We study the heat capacity and neutrino emission reactions (direct and modified Urca processes, nucleon±nucleon bremsstrahlung, Cooper pairing of nucleons) in the supranuclear density matter of neutron star cores with superfluid neutrons and protons. Various superfluidity types are analysed (singlet-state pairing and two types of triplet-state pairing, without and with gap nodes at the nucleon Fermi surface). The results are used for cooling simulations of isolated neutron stars. Both the standard cooling and the cooling enhanced by the direct Urca process are strongly affected by nucleon superfluidity. Comparison of the cooling theory of isolated neutron stars with observations of their thermal radiation may give stringent constraints on the critical temperatures of the neutron and proton superfluidities in the neutron star cores.

Abstract. The bulk viscosity of neutron star cores containing hyperons is studied taking into account nonequilibrium weak process n + n p + Σ − . The rapid growth of the bulk viscosity within the neutron star core associated with switching on new reactions (modified Urca process, direct Urca process, hyperon reactions) is analyzed. The suppression of the bulk viscosity by superfluidity of baryons is considered and found out to be very important.

Abstract.We study the bulk viscosity in neutron star cores due to modified Urca processes involving nucleons, electrons and muons and analyze its reduction by singlet-state or triplet-state superfluidity of nucleons. In combination with the results of our previous paper on the bulk viscosity due to direct Urca processes, a realistic description of the bulk viscosity in superfluid neutron star cores is obtained. Switching off direct Urca processes with decreasing density in a nonsuperfluid matter lowers the bulk viscosity by 3-5 orders of magnitude. The presence of muons opens additional source of bulk viscosity due to muon Urca processes and lowers the threshold density of the electron direct Urca process. The superfluidity may strongly reduce the bulk viscosity and affect thus damping of neutron star vibrations.

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Abstract. We study thermal states of transiently accreting neutron stars (with mean accretion ratesṀ ∼ 10 −14 − 10 −9 M⊙ yr −1 ) determined by the deep crustal heating of accreted matter sinking into stellar interiors. We formalize a direct correspondence of this problem to the problem of cooling neutron stars. Using a simple toy model we analyze the most important factors which affect the thermal states of accreting stars: a strong superfluidity in the cores of low-mass stars and a fast neutrino emission (in nucleon, pion-condensed, kaon-condensed, or quark phases of dense matter) in the cores of high-mass stars. We briefly compare the results with the observations of soft X-ray transients in quiescence. If the upper limit on the quiescent thermal luminosity of the neutron star in SAX J1808. 4-3658 (Campana et al. 2002) is associated with the deep crustal heating, it favors the model of nucleon neutron-star cores with switched-on direct Urca process.