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Dynamics of Cosmic Neutrinos in Galaxies

Abstract The cosmic background of massive (about 1 eV rest-energy) neutrinos can be cooled to extremely low temperatures, reaching almost completely degenerated state. The Fermi velocity of the neutrinos becomes less than 100 km/s. The equations of dynamics for the cosmic background neutrinos are derived for the spherical and axisymmetrical thin circular disk galaxies. The equations comprise the gravitational potential and gravity of the uniform baryonic disk galaxies. Then the equations are integrated analytically over the disk radius. The constant radial neutrino flux in spherical galaxies favors formation of the wide unipotential wells in them. The neutrino flux in the axisymmetrical galaxies suggests to favor the evolution in the direction of a spherically symmetrical potential. The generated unipotential wells are observed as plateaux in the velocity curves of circular stellar orbits. The constant neutrino density at galactic centers gives the linear part of the curves. The derived system of quasilinear differential equations for neutrinos in the axisymmetrical galaxies have been reduced to the system of the Lagrange-Charpit equations: the coupled differential equations, specifying the local neutrino velocities and dynamics of motion along trajectories, and an additional interconnected equation of the neutrino mass conservation, which can be applied for the determination of density of the neutrino component in galaxies.