Do non-relativistic neutrinos constitute the dark matter?

The dark matter of the Abell 1689 galaxy cluster is modeled by thermal, non-relativistic gravitating fermions and its galaxies and X-ray gas by isothermal distributions. A fit yields a mass of $h_{70}^{1/2}(12/{\overline g})^{1/4}$1.445 $(30)$ eV. A dark matter fraction $Ω_ν=h_{70}^{-3/2}0.1893$ $(39)$ occurs for ${\overline g}=12$ degrees of freedom, i. e., for 3 families of left plus right handed neutrinos with masses $\approx 2^{3/4}G_F^{1/2}m_e^2$. Given a temperature of 0.045 K and a de Broglie length of 0.20 mm, they establish a quantum structure of several million light years across, the largest known in the Universe. The virial $α$-particle temperature of $9.9\pm1.1$ keV$/k_B$ coincides with the average one of X-rays. The results are compatible with neutrino genesis, nucleosynthesis and free streaming. The neutrinos condense on the cluster at redshift $z\sim 28$, thereby causing reionization of the intracluster gas without assistance of heavy stars. The baryons are poor tracers of the dark matter density.

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