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.
