### Abstract

We study the gravitational collapse of a rotating supermassive star by means of a (3 + 1) hydrodynamic simulation in a post-Newtonian approximation of general relativity. This problem is particularly challenging because of the vast dynamic range in space that must be covered in the course of collapse. We evolve a uniformly rotating supermassive star from the onset of radial instability at R_{p}/M = 411, where R_{p} is the proper polar radius of the star and M is the total mass-energy, to the point at which the post-Newtonian approximation breaks down. We introduce a scale factor and a "comoving" coordinate to handle the large variation in radius during the collapse (8 ≲ R_{p}/M_{0} ≲ 411, where M _{0} is the rest mass) and focus on the central core of the supermassive star. Since T/W, the ratio of the rotational kinetic energy to the gravitational binding energy, is nearly proportional to 1/R_{p} for an n = 3 polytropic star throughout the collapse, the imploding star may ultimately exceed the critical value of T/ W for dynamic instability to bar-mode formation. Analytic estimates suggest that this should occur near R_{p}/M ∼ 12, at which point T/W ∼ 0.27. For stars rotating uniformly at the onset of collapse, however, we do not find any unstable growth of bars prior to the termination of our simulation at R_{p}/M _{0} ∼ 8. We do find that the collapse is likely to form a supermassive black hole coherently, with almost all of the matter falling into the hole, leaving very little ejected matter to form a disk. In the absence of nonaxisymmetric bar formation, the collapse of a uniformly rotating supermassive star does not lead to appreciable quasi-periodic gravitational wave emission by the time our integrations terminate. The coherent nature of the implosion, however, suggests that rotating supermassive star collapse will be a promising source of gravitational wave bursts. We also expect that, following black hole formation, long-wavelength quasi-periodic waves will result from quasi-normal ringing. These waves may be detectable by the Laser Interferometer Space Antenna.

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

Pages (from-to) | 349-361 |

Number of pages | 13 |

Journal | Astrophysical Journal |

Volume | 569 |

Issue number | 1 I |

DOIs | |

Publication status | Published - 2002 Apr 10 |

Externally published | Yes |

### Fingerprint

### Keywords

- Gravitation
- Gravitational waves
- Hydrodynamics
- Instabilities
- Relativity
- Stars: rotation

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*569*(1 I), 349-361. https://doi.org/10.1086/339268

**Collapse of a rotating supermassive star to a supermassive black hole : Post-Newtonian simulations.** / Saijo, Motoyuki; Baumgarte, Thomas W.; Shapiro, Stuart L.; Shibata, Masaru.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 569, no. 1 I, pp. 349-361. https://doi.org/10.1086/339268

}

TY - JOUR

T1 - Collapse of a rotating supermassive star to a supermassive black hole

T2 - Post-Newtonian simulations

AU - Saijo, Motoyuki

AU - Baumgarte, Thomas W.

AU - Shapiro, Stuart L.

AU - Shibata, Masaru

PY - 2002/4/10

Y1 - 2002/4/10

N2 - We study the gravitational collapse of a rotating supermassive star by means of a (3 + 1) hydrodynamic simulation in a post-Newtonian approximation of general relativity. This problem is particularly challenging because of the vast dynamic range in space that must be covered in the course of collapse. We evolve a uniformly rotating supermassive star from the onset of radial instability at Rp/M = 411, where Rp is the proper polar radius of the star and M is the total mass-energy, to the point at which the post-Newtonian approximation breaks down. We introduce a scale factor and a "comoving" coordinate to handle the large variation in radius during the collapse (8 ≲ Rp/M0 ≲ 411, where M 0 is the rest mass) and focus on the central core of the supermassive star. Since T/W, the ratio of the rotational kinetic energy to the gravitational binding energy, is nearly proportional to 1/Rp for an n = 3 polytropic star throughout the collapse, the imploding star may ultimately exceed the critical value of T/ W for dynamic instability to bar-mode formation. Analytic estimates suggest that this should occur near Rp/M ∼ 12, at which point T/W ∼ 0.27. For stars rotating uniformly at the onset of collapse, however, we do not find any unstable growth of bars prior to the termination of our simulation at Rp/M 0 ∼ 8. We do find that the collapse is likely to form a supermassive black hole coherently, with almost all of the matter falling into the hole, leaving very little ejected matter to form a disk. In the absence of nonaxisymmetric bar formation, the collapse of a uniformly rotating supermassive star does not lead to appreciable quasi-periodic gravitational wave emission by the time our integrations terminate. The coherent nature of the implosion, however, suggests that rotating supermassive star collapse will be a promising source of gravitational wave bursts. We also expect that, following black hole formation, long-wavelength quasi-periodic waves will result from quasi-normal ringing. These waves may be detectable by the Laser Interferometer Space Antenna.

AB - We study the gravitational collapse of a rotating supermassive star by means of a (3 + 1) hydrodynamic simulation in a post-Newtonian approximation of general relativity. This problem is particularly challenging because of the vast dynamic range in space that must be covered in the course of collapse. We evolve a uniformly rotating supermassive star from the onset of radial instability at Rp/M = 411, where Rp is the proper polar radius of the star and M is the total mass-energy, to the point at which the post-Newtonian approximation breaks down. We introduce a scale factor and a "comoving" coordinate to handle the large variation in radius during the collapse (8 ≲ Rp/M0 ≲ 411, where M 0 is the rest mass) and focus on the central core of the supermassive star. Since T/W, the ratio of the rotational kinetic energy to the gravitational binding energy, is nearly proportional to 1/Rp for an n = 3 polytropic star throughout the collapse, the imploding star may ultimately exceed the critical value of T/ W for dynamic instability to bar-mode formation. Analytic estimates suggest that this should occur near Rp/M ∼ 12, at which point T/W ∼ 0.27. For stars rotating uniformly at the onset of collapse, however, we do not find any unstable growth of bars prior to the termination of our simulation at Rp/M 0 ∼ 8. We do find that the collapse is likely to form a supermassive black hole coherently, with almost all of the matter falling into the hole, leaving very little ejected matter to form a disk. In the absence of nonaxisymmetric bar formation, the collapse of a uniformly rotating supermassive star does not lead to appreciable quasi-periodic gravitational wave emission by the time our integrations terminate. The coherent nature of the implosion, however, suggests that rotating supermassive star collapse will be a promising source of gravitational wave bursts. We also expect that, following black hole formation, long-wavelength quasi-periodic waves will result from quasi-normal ringing. These waves may be detectable by the Laser Interferometer Space Antenna.

KW - Gravitation

KW - Gravitational waves

KW - Hydrodynamics

KW - Instabilities

KW - Relativity

KW - Stars: rotation

UR - http://www.scopus.com/inward/record.url?scp=0012345292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012345292&partnerID=8YFLogxK

U2 - 10.1086/339268

DO - 10.1086/339268

M3 - Article

AN - SCOPUS:0012345292

VL - 569

SP - 349

EP - 361

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1 I

ER -