Viscous Dissipation and Heat Conduction in Binary Neutron-Star Mergers

Abstract

Inferring the properties of dense matter is one of the most exciting prospects from the measurement of gravitational waves from neutron star mergers. However, it requires reliable numerical simulations that incorporate viscous dissipation and energy transport as these can play a significant role in the survival time of the post-merger object. We calculate time scales for typical forms of dissipation and find that thermal transport and shear viscosity will not be important unless neutrino trapping occurs, which requires temperatures above 10 MeV and gradients over length scales of 0.1 km or less. On the other hand, if direct-Urca processes remain suppressed, leaving modified-Urca processes to establish flavor equilibrium, then bulk viscous dissipation could provide significant damping to density oscillations right after merger. When comparing with data from state-of-the-art merger simulations, we find that the bulk viscosity takes values close to its resonant maximum in a typical merger, motivating a more careful assessment of the role of bulk viscous dissipation in the gravitational-wave signal from merging neutron stars.

Damping of density oscillations in neutrino-transparent nuclear matter

“…(1) of Ref. [13] this will be true as long as density oscillations (and the resultant thermal gradients) have wavelengths longer than about a meter. This criterion is obeyed in current simulations, whose spatial resolution is tens of meters at best.…”

“…In Fig. 2, we show the bulk viscosity of nuclear matter with the DD2 and IUF EoS, when subjected to a 1 kHz density oscillation, which is a typical frequency for neutron star mergers [13]. The dashed lines are the bulk viscosity with Urca rates calculated in the Fermi Surface approximation while the solid lines use the exact Urca rates.…”

“…To calculate the dissipation time, we need the energy of an oscillation and the rate at which that energy is dissipated by bulk viscosity. The energy density of an adiabatic baryon density oscillation n B (t) = n B + (∆n) sin (ωt) is [13]…”

“…To facilitate comparison with previous work (for example, [13]), we mention that the "stiffness" of nuclear matter is often described via the nuclear incompressibility K [20,37,45]. K is conventionally defined at saturation density, zero temperature, and for symmetric nuclear matter, and is approximately 250 MeV [39].…”

On the use of tracer particles in simulations of binary neutron stars

“…Besides the study of the ejected matter, another area of research in which the use of tracers is particularly beneficial is the evolution of the binary merger product (BMP), that is, of the metastable object that forms after a binary neutron merger. Significant work recently has gone into understanding the nature of the stability of this BMP [10] and tracers provide a novel way of interpreting the resulting behaviour of the BMP that is otherwise inaccessible to only studying the fluid evolution [56,57].…”