  In this work, we estimate how much bulk viscosity driven by Urca processes is
likely to affect the gravitational wave signal of a neutron star coalescence.
In the late inspiral, we show that bulk viscosity affects the binding energy at
fourth post-Newtonian (PN) order. Even though this effect is enhanced by the
square of the gravitational compactness, the coefficient of bulk viscosity is
likely too small to lead to observable effects in the waveform during the late
inspiral, when only considering the orbital motion itself. In the post-merger,
however, the characteristic time-scales and spatial scales are different,
potentially leading to the opposite conclusion. We post-process data from a
state-of-the-art equal-mass binary neutron star merger simulation to estimate
the effects of bulk viscosity (which was not included in the simulation
itself). In that scenario, we find that bulk viscosity can reach high values in
regions of the merger. We compute several estimates of how much it might
directly affect the global dynamics of the considered merger scenario, and find
that it could become significant. Even larger effects could arise in different
merger scenarios or in simulations that include non-linear effects. This
assessment is reinforced by a quantitative comparison with relativistic
heavy-ion collisions where such effects have been explored extensively.
