Neutrino processes in strong magnetic fields and implications for supernova dynamics

The processes [Formula Presented] and [Formula Presented] 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 [Formula Presented] while theoretical considerations give an upper limit of [Formula Presented] for the protoneutron star magnetic fields. We calculate the rates for the above neutrino processes in strong magnetic fields of [Formula Presented] We find that the main effect of such magnetic fields is to change the equations of state through the phase space of [Formula Presented] and [Formula Presented] which differs from the classical case due to quantization of the motion of [Formula Presented] and [Formula Presented] perpendicular to the magnetic field. As a result, the cooling rate can be greatly reduced by magnetic fields of [Formula Presented] 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.