Effects of Rotation on the Revival of a Stalled Shock in Supernova Explosions

In order to infer the effects of rotation on the revival of a stalled shockin supernova explosions, we investigated steady accretion flows with a standingshock. We first obtained a series of solutions for equations describingnon-rotating spherically symmetric flows and confirmed the results of precedingpapers that, for a given mass accretion rate, there is a critical luminosity ofirradiating neutrinos, above which there exists no steady solution. Below thecritical value, we found two branches of solutions; one is stable and the otheris unstable against radial perturbations. With a simple argument based on theRiemann problem, we can identify the critical luminosity as the one, at whichthe stalled shock revives. We also obtained the condition satisfied by the flowvelocity for the critical luminosity, which can be easily applied to therotational case. If a collapsing star rotates, the accretion flow isnon-spherical due to centrifugal forces. Flows are accelerated near therotation axis whereas they are decelerated near the equatorial plane. As aresult, the critical luminosity is lowered, that is, rotation assists therevival of a stalled shock. According to our calculations, the criticalluminosity is $\sim25$% lower for the mass accretion rate of 1M$_{\odot}$/secand the rotation frequency of 0.1 Hz at a radius of 1000 km than that of thespherically symmetric flow with the same mass accretion rate. We found that thecondition of the flow velocity at the critical luminosity is first satisfied atthe rotation axis. This suggests that the shock revival is triggered on therotation axis and a jet-like explosion ensues.Comment: 26 pages, 10 figures, submitted to Ap