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 betaequilibrium. 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.