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) bymeans of a (3+1) hydrodynamical simulation in a post-Newtonian (PN) approxi-mation of general relativity. This problem is particularly challenging becauseof the vast dynamical range in space which must be covered in the course ofcol- lapse. We evolve a uniformly rotating SMS from the onset of radialinstability at R_{p}/M=411, where R_{p} is the proper polar radius of the starand M is the total mass-energy, to the point at which the PN approximationbreaks down. We introduce a scale factor and a "comoving" coordinate to handlethe large varia- tion in radius during the collapse and focus on the centralcore. Since T/W, the ratio of the rotational kinetic energy to thegravitational binding energy, is nearly proportional to 1/R_{p} throughout thecollapse, the imploding star may ultimately exceed the critical value of T/Wfor dynamical instability to bar-mode formation. However, for stars rotatinguniformly at the onset of col- lapse, we do not find any unstable growth ofbars prior to the termination of our simulation. We do find that the collapseis likely to form a supermassive black hole (BH) coherently, with almost all ofthe matter falling into the hole, leaving very little ejected matter to form adisk. In the absence of nonaxi- symmetric bar formation, the collapse of auniformly rotating SMS does not lead to appreciable quasi-periodicgravitational wave (GW) emission by the time our integrations terminate.However, the coherent nature of the implosion suggests that rotating SMScollapse will be a promising source of GW bursts. We also expect that,following BH formation, long wavelength quasi-periodic waves will result fromquasi-normal ringing. These waves may be detectable by LISA.Comment: 13 pages, 18 figures included, uses emulateapj5.sty (included). The Astrophysical Journal, 569, 2002 April 10, in pres