We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of the gravitational collapse of a magnetized rotating massive star as a model of gamma-ray bursts (GRBs). The current calculation focuses on general relativistic MHD with simplified microphysics (we ignore neutrino cooling, physical equation of state, and photodisintegration). Initially, we assume that the core collapse has failed in this star. A few M⊙ black hole is inserted by hand into the calculation. The simulations presented in the paper follow the accretion of gas into a black hole that is assumed to have formed before the calculation begins. The simulation results show the formation of a disklike structure and the generation of a jetlike outflow inside the shock wave launched at the core bounce. We have found that the jet is accelerated by the magnetic pressure and the centrifugal force and is collimated by the pinching force of the toroidal magnetic field amplified by the rotation and the effect of geometry of the poloidal magnetic field. The maximum velocity of the jet is mildly relativistic (∼0.3c). The velocity of the jet becomes larger as the initial rotational velocity of stellar matter gets faster. On the other hand, the dependence on the initial magnetic field strength is a bit more complicated: the velocity of the jet increases with the initial field strength in the weak field regime, then is saturated at some intermediate field strength, and decreases beyond the critical field strength. These results are related to the stored magnetic energy determined by the balance between the propagation time of the Alfvén wave and the rotation time of the disk (or twisting time).
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