We study the gravitational collapse of a rotating supermassive star by means of a (3+1) hydrodynamical simulation in a post-Newtonian 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 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/Mo < 411, where Mo 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 collapse, the imploding star may ultimately exceed the critical value of T/W for dynamical instability to bar-mode formation. Analytic estimates suggest that this should occur near Rp/M ~ 12, at which point T/W ~ 0.27. 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 at Rp/Mo ~ 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. However, the coherent nature of the implosion suggests that rotaing 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 (LISA).
|Center for Theoretical Astrophysics---University of Illinois at
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