Bulk Viscosity of Relativistic $npe\mu$ Matter in Neutron-Star Mergers

We discuss the bulk viscosity of hot and dense $npe\mu$ matter arising from weak-interaction direct Urca processes. We consider two regimes of interest: (a) the neutrino-transparent regime with $T\leq T_{\rm tr}$ ($T_{\rm tr}\simeq 5\div 10$ MeV is the neutrino-trapping temperature); and (b) the neutrino-trapped regime with $T\geq T_{\rm tr}$. Nuclear matter is modeled in relativistic density functional approach with density-dependent parametrization DDME2. The maximum of the bulk viscosity is achieved at temperatures $T \simeq 5\div 6$ MeV in the neutrino-transparent regime, then it drops rapidly at higher temperatures where neutrino-trapping occurs. As an astrophysical application, we estimate the damping timescales of density oscillations by the bulk viscosity in neutron star mergers and find that, e.g., at the oscillation frequency $f=10$ kHz, the damping will be very efficient at temperatures $4\leq T\leq 7$ MeV where the bulk viscosity might affect the evolution of the post-merger object.