The damping of radial pulsations of neutron stars, provided by non-equilibrium Urca processes, is studied for a simple model of a non-superfluid star with the core composed of neutrons, protons, and electrons.

Special attention is paid to the suprathermal pulsation regime for which the disbalance of chemical potentials of particles due to deviations from beta-equilibrium in a pulsating matter is higher than the thermal energy.

It is shown that in this case simultaneous account of thermal balance equation and the equation describing the damping of the radial modes is required. A set of self-consistent solutions of these equations is numerically obtained in the isothermal approximation for a star where the direct Urca process is forbidden.

The dissipation mechanisms included are the viscous damping due to modified Urca process and the shear viscosity in the core. A strong effect of suprathermal oscillations on the neutrino emission in the modified Urca process is also incorporated.

It is demonstrated that radial pulsations evolve for a long time in the regime intermediate between the suprathermal and (traditional small-amplitude) thermal regimes. Such pulsations can substantially influence the neutron star cooling on a time scale of the order of 1000 years.

The work was supported by INTAS grant YSF 03-55-2397, RFBR grant 02-02-17668, and RLSSP project 1115.2003.2.

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