Symmetry energy dependence of the bulk viscosity of nuclear matter

TL;DR

The paper addresses how the weak-interaction-driven bulk viscosity $\zeta_0$ and bulk relaxation time $\tau_{\Pi}$ of neutrino-transparent $npe$ matter depend on the nuclear symmetry energy, characterized by $S$ and its slope $L$ at saturation. Using the Israel-Stewart framework and a parabolic approximation for the symmetry energy, it derives explicit expressions showing $\tau_{\Pi}$ and $\zeta_0$ depend on $S$, $L$, and electron contributions, with $\tau_{\Pi}(n_{sat}) = \frac{n_{sat}}{\lambda}\big[ 8S + \frac{\partial^2 E_l}{\partial Y^2} \big]^{-1}$ and $\zeta_0(n_{sat}) = \frac{n_{sat}^4}{\lambda}\big[ 8S + \frac{\partial^2 E_l}{\partial Y^2} \big]^{-2}\big[ \frac{4L}{3n_{sat}}(2Y-1) + \frac{\partial^2 E_l}{\partial n_B\partial Y} - \frac{1}{n_{sat}}\frac{\partial E_l}{\partial Y} \big]^2$. The parabolic approximation is validated against chiral EFT EOSs, showing that $\zeta_0$ at $n_{sat}$ can vary by orders of magnitude with $L$. The study links these transport properties to both dissipative and conservative tidal responses via the Green's function, implying that gravitational-wave observations of neutron-star inspirals could constrain $L$ through the bulk modulus $\zeta_0/\tau_{\Pi}$ and related quantities, while noting model and density-range limitations.

Abstract

We clarify how the weak-interaction-driven bulk viscosity $ζ$ and the bulk relaxation time $τ_Π$ of neutrino-transparent $npe$ matter depend on the nuclear symmetry energy. We show that, at saturation density, the equation-of-state dependence of these transport quantities is fully determined by the experimentally constrained nuclear symmetry energy $S$ and its slope $L$. Variations of $L$ can change the bulk viscosity by orders of magnitude, which can affect both the dissipative and the conservative tidal response of neutron stars. This suggests that both conservative and dissipative effects encoded in the gravitational-wave signatures of binary neutron star inspirals may help constrain nuclear symmetry energy properties.

Figures (3)

• Figure 1: The dimensionless bulk modulus as a function of the baryon density. The blue curves are calculated directly from the chiral EFT parameterization Tews:2024owlHippert:2024humHebeler:2010jxBedaque:2014sqaTews:2018kmu. The red curves are calculated using the parabolic symmetry energy approximation of the chiral EFT parameterization. The purple region denotes the overlap between blue and red curves (darker colors reflect a higher density of curves).
• Figure 2: Bulk viscosity at $n_{\mathrm{sat}}$ as a function of $S$ or $L$. The blue curve is calculated directly from a chiral EFT parameterization Tews:2024owlHippert:2024humHebeler:2010jxBedaque:2014sqaTews:2018kmu. The red curve is calculated using the parabolic symmetry energy approximation of the chiral EFT parameterization.
• Figure 3: Bulk viscosity vs. relaxation time at $n_{\mathrm{sat}}$. The green box is calculated using $S \in [30, 40]$ MeV and $L \in [30, 150]$ MeV. The red curve is calculated using the chiral EFT parameterizations Tews:2024owlHippert:2024humHebeler:2010jxBedaque:2014sqaTews:2018kmu.