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 approach for the viscosity, which we assume to be constant within the stars, but which we vary in strength for different binaries, thus exploring the possible behaviours and obtaining strict upper limits. In this way, we find that large bulk viscosities are very effective at damping the collision-and-bounce oscillations that characterize the dynamics of the stellar cores right after the merger. As a result, the $m=2$ deformations and the gravitational-radiation efficiency of the remnant are considerably reduced, with qualitative and quantitative changes in the post-merger spectrum that can be large in the case of the most extreme configurations. Overall, our crude but self-consistent results indicate that bulk viscosity reduces the energy radiated in GWs by $\lesssim 1\%$ in the (realistic) scenario of small viscosity, and by $\lesssim 15\%$ in the (unrealistic) scenario of large viscosity.Comment: 8 pages, 2 figure

General-relativistic hydrodynamics of non-perfect fluids: 3+1 conservative formulation and application to viscous black-hole accretion

We consider the relativistic hydrodynamics of non-perfect fluids with the goal of determining a formulation that is suited for numerical integration in special-relativistic and general-relativistic scenarios. To this end, we review the various formulations of relativistic second-order dissipative hydrodynamics proposed so far and present in detail a particular formulation that is fully general, causal, and can be cast into a 3+1 flux-conservative form as the one employed in modern numerical-relativity codes. As an example, we employ a variant of this formulation restricted to a relaxation-type equation for the bulk viscosity in the general-relativistic magnetohydrodynamics code $\texttt{BHAC}$. After adopting the formulation for a series of standard and non-standard tests in 1+1-dimensional special-relativistic hydrodynamics, we consider a novel general-relativistic scenario, namely, the stationary, spherically symmetric viscous accretion onto a black hole. The newly developed solution $-$ which can exhibit even considerable deviations from the inviscid counterpart $-$ can be used as a testbed for numerical codes simulating non-perfect fluids on curved backgrounds.Comment: 55 pages, 5 figure

Crustal magnetic fields do not lead to magnetar-strength amplifications in binary neutron-star mergers

The amplification of magnetic fields plays an important role in explaining numerous astrophysical phenomena associated with binary neutron-star mergers, such as mass ejection and the powering of short gamma-ray bursts. Magnetic fields in isolated neutron stars are often assumed to be confined to a small region near the stellar surface, while they are normally taken to fill the whole stars in the numerical modelling. By performing high-resolution, global, and high-order general-relativistic magnetohydrodynamic simulations we investigate the impact of a purely crustal magnetic field and contrast it with the standard configuration consisting of a dipolar magnetic field with the same magnetic energy but filling the whole star. While the crust-configurations are very effective in generating strong magnetic fields during the Kelvin-Helmholtz-instability stage, they fail to achieve the same level of magnetic-field amplification of the full-star configurations. This is due to the lack of magnetized material in the neutron-star interiors to be used for further turbulent amplification and to the surface losses of highly magnetized matter in the crust-configurations. Hence, the final magnetic energies in the two configurations differ by more than one order of magnitude. We briefly discuss the impact of these results on astrophysical observables and how they can be employed to deduce the magnetic topology in merging binaries.Comment: 10 pages, 5 figures, videos of the simulations available on https://youtube.com/playlist?list=PLlETUkKHxhvxmRan-H8rZL45cNdZw0uC