Cosmological Neutrino Background Revisited

We solve the Boltzmann equation for cosmological neutrinos around the epoch of the electron-positron annihilation in order to verify the freeze-out approximation and to compute accurately the cosmological neutrino distribution function. We find the radiation energy density to be about 0.3% higher than the one predicted by the freeze-out approximation. As a result, the spectrum of the Cosmic Microwave Background anisotropies changes by 0.3-05%, depending on the angular scale, and the amplitude of the mass fluctuations on scales below about 100 h^{-1} Mpc decreases by about 0.2-0.3%.Comment: An error is corrected, figure revised; submitted to Ap

Thermal Evolution of a Pulsating Neutron Star

We have derived a set of equations to describe the thermal evolution of a neutron star which undergoes small-amplitude radial pulsations. We have taken into account, in the frame of the General Theory of Relativity, the pulsation damping due to the bulk and shear viscosity and the accompanying heating of the star. The neutrino emission of a pulsating non-superfluid star and its heating due to the bulk viscosity are calculated assuming that both processes are determined by the non-equilibrium modified Urca process. Analytical and numerical solutions to the set of equations of the stellar evolution are obtained for linear and strongly non-linear deviations from beta-equilibrium. It is shown that a pulsating star may be heated to very high temperatures, while the pulsations damp very slowly with time (a power law damping for 100-1000 years), as long as the damping is determined by the bulk viscosity. The contribution of the shear viscosity to the damping becomes important in a rather cool star with a low pulsation energy.Comment: 10 pages, 3 figures, an important reference to the paper by Finzi & Wolf (1968) is added; analytical consideration of the problem (Section 5) is essentially extende