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

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).

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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