Temperature-dependent pulsations of superfluid neutron stars

We examine radial oscillations of superfluid neutron stars at finite internal temperatures. For this purpose we generalize the description of relativistic superfluid hydrodynamics to the case of superfluid mixtures. We show that in a neutron star at hydrostatic and beta-equilibrium the red-shifted temperature gradient is smoothed out by neutron superfluidity (but not by proton superfluidity). We calculate radial oscillation modes of neutron stars assuming "frozen" nuclear composition in the pulsating matter. The resulting pulsation frequencies show a strong temperature dependence in the temperature range (0.1-1) T_cn, where T_cn is the critical temperature of neutron superfluidity. Combining our results with thermal evolution, we obtain a significant evolution of the pulsation spectrum, associated with highly efficient Cooper pairing neutrino emission, for 20 years after superfluidity onset.