Neutrino Processes in Strong Magnetic Fields and Implications for Supernova Dynamics

The processes of neutrino (antineutrino) absorption and electron (positron) capture on nucleons 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 10^15 G while theoretical considerations give an upper limit of 10^18 G for the protoneutron star magnetic fields. We calculate the rates for the above neutrino processes in strong magnetic fields of 10^16 G. We find that the main effect of such magnetic fields is to change the equations of state through the phase space of electron and positron, which differs from the classical case due to quantization of the motion of electron and positron perpendicular to the magnetic field. As a result, the cooling rate can be greatly reduced by magnetic fields of 10^16 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 nucleons. The implications of our results for the neutrino-driven supernova mechanism are discussed.