Multipolar Neutrino Radiation in Binary Neutron Star Mergers: Angular Structure, Rotational Variability, and Implications for Electron Fraction

Abstract: The angular structure and temporal variability of neutrino emission from binary neutron star mergers are characterized using fully general-relativistic simulations with energy-integrated M1 neutrino transport across a representative set of equations of state, total masses, and mass ratios. The angle-dependent neutrino energy flux is extracted on a spherical surface outside the remnant and decomposed into spherical harmonics to quantify its multipolar content and evolution. Following the initial post-merger transient, the neutrino radiation flux approaches an axisymmetric configuration dominated by a strong quadrupolar component, producing persistent polar flux enhancement and equatorial suppression due to torus shadowing. The dipolar contribution remains subdominant, indicating the absence of sustained one-sided emission. The degree of anisotropy increases with mass asymmetry and for softer equations of state, reflecting the compactness and morphology of the remnant--disk system. Superimposed on this time-averaged geometry, coherent azimuthal modulations associated with the $m=1$ mode are identified. Fourier analysis reveals a characteristic frequency of $\sim 0.6$--$0.7$ kHz, consistent with differential rotation in the remnant and inner disk layers, indicating a dynamical coupling between rotational structure and neutrino emission variability. Finally, we quantify how the same quadrupole-dominated radiation geometry induces a latitude-dependent equilibrium electron fraction. The polar material is driven close to the neutrino-equilibrium target, whereas equatorial material remains systematically more neutron-rich and below equilibrium.