Neutrino emission from spin waves in neutron spin-triplet superfluid

The linear response of a neutron spin-triplet superfluid onto external weak axial-vector field is studied for the case of $^{3}P_{2}$ pairing with a projection of the total angular momentum $m_{j}=0$. The problem is considered in the BCS approximation discarding Fermi-liquid effects. The anomalous axial-vector vertices of neutron quasiparticles possess singularities at some frequencies which specify existence of undamped spin-density waves in the Cooper condensate. The spin waves are of a low excitation energy and are kinematically able to decay into neutrino pairs through neutral weak currents. We evaluate the neutrino emissivity from the spin wave decays in the bulk neutron superfluid in old neutron stars. This calculation predicts significant energy losses from within a neutron star at lowest temperatures when all other mechanisms of neutrino emission are killed by the neutron and proton superfluidity.