North‐South Neutrino Heating Asymmetry in Strongly Magnetized and Rotating Stellar Cores

We perform a series of two-dimensional magnetohydrodynamic simulations ofsupernova cores. Since the distributions of the angular momentum and themagnetic fields of strongly magnetized stars are quite uncertain, wesystematically change the combinations of the strength of the angular momentum,the rotations law, the degree of differential rotation, and the profiles of themagnetic fields to construct the initial conditions. By so doing, we estimatehow the rotation-induced anisotropic neutrino heating are affected by thestrong magnetic fields through parity-violating effects and first investigatehow the north-south asymmetry of the neutrino heating in a strongly magnetizedsupernova core could be. As for the microphysics, we employ a realisticequation of state based on the relativistic mean field theory and take intoaccount electron captures and the neutrino transport via the neutrino leakagescheme. With these computations, we find that the parity-violating correctionsreduce $ \lesssim 0.5 %$ of the neutrino heating rate than that without themagnetic fields in the vicinity of the north pole of a star, on the other hand,enhance about $ \lesssim 0.5 %$ in the vicinity of the south pole. If theglobal asymmetry of the neutrino heating in the both of the poles develops inthe later phases, the newly born neutron star might be kicked toward the northpole in the subsequent time.