Neutrino opacities in magnetic fields for binary neutron star merger simulations

Neutrino interactions play a central role in transport and flavor evolution in the ejecta of binary neutron star mergers. Simulations suggest that neutron star mergers may produce magnetic fields as strong as $10^{17}$ G, but computational difficulties have hampered the inclusion of magnetic field effects in neutrino interaction rates. In this paper we give approximate interaction rates for neutrinos in the presence of strong magnetic fields, including the effects of Landau quantization and anomalous magnetic moments with errors of order $\sqrt{T/M}$. We also comment on a neutrino production channel from individual neutrons that can produce low-energy $ν\barν$ pairs even at low density.

💡 Research Summary

This paper addresses a critical gap in binary neutron‑star (BNS) merger modeling: the lack of magnetic‑field‑dependent neutrino interaction rates. State‑of‑the‑art merger simulations predict magnetic fields up to ~10¹⁷ G in the remnant, yet existing neutrino opacity prescriptions (e.g., Burrows‑Reddy‑Thompson, BRT) ignore magnetic effects. The authors therefore develop approximate, yet accurate, expressions for both charged‑current (CC) and neutral‑current (NC) neutrino processes that incorporate Landau quantization of charged particles and the anomalous magnetic moments of nucleons. Their approximations achieve an error of order √(T/M), which is sufficient for the temperature (T ≈ 5–30 MeV) and density (ρ ≈ 10⁹–10¹² g cm⁻³) regimes relevant to the neutrino‑decoupling region of BNS mergers.

Physical Setup and Approximations

• Electrons and protons experience quantized transverse motion in a magnetic field B, occupying Landau levels (LL) labeled by integers n_e, n_p. The electron energy is relativistic: E_e² = p_z² + m_e² + 2 n_e eB, while nucleons are treated non‑relativistically with spin‑dependent shifts: E_n ≈ k²/(2M) − g_n eB s/(4M) and E_p ≈ k²/(2M) + n_p eB/M − (g_p‑2) eB s/(4M).
• The anomalous gyromagnetic ratios (g_n ≈ ‑3.826, g_p ≈ 5.586) introduce spin‑dependent energy terms comparable to the nucleon mass splitting ΔM ≈ 1.3 MeV when B ≈ 10¹⁶–10¹⁷ G.
• Electrons are kept fully degenerate (Fermi‑Dirac distribution) because T ≫ m_e, while protons and neutrons are assumed non‑degenerate (Maxwell‑Boltzmann) for most of the parameter space; a degenerate‑neutron interpolation is provided for the highest densities.
• The wave‑functions in the transverse plane involve generalized Laguerre polynomials I_{n,r}(ζ) with ζ = k_⊥²/(2eB). The overlap factor for two charged particles in LL n and n′ is |I_{n,n′}(ζ)|². The authors note that this factor is exponentially suppressed unless √n − √n′ ≲ √ζ ≲ √n + √n′, which allows them to treat the electron LL sum as a continuum (valid because the characteristic electron momentum k ∼ T is much smaller than the proton momentum √(MT)). Consequently only the proton LL sum needs to be performed explicitly.

Charged‑Current Opacities
The two CC reactions considered are neutron capture of ν_e (n + ν_e → p + e⁻) and antineutrino capture on protons (p + \barν_e → n + e⁺). Using the above approximations, the opacity for ν_e absorption on neutrons is derived as

κ_{ν n} = (G_F² cos²θ_C eB ρ_n δ_n W_M π cosh(g_n eB/4MT) X_{s_n,s_p} n_FD