Bulk Viscosity of Relativistic npeμ Matter in Neutron-Star Mergers

Abstract

We discuss the bulk viscosity of hot and dense npeμ matter arising from weak-interaction direct Urca processes. We consider two regimes of interest: (a) the neutrino-transparent regime with T≤Ttr (Ttr≃5÷10 MeV is the neutrino-trapping temperature); and (b) the neutrino-trapped regime with T≥Ttr. Nuclear matter is modeled in relativistic density functional approach with density-dependent parametrization DDME2. The maximum of the bulk viscosity is achieved at temperatures T≃5÷6 MeV in the neutrino-transparent regime, then it drops rapidly at higher temperatures where neutrino-trapping occurs. As an astrophysical application, we estimate the damping timescales of density oscillations by the bulk viscosity in neutron star mergers and find that, e.g., at the oscillation frequency f=10 kHz, the damping will be very efficient at temperatures 4≤T≤7 MeV where the bulk viscosity might affect the evolution of the post-merger object.

Relativistic bulk viscous fluids of Burgers type and their presence in neutron stars

“…It is immediate to verify that our formula for ζ coincides with equation ( 43) of [48]. This confirms that the Burgers model has the correct 'infrared behaviour' in the Navier-Stokes limit.…”

“…3 The fact that escaping neutrinos take energy away does not affect the outcome of the mathematical analysis we carried out till this point. One only needs to correct the conservation law ∇µT µν = 0 with a luminosity term [44]: 4 With analogous calculations to those presented here, it is straightforward to show that the Burgers approximation holds also in the case of trapped neutrinos, provided that the matter is in the slow lepton-equilibration limit [46,48] Plugging these formulas into ( 15) and ( 21), and introducing the compact notation D = A 1 A 2 − (A n + A p ) 2 , we obtain…”

“…Our goal is to prove that equation (20) exactly reproduces the results of Alford, Harutyunyan, and Sedrakian [46,48] about bulk viscosity in hot and dense npeµ matter. To this end, we need first to express the Burgers transport coefficients λ 2 , λ 1 , ζ, and χ in terms of the quantities A n , A p , A 1 , A 2 , C 1 , C 2 , λ e , and λ µ introduced in [46,48].…”

“…To this end, we need first to express the Burgers transport coefficients λ 2 , λ 1 , ζ, and χ in terms of the quantities A n , A p , A 1 , A 2 , C 1 , C 2 , λ e , and λ µ introduced in [46,48]. Comparing our formalism with that of [48], going through some simple (albeit tedious) algebra, one can show that, in the ordered chemical basis {e, µ}, the following 'dictionary relations' hold:…”

“…In order to compare the dynamics of the Burgers model with that of the multicomponent model of [46,48], we need to work in the same physical setting, and compare analogous quantities. The analysis of [46,48] focuses on small periodic oscillations, so that we need to set δQ ∝ e −iωt (note the different sign convention for ω in [46,48]) for all quantities δQ, where the frequency ω ∈ R is not necessarily small, in the sense that we may also have |ωτ a b | ≫ 1. Then, equation (20) becomes…”