Relativistic Mean-Field Treatment of Pulsar Kick from Neutrino Propagation in Magnetized Proto-Neutron

We make a perturbative calculation of neutrino scattering and absorption in hot and dense hyperonic neutron-star matter in the presence of a strong magnetic Field. We calculate that the absorption cross-sections in a fully relativistic mean-field theory. We find that there is a remarkable angular dependence, i.e. the neutrino absorption strength is reduced in a direction parallel to the magnetic Field and enhanced in the opposite direction. This asymmetry in the neutrino absorption is estimated to be as much as 2.2 % of the entire neutrino momentum for an interior magnetic Field of 2 x 10^{17} G. The pulsar kick velocities associated with this asymmetry are shown to be comparable to observed velocities.

💡 Research Summary

The paper investigates a plausible mechanism for the high space velocities observed in many pulsars, commonly referred to as “pulsar kicks,” by examining how neutrino transport in a strongly magnetized proto‑neutron‑star (PNS) environment can generate an anisotropic momentum flux. The authors adopt a relativistic mean‑field (RMF) description of hot, dense matter that includes hyperonic degrees of freedom (Λ, Σ, etc.) and embed a uniform magnetic field of order B≈2×10¹⁷ G, a strength that may be realized in the interior of magnetars. Within this framework, they compute neutrino scattering and absorption cross‑sections using a perturbative expansion to first order in the magnetic field. The magnetic field polarizes the baryonic spin states and quantizes the motion of charged particles (electrons, protons, and hyperons) into Landau levels, thereby modifying the vector–axial (V–A) weak interaction matrix elements in a direction‑dependent manner.

The central result is an angular dependence of the neutrino absorption cross‑section that can be expressed as σ_abs(θ)=σ₀