Impact of muons on the bulk viscosity of neutron star matter metamodels

Abstract

Recent studies invoke a unified description of different neutron star observables using metamodels, which parametrize the Equation of State (EoS) of neutron star matter close to nuclear saturation density in terms of few nuclear parameters. In this light, the bulk viscosity in the neutrino-transparent regime of dense nuclear matter composed of neutrons, protons and electrons has been recently shown to be mostly sensitive to the value of the nuclear symmetry energy. As muons are also present at densities around nuclear saturation, we further analyse in this manuscript their impact on this transport coefficient as a function of the slope $L$ of the symmetry energy. We find that muons introduce both relevant qualitative and quantitative effects in the bulk viscous dissipation. Increasing $L$ by a factor two has an effect of several orders of magnitude on the (frequency-independent) bulk viscosity. We also find that for all values of $L$ the frequency-dependent bulk viscosity presents a double peak structure for some values of the density, absent without muons. This also represents changes in orders of magnitude of the viscosity in narrow windows of densities that could be attainable in a neutron star for enough high values of $L$. We present a systematic numerical analysis of both second-order transport coefficients, frequency-dependent bulk viscosity, and damping times of density oscillations as a function of the density and the slope, and find when these could be relevant for the dynamics of the merger of neutrons stars.

Figures (12)

• Figure 1: Particle fractions $X_a$ as a function of the baryon number density $n_B$ divided by nuclear saturation density $n_0$ at $L=50$ MeV (dotted-dashed lines), $L=70$ MeV (dashed lines) and $L=110$ MeV (continuous lines). The different curves are obtained at $J=32$ MeV, $K=240$ MeV and $K_{\rm sym}=Q=Q_{\rm sym}=0$.
• Figure 2: Density threshold of the dUrca processes $n_{B,\text{dU}}$ in multiples of the saturation density $n_0$ as a function of the symmetry slope. Only for densities above the red/blue curve dUrca processes for electrons/muons are kinematically allowed. The different curves are obtained at $J = 32$ MeV and $K = 240$ MeV, and $K_{\rm sym} = Q = Q_{\rm sym} = 0$.
• Figure 3: Density threshold of the dUrca processes $n_{B,\text{dU}}$ in multiples of the saturation density $n_0$ as a function of the incompressibility $K_{\rm sym}$. Only for densities above the red/blue curve dUrca processes for electrons/muons are kinematically allowed. We vary $L$ as follows: $L=50$ MeV (dashed-dotted lines), $L=70$ MeV (dashed lines) and $L=110$ MeV (continuous lines). The different curves are obtained at $J = 32$ MeV and $K = 240$ MeV, and $K_{\rm sym} = Q = Q_{\rm sym} = 0$.
• Figure 4: Electroweak coefficients $\lambda_1$ (upper panel) and $\lambda_2$ (bottom panel) as a function of temperature $T$ in log scale at $n_B=2 n_0$ (dashed-dotted lines) and $n_B=3n_0$ (solid lines). The red, black and blue curves represent $L=50$ MeV, $L=70$ MeV and $L=110$ MeV, respectively. The different curves are obtained at $J=32$ MeV, $K=240$ MeV and $K_{\rm sym}=Q=Q_{\rm sym}=0$.
• Figure 5: Electroweak rates $\lambda_1$ (upper panel) and $\lambda_2$ (lower panel) as a function of baryon number density $n_B$ (in multiples of the saturation density) in log scale at $T=1$ MeV (dashed-dotted lines) and $T=5$ MeV (continuous lines). The red, black and blue curves represent $L=50$ MeV, $L=70$ MeV and $L=110$ MeV, respectively. The different curves are obtained at $J=32$ MeV, $K=240$ MeV and $K_{\rm sym}=Q=Q_{sym}=0$.