Subjecting dark matter candidates to the cluster test

Galaxy clusters, employed by Zwicky to demonstrate the existence of dark matter, pose new stringent tests. If merging clusters demonstrate that dark matter is self-interacting with cross section $\sigma/m\sim 2$ cm$^2$/gr, MACHOs, primordial black holes and light axions that build MACHOs are ruled out as cluster dark matter. Recent strong lensing and X-ray gas data of the quite relaxed and quite spherical cluster A1835 allow to test the cases of dark matter with Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distribution, next to Navarro-Frenck-White profiles. Fits to all these profiles are formally rejected at over $5\sigma$, except in the fermionic situation. The interpretation in terms of (nearly) Dirac neutrinos with mass of $1.61^{+0.19}_{-0.30}$ eV/$c^2$ is consistent with results on the cluster A1689, with the WMAP, Planck and DES dark matter fractions and with the nondetection of neutrinoless double $\beta$-decay. The case will be tested in the 2018 KATRIN experiment.