Dirac neutrino mass from a neutrino dark matter model for the galaxy cluster Abell 1689

Abstract

The dark matter in the galaxy cluster Abell 1689 is modelled as an isothermal sphere of neutrinos. New data on the 2d mass density allow an accurate description of its core and halo. The model has no "missing baryon problem" and beyond 2.1 Mpc the baryons have the cosmic mass abundance. Combination of cluster data with the cosmic dark matter fraction -here supposed to stem from the neutrinos -leads to a solution of the dark matter riddle by left and right handed neutrinos with mass 1.847 ± 0.016 eV/c 2 . The thus far observed absence of neutrinoless double beta decay points to (quasi-) Dirac neutrinos: uncharged electrons with different flavour and mass eigenbasis, as for quarks. Though the cosmic microwave background spectrum is matched up to some 10% accuracy only, the case is not ruled out because the plasma phase of the early Universe may be turbulent. Nothing matters more than dark matter 11 And nothing energises more than dark energy years across, exceeding the theoretical limit of 1.2 billion light years for the largest possible structures expected from the cosmological principle [19]; for the "cosmic train wreck" galaxy cluster Abell 520, which has a central 3− 4 10 13 M ⊙ mass clump with the enormous mass-to-light ratio 800M ⊙ /L R⊙ , it is difficult to explain why weakly interacting DM would have separated itself from the galaxies [20,21,22]; in the cluster Abell 3827 an offset between baryonic and dark mass occurs [23], which is an order of magnitude larger than ΛCDM can explain [24]. Global issues exist as well: the predicted transition for the most massive galaxies to transform from their initial halo assembly at redshifts z = 8 − 4 to the later baryonic evolution seen in star-forming galaxies and quasars is not observed [25]; the galaxy power spectrum deduced from SDSS-III observations fits well to the stretched exponential exp[−(k/k b ) 1/2 ] predicted by turbulence [26].These and further issues [27,28,29] make us reflect on the whole DM riddle. Of course, the most natural source for DM is neutrinos. In ΛCDM they cannot make up the DM due to free streaming: structure formation is hindered when the total mass in the neutrino families exceeds a bound that is maximally 0.72 eV/c 2 [2]. This corresponds to a cosmic mass fraction Ω ν < 1.6%, far below the cosmic dark matter fraction Ω c = 24.2 ± 0.2% 2 . However, there is an argument against this linear structure formation: the Jeans instability is absolute beyond linear perturbations, since any domain of "Jeans-stable" plane waves contains pairs of plane waves which produce at the bilinear level a beat with wavelength inside the Jeans-unstable regime [30]. Hence the plasma may be (weakly) turbulent, produce nonlinear structures like galaxy clusters [31], explain many perplexing observations [27,28] and leave signatures of turbulence in the galaxy distribution [26]. Indeed, the quark-gluon plasma has a low viscosity, which leads to a very large Reynolds number Re ∼ 10 19 for a patch of acoustic horizon size [32,33]. Since this horizon is larger than the...