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We discuss the bulk viscosity of hot and dense $npe\mu$ matter arising fromweak-interaction direct Urca processes. We consider two regimes of interest:(a) the neutrino-transparent regime with $T\leq T_{\rm tr}$ ($T_{\rm tr}\simeq5\div 10$ MeV is the neutrino-trapping temperature); and (b) theneutrino-trapped regime with $T\geq T_{\rm tr}$. Nuclear matter is modeled inrelativistic density functional approach with density-dependent parametrizationDDME2. The maximum of the bulk viscosity is achieved at temperatures $T \simeq5\div 6$ MeV in the neutrino-transparent regime, then it drops rapidly athigher temperatures where neutrino-trapping occurs. As an astrophysicalapplication, we estimate the damping timescales of density oscillations by thebulk viscosity in neutron star mergers and find that, e.g., at the oscillationfrequency $f=10$ kHz, the damping will be very efficient at temperatures $4\leqT\leq 7$ MeV where the bulk viscosity might affect the evolution of thepost-merger object.

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