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We study the bulk viscosity of moderately hot and dense, neutrino-transparentrelativistic $npe\mu$ matter arising from weak-interaction direct Urcaprocesses. This work parallels our recent study of the bulk viscosity of$npe\mu$ matter with a trapped neutrino component. The nuclear matter ismodeled in a relativistic density functional approach with two differentparametrizations -- DDME2 (which does not allow for the low-temperaturedirect-Urca process at any density) and NL3 (which allows for low-temperaturedirect-Urca process above a low-density threshold). We compute theequilibration rates of Urca processes of neutron decay and lepton capture, aswell as the rate of the muon decay, and find that the muon decay process issubdominant to the Urca processes at temperatures $T\geq 3$MeV in the case ofDDME2 model and $T\geq 1$MeV in the case of NL3 model. Thus, theUrca-process-driven bulk viscosity is computed with the assumption that pureleptonic reactions are frozen. As a result the electronic and muonic Urcachannels contribute to the bulk viscosity independently and at certaindensities the bulk viscosity of $npe\mu$ matter shows instead of the standardone-peak (resonant) form a "flattened" shape. In the final step, we estimatethe damping timescales of density oscillations by the bulk viscosity. We findthat, e.g., at a typical oscillation frequency $f=1$kHz, the damping ofoscillations is most efficient at temperatures $3\leq T\leq 5$MeV and densities$n_B\leq 2n_0$ where they can affect the evolution of the post-merger object.

Bulk viscosity from Urca processes: $npe\mu$ matter in the neutrino-transparent regime