Collapse of a Rotating Supermassive Star to a Supermassive Black Hole: Post-Newtonian Simulations

Details 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

2002-02-06

arxiv.org/abs/astro-ph/0202112v1

Astrophys.J. 569 (2002) 349-361

Astronomy and Astrophysics

Astrophysics

13 pages, 18 figures included, uses emulateapj5.sty (included). The Astrophysical Journal, 569, 2002 April 10, in press

Scientific paper

10.1086/339268

We study the gravitational collapse of a rotating supermassive star (SMS) by means of a (3+1) hydrodynamical simulation in a post-Newtonian (PN) approxi- mation 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 varia- tion 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 col- lapse, 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 nonaxi- symmetric 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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