A Systematic Study of Magnetic Fields Impacts on Neutrino Transport in Core-Collapse Supernovae

We quantify the impact of strong magnetic fields (assuming $B=B_0\cdot r_0^3/r^3$ with $B_0\gtrsim 10^{16}$ G) on the neutrino transport in core-collapse supernovae (CCSNe). Magnetic fields quantize the momenta of electrons and positrons, resulting in an enhanced absorption cross section for low-energy neutrinos and suppressed chemical potentials for $e^\pm$. We include these changes in the M1 scheme for neutrino transport and perform 1-D CCSNe simulations with \texttt{GR1D}. The increased low-energy cross sections reduce the $\bar{\nu}_e$ mean energy $\langle E_{\bar\nu_e}\rangle$ while elevating the neutrino number luminosities $\mathcal{L_\nu}$ for both ${\nu}_e$ and $\bar{\nu}_e$ due to the lower energy weighted spectra. The reduction of chemical potential enhances the $\bar{\nu}_e$ emission while suppressing that of $\nu_e$, thereby driving an increase in the electron fraction behind the stalled shock at $\sim30$--$100$ km. This further amplifies $\langle E_{\nu_e}\rangle$ through an increased electron density. Consequently, magnetic fields amplify $L_{\nu_e}$ by increasing both $\mathcal{L}_{\nu_e}$ and $\langle E_{\nu_e}\rangle$ whereas for $\bar\nu_e$, the rise in $\mathcal{L}_{\bar\nu_e}$ is offset by a decreased $\langle E_{\bar\nu_e}\rangle$, leading to a minimal change in $L_{\bar\nu_e}$. A systematic parameter scan of dipole field configurations suggests that, for $r_0 > 30$ km, $\langle E_{\bar{\nu}_e} \rangle$ is significantly suppressed and $L_{\nu_e}$ is enhanced if $B_0 \geq {2.7} \times 10^{16}$ G. These magnetic effects become negligible for $B_0$ below $\sim {7.4} \times 10^{15}$ G.