We perform two-dimensional, axisymmetric, magnetohydrodynamic simulations of the collapse of a rotating star of 40 M⊙ in light of the collapsar model of gamma-ray bursts. Considering two distributions of angular momentum, up to ∼ 1017 cm2 s-1, and the uniform vertical magnetic field, we investigate the formation of an accretion disk around a black hole and the jet production near the black hole. After material reaches the black hole with high angular momentum, the disk forms inside a surface of weak shock. The disk reaches a quasi-steady state for stars whose magnetic field is less than 1010G before the collapse. We find that the jet can be driven by the magnetic fields even if the central core does not rotate as rapidly as previously assumed as long as the outer layers of the star have sufficiently high angular momentum. The magnetic fields are chiefly amplified inside the disk due to the compression and the wrapping of the field. The fields inside the disk propagate to the polar region along the inner boundary near the black hole through the Alfvén wave and eventually drive the jet. The quasi-steady disk is not an advection-dominated disk but a neutrino cooling-dominated one. Mass accretion rates in the disks are greater than 0.01 M⊙ s-1 with large fluctuations. The disk is transparent for neutrinos. The dense part of the disk, which is located near the black hole, emits neutrinos efficiently at a constant rate of <8 × 1051 ergs s-1. The neutrino luminosity is much smaller than those from supernovae after the neutrino burst.
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