Transport of Magnetic Fields in Convective, Accreting Supernova Cores

We consider the amplification and transport of a magnetic field in thecollapsed core of a massive star, including both the region between theneutrinosphere and the shock, and the central, opaque core. An analyticalargument explains why rapid convective overturns persist within a newly formedneutron star for roughly 10 seconds ($> 10^3$ overturns), consistent withrecent numerical models. A dynamical balance between turbulent and magneticstresses within this convective layer corresponds to flux densities in excessof $10^{15}$G. Material accreting onto the core is heated by neutrinos and alsobecomes strongly convective. We compare the expected magnetic stresses in thisconvective `gain layer' with those deep inside the neutron core. Buoyant motions of magnetized fluid are greatly aided by the intense neutrinoflux. We calculate the transport rate through a medium containing free neutronsprotons, and electrons, in the limiting cases of degenerate or non-degeneratenucleons. Fields stronger than $\sim 10^{13}$ G are able to rise through theouter degenerate layers of the neutron core during the last stages ofKelvin-Helmholtz cooling (up to 10 seconds post-collapse), even though theselayers have become stable to convection. We also find the equilibrium shape ofa thin magnetic flux rope in the dense hydrostatic atmosphere of the neutronstar, along with the critical separation of the footpoints above which the ropeundergoes unlimited expansion against gravity. The implications of theseresults for pulsar magnetism are summarized, and applied to the case of latefallback over the first 1,000-10,000 s of the life of a neutron starComment: 45 pages, 3 figures, Astrophysical Journal, in pres