Transport properties in binary neutron star mergers: Effect of magnetic field

In extreme environments such as binary neutron star mergers, temperatures as high as 50 MeV and magnetic fields up to 10 17 G, reach a regime where neutrino transport governs the macroscopic thermodynamic and chemical evolution. Existing merger simulations rely on zero magnetic field neutrino emissivity and opacity, potentially missing critical transport physics in highly magnetized neutron star cores. We present an exact framework for computing charged current Urca emissivity and neutrino opacity at finite temperature and magnetic field. We employ the Nucleon Width Approximation framework to account for the collisional broadening effects dominant in the high-density core. Our calculations demonstrate that extreme magnetic fields significantly enhance charged current neutrino opacity, effectively reducing the mean free path for thermal neutrinos.

The dominant channels for neutrino emission are flavor-changing weak interactions. In standard nucleonic matter composed of neutrons, protons, and electrons these are the neutron decay and electron capture processes: n → p + e− + ν̄e (nd) and p + e− → n + νe (ec). These direct Urca (dU) processes are strongly restricted due to kinematic constraints below a threshold density by momentum conservation requiring proton fraction xp > 11%. In the regions of neutron star where density is insufficient to achieve this threshold proton fraction the dominant reactions are the modified Urca (mU) processes, N + n → N + p + e− + ν̄e (nd) and N + p + e− → N + n + νe (ec), where N = n, p is a spectator nucleon. This additional nucleon opens the phase space for the reactions to occur at any density but the requirement of this additional nucleon in the initial and final state suppresses the reaction rates and thus the neutrino emissivity from mU processes by several orders of magnitude compared to the dU processes. The large difference between the emissivities of the dU and mU processes lead to a theoretical distinction between neutron star cooling models.

This threshold behavior is however an artifact of the approximation of treating nucleons in the medium as non-interacting particles with infinite lifetime. In a highly dense and strongly interacting medium such as in the core of a neutron star, there are frequent nucleon scattering via strong interaction. Thus the nucleons in this medium have finite lifetime between collisions and thus finite widths in their energy spectra. The recently developed Nucleon Width Approximation (NWA) framework takes these collisional broadening effects into account. We recently computed the rates of dU reaction processes in presence of magnetic fields, going beyond the Fermi-surface approximation to incorporate thermal effects. We subsequently extended this work using the NWA framework to evaluate the thermal and magnetic field effects on the total Urca rates. In this article, we extend the framework to calculate, for the first time, the total neutrino emissivity from Urca processes consistently using the NWA formalism to incorporate the effects of finite temperature and magnetic field. Furthermore, because the transport properties like bulk viscosity depend on the equilibrium composition of nuclear matter, we also compute the neutrino absorption opacity (νe + n → p + e−) and antineutrino absorption opacity (ν̄e + p + e− → n) and the corresponding absorption mean free paths. Together the emission and absorption results thus obtained are highly relevant for improving numerical simulations of BNS mergers and core-collapse supernovae, environments where such thermal and magnetic field effects play a significant role.

In this work we compute thermal and magnetic field effects on the neutrino transport properties such as emissivity and opacity, above and below the direct Urca threshold density. We only consider nuclear matter composed of neutrons, protons and electrons (npe matter). The extension to include muons is straightforward but would not make a significant difference. We formulate the calculation of the total neutrino emissivity from Urca processes in presence of finite magnetic field and temperature. The antineutrino emissivity from neutron decay direct Urca process in presence of magnetic field is given by an expression involving the Fermi-Dirac distribution functions for constituent particles, normalized Laguerre functions, and Landau level numbers for the electron and proton. The neutrino emissivity from electron capture process is given by a similar expression by replacing the Fermi-Dirac factors and the neutrino energy. The total neutrino emissivity in the NWA framework is given by integrating the direct Urca emissivity over the mass-spectral functions for nucleons, which depend on the in-medium mass of the nucleon and the nucleon width given by WN = T2/TW with TW = 5 MeV. Using the same formalism as above for neutrino emissivity we can also compute neutrino absorption opacity. The neutrino absorption opacity within the NWA framework is given by a similar expression, and the antineutrino absorption opacity (ν̄e + p + e− → n) within the NWA framework is given by similar expression with Fermi-Dirac factors replaced. The neutrino and antineutrino mean free path is just the inverse of their absorption opacities, λν = κν−1. As in our previous works, we use realistic equations of state (EoS) for nuclear matter which consistently include thermal effects. We do not consider modifications to the EoS due to magnetic field (e.g. Landau quantisation or anomalous magnetic moment) as these effects are not significant for the EoS even for the highest field of B = 5 × 10 17 G considered in this work. We select two realistic finite-temperature relativistic mean field EoS models to describe nuclear matter that satisfy the current nuclear and astrophysical constraints: IUF and QMC-RMF3. The IUF EoS has a direct Urca threshold at baryon density nB = 4.1n0, where n0 is the nuclear saturation density taken to be 0.16 fm−3. The QMC-RMF3 EoS has no direct Urca threshold within the density of interest in this study.

