Neutrino Processes in Strong Magnetic Fields and Implications for Supernova Dynamics

The processes νe+n ⇋ p+e − and ν̄e+p ⇋ 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 ∼ 10 G while theoretical considerations give an upper limit of ∼ 10 G for the protoneutron star magnetic fields. We calculate the rates for the above neutrino processes in strong magnetic fields of ∼ 10 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 ∼ 10 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.