Magnetic field amplification and magnetically supported explosions of collapsing, non-rotating stellar cores

We study the amplification of magnetic fields in the collapse and the post-bounce evolution of the core of a non-rotating star of 15 solar masses in axisymmetry. To this end, we solve the coupled equations of magnetohydrodynamics and neutrino transport in the two-moment approximation. The pre-collapse magnetic field is strongly amplified by compression in the infall. Initial fields of the order of 1010 G translate into proto-neutron star fields similar to the ones observed in pulsars, while stronger initial fields yield magnetar-like final field strengths. After core bounce, the field is advected through the hydrodynamically unstable neutrino-heating layer, where non-radial flows due to convection and the standing accretion shock instability amplify the field further. Consequently, the resulting amplification factor of order five is the result of the number of small-eddy turnovers taking place within the time scale of advection through the post-shock layer. Due to this limit, most of our models do not reach equipartition between kinetic and magnetic energy and, consequently, evolve similarly to the non-magnetic case, exploding after about 800 ms when a single or few high-entropy bubbles persist over several dynamical time scales. In the model with the strongest initial field we studied, \$10^{12}\$ G, for which equipartition between flow and field is achieved, the magnetic tension favours a much earlier development of such long-lived high-entropy bubbles and enforces a fairly ordered large-scale flow pattern. Consequently, this model, after exhibiting very regular shock oscillations, explodes much earlier than non-magnetic ones.