Thermal and Magnetic effects on Bulk Viscosity in Binary Neutron Star Mergers

TL;DR

This work addresses how finite temperature and strong magnetic fields modify Urca-process rates and the resulting bulk viscosity in npe matter relevant to binary neutron star mergers. It employs the nucleon width approximation (NWA) to consistently include both direct and modified Urca contributions in a magnetized, finite-temperature environment, across densities below and above the direct Urca threshold for two finite-temperature EoS (IUF and QMC-RMF3) under neutrino-transparent conditions. The study finds that magnetic fields around 10^17 G significantly boost neutron-decay rates below threshold, reduce the finite-temperature flavor-imbalance Delta_mu, and shift the bulk-viscosity resonance to lower temperatures, enhancing damping of 1 kHz density oscillations in cooler merger regions. Overall, the NWA framework provides a powerful tool to quantify magnetic-field effects on flavor equilibration and bulk dissipation in hot, dense astrophysical environments, with potential extensions to other strongly interacting, magnetized systems.

Abstract

Astrophysical scenarios such as binary neutron star mergers, proto-neutron stars and core-collapse supernovae involve finite temperatures and strong magnetic fields. Previous studies on the effect of magnetic fields on flavor-equilibration processes relied on the Fermi surface approximation, which is not a reliable approximation in the neutrino-transparent regime of matter in supernovae or neutron star mergers. In a recent study, we went beyond the Fermi surface approximation, performing the full phase space integral to obtain direct Urca rates in a background magnetic field. In this work, we extend these calculations to incorporate the collisional broadening (``modified Urca'') contribution. We use the recently developed Nucleon Width Approximation, which naturally includes the magnetic field dependence of all contributions. We demonstrate the impact of magnetic fields on the flavor-equilibrium condition for two finite-temperature equations of state with different direct Urca thresholds. We also study the impact of magnetic fields on the bulk viscous dissipation of density oscillations relevant in postmerger scenarios.

Figures (13)

• Figure 1: Momentum deficit $k_\text{Fn}-k_\text{Fp}-k_\text{Fe}$ for the IUF and QMC-RMF3 EoS at $T=0$ MeV. Direct Urca is kinematically suppressed for positive values of the deficit.
• Figure 2: Neutron Decay rates for IUF matter at $T=1\,\text{MeV}$, comparing direct Urca at magnetic field $B=0$ and NWA result for various values of $B$.
• Figure 3: Neutron decay rates at three temperatures, $T=1,3,5\,\text{MeV}$, and magnetic fields $B=10^{17}, 3\times10^{17},$ and $5\times10^{17}\,\text{G}$ using the IUF EoS.
• Figure 4: Electron capture rates at three temperatures, $T=1,3,5\,\text{MeV}$, and magnetic fields $B=10^{17}, 3\times10^{17},$ and $5\times10^{17}\,\text{G}$ using the IUF EoS.
• Figure 5: Correction $\Delta\mu$ to the flavor equilibrium condition at three temperatures, $T=1,3,5\,\text{MeV}$, using the NWA rates for IUF EoS. We see that $\Delta\mu$ decreases with increasing magnetic field.