We now compute the total emissivity from Urca processes in the NWA formalism in presence of magnetic field and finite temperature as shown by Fig. 1, 2 for IUF and QMF-RMF3 EoSs respectively. In npe matter isospin equilibrium is achieved when the neutron decay and electron capture rates are equal, Γnd = Γec. In presence of finite temperature and magnetic field an additional isospin chemical potential ∆µ is required to achieve this equilibrium as shown in our previous work. Thus the true equilibrium condition in presence of finite temperature and magnetic field is µn = µp + µe + ∆µ. The total Urca emissivity in this work is computed at this true isospin equilibrium condition at all densities as obtained in our previous paper. We find that magnetic field enhances the Urca emissivity significantly at low temperatures. We compute emissivity at the true chemical equilibrium condition given by µn = µp + µe + ∆µ, where ∆µ is estimated by equating the neutron decay and electron capture rates. At low temperatures T ∼ 1 − 3 MeV, the Urca emissivity is enhanced by an order of magnitude with increasing magnetic field below the direct Urca threshold density. At higher temperatures T ∼ 5 MeV, the Urca emissivity increases by a factor of 2 for the highest magnetic field B = 5 × 10 17 G considered in our study. Magnetic field has no significant effect on the Urca emissivity above the direct Urca threshold density.

In Figs. 3, 4, we show contour plots for electron neutrino and antineutrino absorption opacity and mean free path due to Urca processes as a function of temperature and magnetic field for soft neutrinos with energy equal to the temperature, Eνe,ν̄e = T. We find that the charged current opacity increases for neutrino and antineutrino in presence of magnetic field. For low temperatures T < 3 MeV, the opacities increase by upto 2 orders of magnitude with an increasing magnetic field. The antineutrino absorption opacity increases by an order of magnitude even at higher temperatures. Correspondingly, we see that the mean free paths due to charged current reactions for both neutrino and antineutrino decreases with increasing magnetic field. For low temperature, T ∼ 1 MeV and low magnetic field B ∼ 10 16 G the neutrino and antineutrino absorption mean free paths are larger than the radius of the star, λν > 10 km. The absorption mean free path decreases with increasing magnetic field and temperatures. The combined effects of thermal blurring of Fermi-surfaces, collisional broadening of in-medium nucleons and the magnetic field increase the phase space available for absorption of neutrinos and antineutrinos. Thus our calculations show that in BNS mergers where magnetic fields as high as B = 5 × 10 17 G are reached and the temperatures in the cores are within a few MeV, the neutrino and antineutrino absorption mean free paths can become smaller than the radius of the star. Thus the distribution of neutrinos in BNS merger scenarios will be non-trivial in presence of high magnetic fields even at lower temperatures. This will modify the equilibrium composition of matter in the merger scenarios and also affect the viscous damping of density oscillations.

