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 investigate steady accretion flows with a standing shock. We first obtain a series of solutions for equations describing nonrotating, spherically symmetric flows and confirm 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 find 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 that at which the stalled shock revives. We also obtain a condition satisfied by the flow velocity for the critical luminosity, which can easily be applied to the rotational case. If a collapsing star rotates, the accretion flow is nonspherical as a consequence of 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 $25% lower for a mass accretion rate of 1 M s À1 and a rotational frequency of 0.1 Hz at a radius of 1000 km than that for a spherically symmetric flow with the same mass accretion rate. We find that the condition on the flow velocity at the critical luminosity is first satisfied at the rotation axis. This suggests that shock revival is triggered on the rotation axis and a jetlike explosion ensues.

Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport

“…Rotation turns out to be helpful, but to a much lesser extent than estimated by Yamasaki & Yamada (2005). Certainly, the shock radius is significantly larger than in the non-rotating models of the 15 M star (Fig.…”

“…This corresponds to a rotation period of 10 s and is therefore only slightly faster than the rotation considered in Model s15_64_r (where the initial spin period is 12 s in the iron core). Yamasaki & Yamada (2005) found a sizable reduction by 25% of the "critical neutrino luminosity" for starting a neutrino-driven explosion at a mass accretion rate of about 1 M s −1 or lower. The effects of rotation are, however, diverse and modify the structure of the collapsing star, the convection in the core, the gas motion behind the shock, and the radius and neutrino emission of the forming neutron star.…”

“…The analysis by Yamasaki & Yamada (2005) suggests that rotation can appreciably improve the conditions for shock revival in case the initial rotation frequency is at least f ∼ 0.1 Hz at 1000 km. This corresponds to a rotation period of 10 s and is therefore only slightly faster than the rotation considered in Model s15_64_r (where the initial spin period is 12 s in the iron core).…”

“…The effects of rotation are, however, diverse and modify the structure of the collapsing star, the convection in the core, the gas motion behind the shock, and the radius and neutrino emission of the forming neutron star. A separate discussion of selected effects as done by Yamasaki & Yamada (2005) can therefore be misleading. In our simulations all effects of rotation are fully coupled and we can assess the question how these effects in combination determine the conditions for the delayed explosion mechanism.…”

Standing accretion shock instability: numerical simulations of core-collapse supernova

“…[6] with neutrino luminosity of 3.0 × 10 52 erg/s. The steady state solutions obtained by [11] for a fixed density at the inner boundary, ρ in = 10 11 g cm −3 , and an accretion rate of 1 M s −1 are utilized. To induce the non-spherical instability, we have added = 1 velocity perturbations of 1% to the initial state mentioned above.…”