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

Abstract

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.