Superfluid phases of triplet pairing and neutrino emission from neutron stars

Neutrino energy losses through neutral weak currents in the triplet-spin superfluid neutron liquid are studied for the case of condensate involving several magnetic quantum numbers. Low-energy excitations of the multicomponent condensate in the timelike domain of the energy and momentum are analyzed. Along with the well-known excitations in the form of broken Cooper pairs, the theoretical analysis predicts the existence of collective waves of spin density at very low energy. Because of a rather small excitation energy of spin waves, their decay leads to a substantial neutrino emission at the lowest temperatures, when all other mechanisms of neutrino energy loss are killed by a superfluidity. Neutrino energy losses caused by the pair recombination and spin-wave decays are examined in all of the multicomponent phases that might represent the ground state of the condensate, according to modern theories, and for the case when a phase transition occurs in the condensate at some temperature. Our estimate predicts a sharp increase in the neutrino energy losses followed by a decrease, along with a decrease in the temperature, that takes place more rapidly than it would without the phase transition. We demonstrate the important role of the neutrino radiation caused by the decay of spin waves in the cooling of neutron stars.