Neutrino processes in strong magnetic fields and implications for supernova dynamics

The processes ${\nu }_e+n\rightleftharpoons {p+e}^{-}$ and ${\overline{\nu }}_e+p\rightleftharpoons {n+e}^{+}$ provide the dominant mechanisms for heating and cooling the material between the protoneutron star and the stalled shock in a core-collapse supernova. Observations suggest that some neutron stars are born with magnetic fields of at least $\sim {10}^{15}\mathrm{G}$ while theoretical considerations give an upper limit of $\sim {10}^{18}\mathrm{G}$ for the protoneutron star magnetic fields. We calculate the rates for the above neutrino processes in strong magnetic fields of $\sim {10}^{16}\mathrm{G}.$ We find that the main effect of such magnetic fields is to change the equations of state through the phase space of $e^{-}$ and $e^{+},$ which differs from the classical case due to quantization of the motion of $e^{-}$ and $e^{+}$ perpendicular to the magnetic field. As a result, the cooling rate can be greatly reduced by magnetic fields of $\sim {10}^{16}\mathrm{G}$ for typical conditions below the stalled shock and a nonuniform protoneutron star magnetic field (e.g., a dipole field) can introduce a large angular dependence of the cooling rate. In addition, strong magnetic fields always lead to an angle-dependent heating rate by polarizing the spin of n and p. The implications of our results for the neutrino-driven supernova mechanism are discussed.