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Neutrino Emission from Superfluid Neutron-Star Cores: Various Types of Neutron Pairing

We calculate and provide analytic fits of the factors which describe the reduction of the neutrino emissivity of modified Urca and nucleon-nucleon bremsstrahlung processes by superfluidity of neutrons and protons in neutron-star cores. We consider $^1$S$_0$ pairing of protons and either $^1$S$_0$ or $^3$P$_2$ pairing of neutrons. We analyze two types of $^3$P$_2$ pairing: the familiar pairing with zero projection of the total angular momentum of neutron pairs onto quantization axis, $m_J=0$; and the pairing with $|m_J|=2$ which leads to the gap with nodes at the neutron Fermi surface. Combining the new data with those available in the literature we fully describe neutrino emission by nucleons from neutron star cores to be used in simulations of cooling of superfluid neutron stars.