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

TL;DR

This work quantifies how strong magnetic fields influence neutrino transport in core-collapse supernovae by incorporating Landau quantization of $e^ extpm$ and magnetic-field–induced shifts in the electron chemical potential into a 1-D neutrino transport framework. Using GR1D with a two-moment M1 scheme and a dipole field profile $B=B_0\cdot r_0^3/r^3$, the authors perform a systematic parameter scan to identify regimes where transport properties deviate from the nonmagnetic case. They find that enhanced low-energy neutrino cross sections reduce $\langle E_{\bar{\nu}_e}\rangle$ and increase the neutrino number luminosities $\mathcal{L}_{\nu}$, while a suppressed $\mu_e(B)$ in strong fields drives an increase in $Y_e$ behind the stalled shock and increases $\langle E_{\nu_e}\rangle$, collectively boosting $L_{\nu_e}$ but leaving $L_{\bar{\nu}_e}$ largely unchanged. The results show significant effects only for $r_0>\sim 30$ km and $B_0\gtrsim 2.7\times10^{16}$ G, with negligible impacts for weaker fields below $\sim 7.4\times10^{15}$ G, implying potential imprints on CCSN nucleosynthesis under certain magnetic-field configurations.

Abstract

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 $\barν_e$ mean energy $\langle E_{\barν_e}\rangle$ while elevating the neutrino number luminosities $\mathcal{L_ν}$ for both $ν_e$ and $\barν_e$ due to the lower energy weighted spectra. The reduction of chemical potential enhances the $\barν_e$ emission while suppressing that of $ν_e$, thereby driving an increase in the electron fraction behind the stalled shock at $\sim30$--$100$ km. This further amplifies $\langle E_{ν_e}\rangle$ through an increased electron density. Consequently, magnetic fields amplify $L_{ν_e}$ by increasing both $\mathcal{L}_{ν_e}$ and $\langle E_{ν_e}\rangle$ whereas for $\barν_e$, the rise in $\mathcal{L}_{\barν_e}$ is offset by a decreased $\langle E_{\barν_e}\rangle$, leading to a minimal change in $L_{\barν_e}$. A systematic parameter scan of dipole field configurations suggests that, for $r_0 > 30$ km, $\langle E_{\barν_e} \rangle$ is significantly suppressed and $L_{ν_e}$ 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.

Figures (7)

• Figure 1: Comparison of neutrino opacities between $B_0={5.4}\times 10^{16}$ G, $r_0=40$ km model (solid lines) and $B=0$ baseline (dotted-lines). Left, middle and right panel corresponds to $r=40$ km, 60 km and 80 km, respectively. The magnetic field forms a discontinuous opacities compare with the baseline. The simulation uses a 4 point Gauss-Laguerre quadrature weights to calculate opacities to ensure numerical stability, as shown in unfilled circles.
• Figure 2: Left panel: Comparison of the $\langle E_{{\nu_e}} \rangle$ and $\langle E_{\bar{\nu_e}} \rangle$ evolution between the $B_0={5.4}\times10^{16}$ G, $r_0=40$ km model (solid lines) and the $B=0$ baseline (dashed lines). Right panel: Comparison of the $L_{\nu_e}$ and $L_{\bar{\nu}_e}$ evolution for these two cases. The line-color style follows the left panel. The inset of both panels displays the zoom-in of the initial changes when the magnetic field is just introduced at $t_{pb}\sim 0.02$ s.
• Figure 3: The neutrino energy spectra at post-bounce time $t_{pb}=0.023$ s. The spectra are shown for $r = \{50,100,250\}$ km for left, middle, and right panels, respectively. Magnetic field effects produce low-energy spectral enhancement ($E_\nu<10$ MeV) via modified cross sections $\sigma_B$ (solid lines). This effect is particularly pronounced for $\bar{\nu}_e$ due to a lower emitted $e^+$ momentum. A dipole magnetic field with $B_0={5.4}\times10^{16}$ G and $r_0=40$ km is applied for the solid curves. Dashed curves show baseline non-magnetic case.
• Figure 4: Left panel: The neutrino number luminosity $\mathcal{L}_{\nu_e}$ and $\mathcal{L}_{\bar{\nu}_e}$ evolution for the model $B_0={5.4}\times10^{16}\,{\rm G} ,r_0=40$ km. Right panel: $\mathcal{L}_{\nu_e}$ and $\mathcal{L}_{\bar{\nu}_e}$ evolution for the model $B_0={5.4}\times10^{16}\,{\rm G} ,r_0=50$ km. With modified cross sections $\sigma_B$ (dash-dotted lines), both $\mathcal{L}_{\nu_e}$ and $\mathcal{L}_{\bar{\nu}_e}$ show slightly enhancement compare with the $B=0$ baseline (dashed lines). For the full magnetic field impact, i.e., $\sigma_B$ and $\mu_e$ modification (solid lines), $\mathcal{L}_{\nu_e}$ demonstrates a suppression while $\mathcal{L}_{\bar{\nu}_e}$ amplifies.
• Figure 5: $Y_e$ of the stellar matter when $0.02<t_{pb}<0.04$ s. The ratio compared to the $B=0$ baseline is shown in the lower panel for both $\sigma_B$ modification model (dash-dotted lines) and full magnetic field modification model (solid lines).