  The influence of nucleons superfluidity on the beta relaxation time of
degenerate neutron star cores, composed of neutrons, protons and electrons, is
investigated. We numerically calculate the implied reduction factors for both
direct and modified Urca reactions, with isotropic pairing of protons or
anisotropic pairing of neutrons. We find that due to the non-zero value of the
temperature and/or to the vanishing of anisotropic gaps in some directions of
the phase-space, superfluidity does not always completely inhibit beta
relaxation, allowing for some reactions if the superfluid gap amplitude is not
too large in respect to both the typical thermal energy and the chemical
potential mismatch. We even observe that if the ratio between the critical
temperature and the actual temperature is very small, a suprathermal regime is
reached for which superfluidity is almost irrelevant. On the contrary, if the
gap is large enough, the composition of the nuclear matter can stay frozen for
very long durations, unless the departure from beta equilibrium is at least as
important as the gap amplitude. These results are crucial for precise
estimation of the superfluidity effect on the cooling/slowing-down of pulsars
and we provide online subroutines to be implemented in codes for simulating
such evolutions.
