Transport of Magnetic Fields in Convective, Accreting Supernova Cores

We consider the amplification and transport of a magnetic field in the collapsed core of a massive star, including both the region between the neutrinosphere and the shock, and the central, opaque core. An analytical argument explains why rapid convective overturns persist within a newly formed neutron star for roughly 10 seconds ($> 10^3$ overturns), consistent with recent numerical models. A dynamical balance between turbulent and magnetic stresses within this convective layer corresponds to flux densities in excess of $10^{15}$G. Material accreting onto the core is heated by neutrinos and also becomes strongly convective. We compare the expected magnetic stresses in this convective `gain layer' with those deep inside the neutron core. Buoyant motions of magnetized fluid are greatly aided by the intense neutrino flux. We calculate the transport rate through a medium containing free neutrons protons, and electrons, in the limiting cases of degenerate or non-degenerate nucleons. Fields stronger than $\sim 10^{13}$ G are able to rise through the outer degenerate layers of the neutron core during the last stages of Kelvin-Helmholtz cooling (up to 10 seconds post-collapse), even though these layers have become stable to convection. We also find the equilibrium shape of a thin magnetic flux rope in the dense hydrostatic atmosphere of the neutron star, along with the critical separation of the footpoints above which the rope undergoes unlimited expansion against gravity. The implications of these results for pulsar magnetism are summarized, and applied to the case of late fallback over the first 1,000-10,000 s of the life of a neutron star