Impact of a Magnetic Field on Neutrino-Matter Interactions in Core-collapse Supernovae

We explore the impact of a magnetic field on neutrino-matter interactions in core-collapse supernovae. We first derive the modified source terms for neutrino-nucleon scattering and neutrino absorption and emission processes in the moment formalism. Then, we perform full relativistic, three-dimensional, magnetorotational core-collapse supernova simulations of a $20\,{M}_{\odot }$ star with spectral neutrino transport. Our simulations self-consistently treat the parity-violation effects of weak interaction in the presence of an external magnetic field. The result shows significant global asymmetry, mostly confined in the proto-neutron star, clearly reflecting the magnetic field structure. The asymmetric property arises from two factors: the angle between the neutrino flux and magnetic field, and the term that is parallel to the magnetic field and is also proportional to the deviation of the distribution function of neutrinos from thermal equilibrium. The typical correction value amounts to ∼1% relative to the total neutrino-matter interaction rate for the magnetic field strength of $\sim {10}^{15\mbox{--}16}$ G. Although these asymmetric properties do not immediately affect the explosion dynamics, our results imply that they would be significant once the neutrinos diffuse out of the proto-neutron- star core carrying those asymmetries away. We also show that, during our simulation time of ∼370 ms after bounce, our results indicate that the correction value due to the modified inelastic scattering process dominates over that of the modified neutrino absorption and emission process.