Far-from-equilibrium bulk-viscous transport coefficients in neutron star mergers

We investigate the weak-interaction-driven bulk-viscous transport properties of npe matter in the neutrino transparent regime. Previous works assumed that the induced bulk viscosity correction to pressure, near beta equilibrium, is linear in deviations from the equilibrium charge fraction. We show that this is not always true for (some) realistic equations of state at densities between one and three times saturation density. This nonlinear nature of the perturbation around equilibrium motivates a far-from-beta-equilibrium description of bulk-viscous transport in neutron star mergers, which can be precisely achieved using a new Israel-Stewart formulation with resummed bulk and relaxation time transport coefficients. The computation of these transport coefficients depends on out-of-beta-equilibrium pressure corrections, which can be computed for a given equation of state. We calculate these coefficients for equations of state that satisfy the latest constraints from multimessenger observations from LIGO/Virgo and NICER detectors. We show that varying the nuclear symmetry energy $J$ and its slope $L$ can significantly affect the transport coefficients and the nonlinear behavior of the out-of-equilibrium pressure corrections. Therefore, having better constraints on $J$ and $L$ will directly impact our understanding of bulk-viscous processes in neutron star mergers.

Figure 1

Mass-radius relation of our EoS. (a) EoS with varying symmetry energy. (b) EoS with varying symmetry slope. Observational constraints on the neutron star mass-radius plane from LIGO/Virgo [1, 15, 71] and NICER [72, 73, 74, 75] results. The yellow and brown regions correspond to $90\%$ confidence regions obtained from the GW170817 event by universal relations and spectral EoS approaches, respectively. The green and red regions correspond to $90\%$ confidence regions obtained from NICER data on PSR $\mathrm{J0030}+0451$ and $\mathrm{J0740}+6620$. The green regions are obtained using the Illinois-Maryland analysis, and the red regions are obtained using the Amsterdam analysis.

Figure 2

Temperature dependence of the bulk viscosity ${\zeta }_0$ determined using parameters in beta equilibrium. (a) Results for different EoSs corresponding to several values of the symmetry energy, with the inset showing the difference between J1 and J6. (b) Similar plot for EoSs with different symmetry slopes.

Figure 3

Temperature dependence of the AC bulk viscosity determined using parameters in beta equilibrium. (a) Results for different EoSs obtained by varying the symmetry energy. (b) Results for different EoSs obtained by varying the symmetry slope. The oscillation frequency is fixed at $1\text{kHz}$.

Figure 4

Resummed $\zeta$ as a function of the deviation from the equilibrium charge fraction, at temperature $T=2$ MeV, for several symmetry energies. (a) Symmetry energy dependence of $\zeta$ evaluated at the energy density corresponding to nuclear saturation density. (b) Same quantity, computed at twice the nuclear saturation density.

Figure 5

Resummed $\zeta$ as a function of the deviation from the equilibrium charge fraction, for several symmetry slopes at temperature $T=2$ MeV. (a) Symmetry slope dependence of the $\zeta$ evaluated at the energy density corresponding to nuclear saturation density. (b) Same quantity, now computed at twice the nuclear saturation density.

Figure 6

Resummed ${\tau }_{\mathrm{\Pi }}$ as a function of the deviation from the equilibrium charge fraction, for several symmetry energies, at temperature $T=2$ MeV. (a) Symmetry energy dependence of the resummed ${\tau }_{\mathrm{\Pi }}$ for the energy density corresponding to nuclear saturation density. (b) The same quantity is evaluated at twice the nuclear saturation density.

Figure 7

Resummed ${\tau }_{\mathrm{\Pi }}$ as a function of the deviation from the equilibrium charge fraction, for several symmetry slopes, at temperature $T=2$ MeV. (a) Resummed ${\tau }_{\mathrm{\Pi }}$ for the energy density corresponding to nuclear saturation density. (b) The same quantity is evaluated at twice the nuclear saturation density.

Figure 8

Bulk scalar $\mathrm{\Pi }$ (normalized by the equilibrium pressure) as a function of the deviation from the equilibrium charge fraction, for several symmetry energies, at temperature $T=2$ MeV. (a) $\mathrm{\Pi }$ for the energy density corresponding to nuclear saturation density. (b) The same quantity is evaluated at twice the nuclear saturation density.

Figure 9

Bulk scalar $\mathrm{\Pi }$ (normalized by the equilibrium pressure) as a function of the deviation from the equilibrium charge fraction for several symmetry slopes at temperature $T=2$ MeV. (a) $\mathrm{\Pi }$ for the energy density corresponding to nuclear saturation density. (b) The same quantity is evaluated at twice the nuclear saturation density.

Figure 10

Bulk scalar $\mathrm{\Pi }$ (normalized by the equilibrium pressure) of the J4 EoS as a function of the deviation from the equilibrium charge fraction, at temperature $T=2$ MeV. The different curves represent energy densities corresponding to baryon densities ranging from one to three times saturation density. Note that $\mathrm{\Pi }$ displays a clear minimum for the J4 EoS at twice the saturation density.

Figure 11

The relative difference between the charge fraction at the point of minimum $\mathrm{\Pi }$ as a function of the density for different values of the symmetry energy.

Figure 12

(a) Equilibrium electron fraction $Y_e^{\text{eq}}$ as a function of the symmetry energy for $T=2$ MeV. (b) $Y_e^{\text{eq}}$ as a function of the symmetry slope. Each point corresponds to an equation of state.

Figure 13

Transport coefficients for the L5 EoS against the deviation from the equilibrium charge fraction, at the energy density corresponding to three times the saturation density, and temperature $T=2$ MeV. (a) Resummed $\zeta$ against the electron fraction $Y_e$. (b) Resummed ${\tau }_{\mathrm{\Pi }}$ against $Y_e$.

Figure 14

Bulk viscosity ${\zeta }_0$ for the QMC-RMF1 EoS as a function of temperature.

Figure 15

Bulk scalar $\mathrm{\Pi }$ of the QMC-RMF1 EoS (normalized by the equilibrium pressure), as a function of the deviation from the equilibrium charge fraction, at $T=2$ MeV. We show the results evaluated at energy densities corresponding to number densities one to three times the nuclear saturation density.

Figure 16

Resummed ${\tau }_{\mathrm{\Pi }}$ of the QMC-RMF1 EoS, as a function of the deviation from the equilibrium charge fraction, evaluated at the energy density corresponding to a density twice the saturation density. The temperature is $T=2$ MeV.

Figure 17

Resummed $\zeta$ of the QMC-RMF1 EoS, as a function of the deviation from the equilibrium charge fraction, evaluated at the energy density corresponding to a density twice the saturation density. The temperature is $T=2$ MeV.