### 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^{-1} 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.

Original language | English |
---|---|

Pages (from-to) | 1000-1010 |

Number of pages | 11 |

Journal | Astrophysical Journal |

Volume | 623 |

Issue number | 2 I |

DOIs | |

Publication status | Published - 2005 Apr 20 |

### Fingerprint

### Keywords

- Hydrodynamics
- Shock waves
- Stars: rotation
- Supernovae: general

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*623*(2 I), 1000-1010. https://doi.org/10.1086/428496

**Effects of rotation on the revival of a stalled shock in supernova explosions.** / Yamasaki, Tatsuya; Yamada, Shoichi.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 623, no. 2 I, pp. 1000-1010. https://doi.org/10.1086/428496

}

TY - JOUR

T1 - Effects of rotation on the revival of a stalled shock in supernova explosions

AU - Yamasaki, Tatsuya

AU - Yamada, Shoichi

PY - 2005/4/20

Y1 - 2005/4/20

N2 - 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-1 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.

AB - 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-1 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.

KW - Hydrodynamics

KW - Shock waves

KW - Stars: rotation

KW - Supernovae: general

UR - http://www.scopus.com/inward/record.url?scp=20444412742&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=20444412742&partnerID=8YFLogxK

U2 - 10.1086/428496

DO - 10.1086/428496

M3 - Article

AN - SCOPUS:20444412742

VL - 623

SP - 1000

EP - 1010

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2 I

ER -