Bulk Viscous Damping of Density Oscillations in Neutron Star Mergers

Abstract

In this paper, we discuss the damping of density oscillations in dense nuclear matter in the temperature range relevant to neutron star mergers. This damping is due to bulk viscosity arising from the weak interaction "Urca" processes of neutron decay and electron capture. The nuclear matter is modelled in the relativistic density functional approach. The bulk viscosity reaches a resonant maximum close to the neutrino trapping temperature, then drops rapidly as temperature rises into the range where neutrinos are trapped in neutron stars. We investigate the bulk viscous dissipation timescales in a post-merger object and identify regimes where these timescales are as short as the characteristic timescale ∼10 ms, and, therefore, might affect the evolution of the post-merger object. Our analysis indicates that bulk viscous damping would be important at not too high temperatures of the order of a few MeV and densities up to a few times saturation density.

Equation of State and Composition of Proto-Neutron Stars and Merger Remnants with Hyperons

“…In the high-temperature regime, the phase-space for Urca processes opens due to the thermal smearing of Fermi surfaces of baryons. This has important ramifications on the oscillations of post-merger remnants through the damping effect of the bulk viscosity driven by Urca processes [34,58,[60][61][62]. Under the supernova conditions, µ-ons are greatly suppressed and the corresponding neutrinos are extinct.…”

Beta Equilibrium under Neutron Star Merger Conditions

“…This condition leads to the upper limits on the proton and electron momenta. If we perform the integrals in the order shown in (19) then the electron momentum integral is the inner integral, so it is performed for known values of k n and k p , so the constraint E ν > 0 corresponds to E e < E n − E p . Similarly, the k p integral is performed for a known value of k n , so its range is constrained by requiring that there be enough energy to create an electron (of unknown momentum) and a neutrino, E p < E n − m e .…”

“…[18] uses the Fermi surface approximation, but develops a way to incorporate the finite 3-momentum of the neutrino, slightly blurring the threshold at finite temperature. Some works do the full phase space integration, but use nonrelativistic approximations for the matrix element and nucleon dispersion relations [5,[19][20][21]. The vast majority of calculations use nonrelativistic approximations of the matrix element and the nucleon dispersion relations, together with the Fermi surface approximation [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Thermal aspects of neutron star mergers

“…The results for µ ∆ from fig. 5 represent a first step towards a discussion of the reactions that serve to reinstate equilibrium and issues relating to, for example, bulk viscosity [10,52], as they allow us to quantify the rate at which the system equilibrates and assess the relevance of bulk viscosity on the fluid dynamics. This argument is notably different from the recent discussion in [53].…”