Bounds on very heavy relic neutrinos by their annihilation in the Galactic halo

Taking into account neutrino condensation in the gravitational field of collapsing matter, we investigate the annihilation of heavy relic neutrinos in the Galaxy resulting in the generation of cosmic rays. The main neutrino annihilation processes are considered: i.e., νν¯→ff¯ and νν¯→${\mathit{W}}^{+}$ ${\mathit{W}}^{\mathrm{-}}$. The condensation mechanism allows one to get information on the density distribution in the Galaxy halo without any recourse to an explicit dynamical halo model, and the resulting cosmic ray spectrum provides constraints on the heavy neutrino mass. The comparison of the predicted cosmic ray flux with the observed one excludes the heavy neutrino mass range 60 GeV <${\mathit{m}}_{\nu }$<115 GeV. Such a restriction leads to a bound on the present energy density of very heavy neutrinos which may be comparable to the corresponding baryonic one only in the range 115 GeV <${\mathit{m}}_{\nu }$<300 GeV. Our approach is valid for multicomponent dark matter and can be used for species that give even a negligible contribution to the critical cosmological density.