Magneto-driven Shock Waves in Core-Collapse Supernova
  We perform a series of two-dimensional magnetohydrodynamic simulations of the rotational core-collapse of a magnetized massive star. We employ a realistic equation of state and take into account the neutrino cooling by the so-called leakage scheme. In this study we systematically investigate how the strong magnetic field and the rapid rotation affect the propagation of the shock waves. Our results show that in the case of the strong initial poloidal magnetic field, the toroidal magnetic field amplified by the differential rotation, becomes strong enough to generate a tightly collimated shock wave along the rotational axis. On the other hand, in the case of the weak initial magnetic field, although the differential rotation amplifies toroidal magnetic field over the long rotational period, the launched shock wave is weak and the shape of it becomes wider. The former case is expected to be accompanied by the formation of the so-called magnetar. Our models with rapid rotation and strong magnetic field can create a nozzle formed by the collimated shock wave. This might be the analogous situation of the collapsar that is plausible for the central engine of the Gamma-Ray Bursts. 
Tomoya Takiwaki, Kei Kotake, Shigehiro Nagataki, and Katsuhiko Sato