Neutrino emission caused by singlet Cooper pairing of baryons in neutron stars is recalculated by accurately taking into account for conservation of the vector weak currents. The neutrino emissivity via the vector weak currents is found to be several orders of magnitude smaller than that obtained before by different authors. This makes unimportant the neutrino radiation from singlet pairing of protons or hyperons.

Neutrino emission due to the pair breaking and formation processes in the bulk triplet superfluid in neutron stars is investigated with taking into account of anomalous weak interactions. We consider the problem in the BCS approximation discarding Fermi-liquid effects. In this approach we derive self-consistent equations for anomalous vector and axial-vector vertices of weak interactions taking into account the $^{3}P_{2}- ^{3}F_{2}$ mixing. Further we simplify the problem and consider the pure $^{3}P_{2}$ pairing with $m_{j}=0$, as is adopted in the minimal cooling paradigm. As was expected because of current conservation we have obtained a large suppression of the neutrino emissivity in the vector channel. More exactly, the neutrino emission through the vector channel vanishes in the nonrelativistic limit $V_F=0$. The axial channel is also found to be moderately suppressed. The total neutrino emissivity is suppressed by a factor of $1.9\times10^{-1}$ relative to original estimates using bare weak vertices.Comment: 22 pages, 4 figure

Direct Chandra observations of a surface temperature of isolated neutron star in Cassiopeia A (Cas A NS) and its cooling scenario which has been recently simultaneously suggested by several scientific teams put stringent constraints on poorly known properties of the superfluid neutron star core. It was found also that the thermal energy losses from Cas A NS are approximately twice more intensive than it can be explained by the neutrino emission. We use these unique data and well-defined cooling scenario to estimate the strength of KSVZ axion interactions with neutrons. We speculate that enlarged energy losses occur owing to emission of axions from superfluid core of the neutron star. If the axion and neutrino losses are comparable we find c 2 n m 2 a ∼ 5.7 × 10 −6 eV 2 , where m a is the axion mass, and c n is the effective Peccei-Quinn charge of the neutron. (Given the QCD uncertainties of the hadronic axion models, the dimensionless constant c n could range from −0.05 to 0.14.)

The linear response of a nonrelativistic superfluid baryon system on an external weak field is investigated while taking into account the Fermi-liquid interactions. We generalize the theory developed by Leggett for a superfluid Fermi-liquid at finite temperature to the case of time-like momentum transfer typical of the problem of neutrino emission from neutron stars. A space-like kinematics is also analyzed for completeness and compared with known results. We use the obtained response functions to derive the neutrino energy losses caused by recombination of broken pairs in the electrically neutral superfluid baryon matter. We find that the dominant neutrino radiation occurs through the axial-vector neutral currents. The emissivity is found to be of the same order as in the BCS approximation, but the details of its temperature dependence are modified by the Fermi-liquid interactions. The role of electromagnetic correlations in the pairing case of protons interacting with the electron background is discussed in the conclusion.