In this work, we extended our recently developed formalism to obtain weak interaction rates including thermal and magnetic field effects within the NWA framework to calculate transport properties consistently in the post-merger scenario. We found that magnetic field enhances the Urca emissivity significantly at low temperatures below the direct Urca threshold density. This will lead to a faster cooling of the highly magnetized post-merger remnant core. We also computed the absorption opacities for neutrinos and antineutrinos in presence of magnetic field incorporating thermal and collisional broadening effects. We saw that the opacities are enhanced with increasing magnetic field at low temperatures. Thus the absorption mean free path decreases by orders of magnitude at low temperatures with increasing magnetic fields, becoming smaller than the radius of the star even at low temperatures. This will modify the equilibrium composition of matter in the core of the post-merger. This will also modify the bulk viscous damping of oscillations in BNS mergers. Therefore it becomes crucial to incorporate the magnetic field effects on the neutrino opacities in simulations of BNS mergers. Our calculations show that magnetic field effects can have important consequences on the calculations of transport properties of the BNS post-merger remnant, where such magnetic fields and temperatures may be encountered. The results of this work can be followed up with more detailed numerical simulations, incorporating more sophisticated magnetic field and thermal evolution as well as neutrino transport. Thermal evolution of the remnant determines its stability as well as the threshold mass before collapse to a black hole, with consequences for multi-messenger astrophysical observations following the detection of gravitational waves from a merger event.

Improvements to AI Systems:

1. Magnetic-Field-Aware Neutrino Transport Models

• Integrate the NWA-based emissivity and opacity calculations (including magnetic field dependence) into AI-driven neutrino transport codes for binary neutron star (BNS) merger simulations.

• The improved AI system can dynamically adjust neutrino mean free paths and cooling rates based on local magnetic field strength (up to 5×1017 G) and temperature, replacing zero-field approximations.

2. Enhanced Equation-of-State (EoS) Coupling for Merger Simulations

• Train AI surrogate models to map thermodynamic conditions (density, temperature, proton fraction) and magnetic field to corrected Urca emissivities and opacities, using the IUF and QMC-RMF3 EoS data.

• The improved system can predict non-equilibrium composition shifts (via the additional isospin chemical potential Δµ) and feed them into hydrodynamics, improving accuracy of post-merger remnant evolution.

3. Real-Time Opacity Estimation for Neutrino Cooling and Viscosity

• Develop AI modules that compute absorption opacities (νe + n → p + e−, ν̄e + p + e− → n) and mean free paths on-the-fly, incorporating thermal blurring, collisional broadening, and Landau-level quantization effects.

• The improved system can flag regimes where mean free paths drop below stellar radius (e.g., T 1016 G), enabling more realistic neutrino trapping and reabsorption in merger cores.

4. Threshold-Density Correction for Direct Urca Processes

• Use AI to replace the simplified proton fraction threshold (x p > 11%) with a continuous, magnetic-field- and temperature-dependent transition between direct and modified Urca regimes, based on NWA results.

• The improved system can accurately model cooling rates both below and above the threshold, avoiding artificial discontinuities in simulations.

5. Bulk Viscosity and Damping Prediction

• Train AI to compute bulk viscosity coefficients from the magnetic-field-enhanced Urca rates and equilibrium composition shifts.

• The improved system can predict enhanced viscous damping of density oscillations in BNS remnants, informing gravitational wave signal modeling and post-merger stability analysis.

6. Multi-Messenger Observational Forecasting

• Use AI to simulate thermal evolution of magnetized remnants with the new transport physics, predicting cooling timescales and black hole collapse thresholds.

• The improved system can generate synthetic multi-messenger signals (gravitational waves, kilonova light curves, neutrino bursts) that account for magnetic field effects, aiding interpretation of LIGO/Virgo and future observatory data.

7. Uncertainty Quantification for Extreme Conditions

• Implement AI-based uncertainty propagation for the NWA parameters (e.g., nucleon width W N = T2/T W, magnetic field strength, EoS choices) to quantify model robustness in simulations.

• The improved system can provide confidence intervals for transport properties, guiding experimental and observational constraints.

8. Fast Surrogate for Parameter Space Exploration

• Create neural network emulators of the full emissivity/opacity tables (as functions of T, B, density, and neutrino energy) to replace costly direct integration in simulations.

• The improved system can run high-resolution 3D BNS merger simulations with magnetic field effects at reduced computational cost, enabling broader parameter sweeps.