Impact of bulk viscosity on the post-merger gravitational-wave signal from merging neutron stars

In the violent post-merger of binary neutron-star mergers strong oscillations are present that impact the emitted gravitational-wave (GW) signal. The frequencies, temperatures and densities involved in these oscillations allow for violations of the chemical equilibrium promoted by weak-interactions, thus leading to a nonzero bulk viscosity that can impact dynamics and GW signals. We present the first simulations of binary neutron-star mergers employing the self-consistent and second-order formulation of the equations of relativistic hydrodynamics for dissipative fluids proposed by M\"uller, Israel and Stewart. With the spirit of obtaining a first assessment of the impact of bulk viscosity on the structure and radiative efficiency of the merger remnant we adopt a simplified but realistic approach for the viscosity, which we assume to be determined by direct and modified Urca reactions and hence to vary within the stars. At the same time, to compensate for the lack of a precise knowledge about the strength of bulk viscosity, we explore the possible behaviours by considering three different scenarios of low, medium, and high bulk viscosity. In this way, we find that large values of the bulk viscosities damp the collision-and-bounce oscillations that characterize the dynamics of the stellar cores right after the merger. At the same time, large viscosities tend to preserve the $m=2$ deformations in the remnant, thus leading to a comparatively more efficient GW emission and to changes in the post-merger spectrum that can be up to $100\,{\rm Hz}$ in the case of the most extreme configurations. Overall, our self-consistent results indicate that bulk viscosity increases the energy radiated in GWs soon after the merger by $\lesssim 2\%$ in the (realistic) scenario of small viscosity, and by $\lesssim 30\%$ in the (unrealistic) scenario of large viscosity.