We investigate axisymmetric steady solutions of (magneto)hydrodynamics equations that describe approximately accretion flows through a standing shock wave and discuss the effects of rotation and magnetic field on the revival of the stalled shock wave in supernova explosions. We develop a new powerful numerical method to calculate the 2-dimensional (2D) steady accretion flows self-consistently. We first confirm the results of preceding papers that there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution in spherical models. If a collapsing star has rotation and/or magnetic field, the accretion flows are no longer spherical owing to the centrifugal force and/or Lorentz force and the critical luminosity is modified.In fact we find that the critical luminosity is reduced by about 50% - 70% for rapid rotations and about 20% - 50% for strong toroidal magnetic fields, depending on the mass accretion rate. These results may be also interpreted as an existence of the critical specific angular momentum or critical magnetic field, above which there exists no steady solution and the standing shock wave will revive for a given combination of mass accretion rate and neutrino luminosity.
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