Bulk viscosity in superfluid neutron star cores - I. Direct Urca processesin npe mu matter

The bulk viscosity of the neutron star matter due to the direct Urea proces ses involving nucleons, electrons and muons is studied taking into account possible superfluidity of nucleons in the neutron star cores. The cases of singlet-state pairing or triplet-state pairing (without and with nodes of t he superfluid gap at the Fermi surface) of nucleons are considered. It is s hown that the superfluidity may strongly reduce the bulk viscosity. The pra ctical expressions for the superfluid reduction factors are obtained. For i llustration, the bulk viscosity is calculated for two models of dense matte r composed of neutrons, protons, electrons and muons. The presence of muons affects the bulk viscosity due to the direct Urea reactions involving elec trons and produces additional comparable contribution due to the direct Ure a reactions involving muons. The results can be useful for studying damping of vibrations of neutron stars with superfluid cores.