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

Motoyuki Saijo, Thomas W. Baumgarte, Stuart L. Shapiro, Masaru Shibata

Research output: Contribution to journalArticle

36 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)349-361
Number of pages13
JournalAstrophysical Journal
Volume569
Issue number1 I
DOIs
Publication statusPublished - 2002 Apr 10
Externally publishedYes

Fingerprint

supermassive stars
simulation
stars
ringing
gravitational waves
interferometer
kinetic energy
gravitational binding energy
energy
antenna
laser
hydrodynamics
LISA (observatory)
radii
wavelength
gravitational collapse
implosions
approximation
falling
dynamic range

Keywords

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

ASJC Scopus subject areas

  • Space and Planetary Science

Cite this

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

In: Astrophysical Journal, Vol. 569, No. 1 I, 10.04.2002, p. 349-361.

Research output: Contribution to journalArticle

Saijo, Motoyuki ; Baumgarte, Thomas W. ; Shapiro, Stuart L. ; Shibata, Masaru. / Collapse of a rotating supermassive star to a supermassive black hole : Post-Newtonian simulations. In: Astrophysical Journal. 2002 ; Vol. 569, No. 1 I. pp. 349-361.
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