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Effects of rotation on the revival of a stalled shock in supernova explosions

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 Added by Tatsuya Yamasaki
 Publication date 2004
  fields Physics
and research's language is English




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In order to infer the effects of rotation on the revival of a stalled shock in supernova explosions, we investigated steady accretion flows with a standing shock. We first obtained a series of solutions for equations describing non-rotating spherically symmetric flows and confirmed the results of preceding papers that, for a given mass accretion rate, there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution. Below the critical value, we found two branches of solutions; one is stable and the other is unstable against radial perturbations. With a simple argument based on the Riemann problem, we can identify the critical luminosity as the one, at which the stalled shock revives. We also obtained the condition satisfied by the flow velocity for the critical luminosity, which can be easily applied to the rotational case. If a collapsing star rotates, the accretion flow is non-spherical due to centrifugal forces. Flows are accelerated near the rotation axis whereas they are decelerated near the equatorial plane. As a result, the critical luminosity is lowered, that is, rotation assists the revival of a stalled shock. According to our calculations, the critical luminosity is $sim25$% lower for the mass accretion rate of 1M$_{odot}$/sec and the rotation frequency of 0.1 Hz at a radius of 1000 km than that of the spherically symmetric flow with the same mass accretion rate. We found that the condition of the flow velocity at the critical luminosity is first satisfied at the rotation axis. This suggests that the shock revival is triggered on the rotation axis and a jet-like explosion ensues.



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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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