Star A

Evolution is performed on a 500x500 grid, with outer boundaries at r/M=20.3, where M is the initial mass of the star. In this simulation, the spin parameter is J/M²=1.0, and the rest-mass M₀ satisfies M₀/M_0,sup=1.46, where M_0,sup is the rest-mass limit ("supramassive limit") for uniformly rotating polytropes. Figure 1.1 shows the initial shape of the star, which is hypermassive.

In the meridional clip, the density is plotted on a logarithmic scale normalized to the maximum central density, which occurs at excision (Fig. 2-1).

At t/M=0, the star has an oblate density profile and rapid differential rotation (Fig. 2-2). Poloidal magnetic field lines are indicated by the closed loops. Rotational to gravitational potential energy is T/|W|=0.249. Magnetic braking and MRI destroy differential rotation and transfer angular momentum to the outer layers. Rotational kinetic energy in differential motion is transferred to toroidal magnetic field energy. At time t/M=2550 (66P_rot), the star becomes dynamically unstable and catastrophically collapses to a rotating black hole. An apparent horizon (dark grey) appears at t/M=2570 (67P_rot) as shown in Figure 2-3. Excising the black hole interior (white area) and evolving, we find that the system settles down to a black hole surrounded by a massive ambient disk (Fig. 2-4). The collimated field lines combined with the hot, massive accretion disk make the black hole a promising candidate for a source of gamma ray bursts.

Fig. 2-1 Color code for density profile	Fig. 2-2 Density Profile at t/M = 0
Fig. 2-3 Black hole excision at t/M = 2590	Fig. 2-4 Density profile at t/M = 2910

Fig. 3-1 Density profile at t/M = 2550	Fig. 3-2 Black hole excision at t/M = 2590
Fig. 3-3 Density profile at t/M = 2910

In these clips, we place 20,000 Lagrangian matter tracers that represent fluid elements. The initial distribution of Lagrangian tracers is proportional to the initial rest-mass density. We then calculate the trajectories of the tracers by integrating fluid velocities. The dark grey volume is the apparent horizon and the white volume is the area excised. The red lines trace representative magnetic field lines.

Fig. 4-1 Lagrangian matter tracers with full field at t/M = 0	Fig. 4-2 Field line at t/M = 0
Fig. 4-3 Black hole excision at t/M = 2590	Fig. 4-4 Lagrangian matter tracers at t/M = 2910
Fig. 4-5 Field lines at t/M = 2910	Fig. 4-6 Top view of field lines at t/M = 2910

The star collapses to form a rotating black hole surrounded by a massive disk. Listed in the table below are significant, nondimensional parameters for the spin of the black hole and disk, and the rest mass of the black hole and disk. These parameters indicate the formation of a substantial disk.

J_D/J	0.44
J_BH/J	0.56
M_0,D/M₀(0)	0.10
M_0,BH/M₀(0)	0.90
J_BH/M_0,BH²	0.8
J_BH/M_irr²	0.73