spiral galaxy rotation curves, as they do not influence even some very massive early-types (NGC 4125 and NGC 6482). Finally, we conclude that it is intriguing that the minimum mass of SN particle that can match the CMB is the same as the minimum mass found here to be consistent with equilibrium configurations of MONDian clusters of galaxies.