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Collapse of a rotating supermassive star to a supermassive black hole: post-Newtonian simulations

Collapse of a rotating supermassive star to a supermassive black hole: post-Newtonian simulations
Collapse of a rotating supermassive star to a supermassive black hole: post-Newtonian simulations
We study the gravitational collapse of a rotating supermassive star (SMS) by means of a (3+1) hydrodynamical simulation in a post-Newtonian (PN) approximation of general relativity. This problem is particularly challenging because of the vast dynamical range in space which must be covered in the course of col- lapse. We evolve a uniformly rotating SMS 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 PN approximation breaks down. We introduce a scale factor and a "comoving" coordinate to handle the large variation in radius during the collapse and focus on the central core. Since T/W, the ratio of the rotational kinetic energy to the gravitational binding energy, is nearly proportional to 1/R_p throughout the collapse, the imploding star may ultimately exceed the critical value of T/W for dynamical instability to bar-mode formation. However, for stars rotating uniformly at the onset of collapse, we do not find any unstable growth of bars prior to the termination of our simulation. We do find that the collapse is likely to form a supermassive black hole (BH) 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 SMS does not lead to appreciable quasi-periodic gravitational wave (GW) emission by the time our integrations terminate. However, the coherent nature of the implosion suggests that rotating SMS collapse will be a promising source of GW bursts. We also expect that, following BH formation, long wavelength quasi-periodic waves will result from quasi-normal ringing. These waves may be detectable by LISA.
349-361
Saijo, Motoyuki
f2128aae-e896-4290-a382-d413c868a617
Baumgarte, Thomas W.
fa9007a1-bb4a-4527-b199-5fc26e0ff89c
Shapiro, Stuart L.
b958a84d-02e2-430b-b4fd-967e043460c6
Shibata, Masaru
d3377a09-0505-470a-9e71-e4605ff06c99
Saijo, Motoyuki
f2128aae-e896-4290-a382-d413c868a617
Baumgarte, Thomas W.
fa9007a1-bb4a-4527-b199-5fc26e0ff89c
Shapiro, Stuart L.
b958a84d-02e2-430b-b4fd-967e043460c6
Shibata, Masaru
d3377a09-0505-470a-9e71-e4605ff06c99

Saijo, Motoyuki, Baumgarte, Thomas W., Shapiro, Stuart L. and Shibata, Masaru (2002) Collapse of a rotating supermassive star to a supermassive black hole: post-Newtonian simulations. The Astrophysical Journal, 569 (1), 349-361. (doi:10.1086/339268).

Record type: Article

Abstract

We study the gravitational collapse of a rotating supermassive star (SMS) by means of a (3+1) hydrodynamical simulation in a post-Newtonian (PN) approximation of general relativity. This problem is particularly challenging because of the vast dynamical range in space which must be covered in the course of col- lapse. We evolve a uniformly rotating SMS 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 PN approximation breaks down. We introduce a scale factor and a "comoving" coordinate to handle the large variation in radius during the collapse and focus on the central core. Since T/W, the ratio of the rotational kinetic energy to the gravitational binding energy, is nearly proportional to 1/R_p throughout the collapse, the imploding star may ultimately exceed the critical value of T/W for dynamical instability to bar-mode formation. However, for stars rotating uniformly at the onset of collapse, we do not find any unstable growth of bars prior to the termination of our simulation. We do find that the collapse is likely to form a supermassive black hole (BH) 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 SMS does not lead to appreciable quasi-periodic gravitational wave (GW) emission by the time our integrations terminate. However, the coherent nature of the implosion suggests that rotating SMS collapse will be a promising source of GW bursts. We also expect that, following BH formation, long wavelength quasi-periodic waves will result from quasi-normal ringing. These waves may be detectable by LISA.

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Published date: 2002

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Local EPrints ID: 29410
URI: http://eprints.soton.ac.uk/id/eprint/29410
PURE UUID: 46e2a4a3-6946-4ab8-bb99-0252bc4b0499

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Date deposited: 12 May 2006
Last modified: 08 Jan 2022 18:56

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Contributors

Author: Motoyuki Saijo
Author: Thomas W. Baumgarte
Author: Stuart L. Shapiro
Author: Masaru Shibata

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