Stuart L. Shapiro
Masaru Shibata

reference: Ap. J., 577, 904-908, (2002)

The collapse of a uniformaly rotating, supermassive star (SMS) to a supermassive black hole (SMBH) has been followed recently by means of hydrodynamic simulations in full general relativity (see movies above). The initial SMS of arbitrary mass M in these simulations rotates uniformly at the mass-shedding limit and is marginally unstable to radial collapse. The final black hole has mass M_h/M = 0.9 and spin J_h/M_h² = 0.75, approximately. The remaining mass goes into a disk of mass M_disk/M = 0.1, also approximately. The analytic calculation thereby corroborates and provides a simple physical explanation for the computational discovery that SMS collapse inevitably terminates in the simultaneous formation of a SMBH and a rather substantial ambient disk. This disk arises even though the total spin of the progenitor star, J/M² = 0.97, is safely below the Kerr limit. The calculation performed applies to any marginally unstable n = 3 polytrope uniformly rotating at the break-up speed, independent of stellar mass or the source of internal pressure. It illustrates how the black hole and disk parameters can be determined for the collapse of other types of stars with different initial density and rotation profiles.

J_h/M_h² = spin parameter
J_h/M_h² = 0.75

A_Kerr = 8M²(1 + (1 - (J/M²)²)^1/2)
A_Kerr/16M² = 0.63

M_D = disk mass
M_D/M = 0.13