We review the main neutrino emission mechanisms in neutron star crusts and cores. Among them are the well-known reactions such as the electron-positron annihilation, plasmon decay, neutrino bremsstrahlung of electrons colliding with atomic nuclei in the crust, as well as the Urca processes and neutrino bremsstrahlung in nucleon-nucleon collisions in the core. We emphasize recent theoretical achievements, for instance, band structure effects in neutrino emission due to scattering of electrons in Coulomb crystals of atomic nuclei. We consider the standard composition of matter (neutrons, protons, electrons, muons, hyperons) in the core, and also the case of exotic constituents such as the pion or kaon condensates and quark matter. We discuss the reduction of the neutrino emissivities by nucleon superfluidity, as well as the specific neutrino emission produced by Cooper pairing of the superfluid particles. We also analyze the effects of strong magnetic fields on some reactions, such as the direct Urca process and the neutrino synchrotron emission of electrons. The results are presented in the form convenient for practical use. We illustrate the effects of various neutrino reactions on the cooling of neutron stars. In particular, the neutrino emission in the crust is critical in setting the initial thermal relaxation between the core and the crust. Finally, we discuss the prospects of exploring the properties of supernuclear matter by confronting cooling simulations with observations of the thermal radiation from isolated neutron stars.

Abstract. The upper limit on the effective surface temperature of the neutron star (NS) PSR J0205+6449 in the supernova remnant 3C 58 obtained recently by Slane et al. (2002) is analyzed using a modern theory of NS cooling . The observations can be explained by cooling of a superfluid NS with the core composed of neutrons, protons, and electrons, where direct Urca process is forbidden. However, combined with the data on the surface temperatures of other isolated NSs, it gives evidence (emphasized by Slane et al.) that direct Urca process is open in the inner cores of massive NSs. This evidence turns out to be less stringent than that provided by the well known observations of Vela and Geminga.

Abstract. We simulate cooling of superfluid neutron stars with nucleon cores where the direct Urca process is forbidden. We adopt density-dependent critical temperatures T cp (ρ) and T cn (ρ) of singlet-state proton and triplet-state neutron pairing in a stellar core and consider strong proton pairing (with maximum T max cp > ∼ 5 × 10 9 K) and moderate neutron pairing (T max cn ∼ 6 × 10 8 K). When the internal stellar temperature T falls below T max cn , the neutrino luminosity L CP due to Cooper pairing of neutrons behaves ∝T 8 , just as that produced by the modified Urca process (in a non-superfluid star) but is higher by about two orders of magnitude. In this case the Cooper-pairing neutrino emission acts like an enhanced cooling agent. By tuning the density dependence T cn (ρ) we can explain observations of cooling isolated neutron stars in the scenario in which the direct Urca process or a similar process in kaon/pion condensed or quark matter are absent.

Abstract. Cooling of neutron stars (NSs) with the cores composed of neutrons, protons, and electrons is simulated assuming 1 S0 pairing of neutrons in the NS crust, and also 1 S0 pairing of protons and weak 3 P2 pairing of neutrons in the NS core, and using realistic density profiles of the superfluid critical temperatures Tc(ρ). The theoretical cooling models of isolated middle-aged NSs can be divided into three main types. (I) Low-mass, slowly cooling NSs where the direct Urca process of neutrino emission is either forbidden or almost fully suppressed by the proton superfluidity. (II) Medium-mass NSs which show moderate cooling via the direct Urca process suppressed by the proton superfluidity. (III) Massive NSs which show fast cooling via the direct Urca process weakly suppressed by superfluidity. Confronting the theory with observations we treat RX J0822-43, PSR 1055-52 and RX J1856-3754 as slowly cooling NSs. To explain these sufficiently warm sources we need a density profile Tc(ρ) in the crust with a rather high and flat maximum and sharp wings. We treat 1E 1207-52, RX J0002+62, PSR 0656+14, Vela, and Geminga as moderately cooling NSs. We can determine their masses for a given model of proton superfluidity, Tcp(ρ), and the equation of state in the NS core. No rapidly cooling NS has been observed so far.

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