  The neutrino energy emission rate due to formation of Cooper pairs of
neutrons and protons in the superfluid cores of neutron stars is studied. The
cases of singlet-state pairing with isotropic superfluid gap and triplet-state
pairing with anisotropic gap are analysed. The neutrino emission due to
singlet-state pairing of protons is found to be greatly suppressed with respect
to the cases of singlet- and triplet-state pairings of neutrons. The neutrino
emission due to pairing of neutrons is shown to be very important in the
superfluid neutron-star cores with the standard neutrino luminosity and with
the luminosity enhanced by the direct Urca process. It can greatly accelerate
both, standard and enhanced, cooling of neutron stars with superfluid cores.
This enables one to interpret the data on surface temperatures of six neutron
stars, obtained by fitting the observed spectra with the hydrogen atmosphere
models, by the standard cooling with moderate nucleon superfluidity.
