Star S2

Evolution is performed on a variable grid, with the grid changing as the characteristic radius of the star changes. This is necessary since the characteristic radius of the star decreases by a factor of almost 10³ during the collapse. The grid is initially 400x400 and uniform but ultimately increases to 1400x1400 as collapse proceeds. After collapse, a 600x600 multiple-transition fisheye grid is used. In this simulation, the spin parameter is J/M² = 0.96, R_eq = 640, and P_mag/P = 2.7 x 10^-3. Figure 1.1 shows the initial shape of the star.

In the meridional clip, the density is plotted on a logarithmic scale. The gravitational field is evolved via the BSSN scheme. The MHD equations are solved by a high-resolution shock capturing (HRSC) method.

At t/M=0, the star is rotating near the mass-shedding limit. Rotational to gravitational potential energy is T/|W|=0.009. The star quickly collapses to a black hole, creating an apparent horizon and surrounding torus. The frozen-in magnetic field grows initially by matter compression and winding. Soon after collapse, an outflow develops as matter from the outer layers of the star falls in. The outermost material has enough angular momentum that is it prevented from accreting and instead accumulate near the black hole, eventually heating up the inner torus and creating an outward shock along the surface of the torus. Unlike in the unmagnetized case (S0), the outflows in this case are persistent and not intermittent, as in case S1. In the magnetized cases, the outflow is much stronger and causes more of the torus mass to become unbound. The outflow carries the frozen magnetic field with it, causing the field lines near the outflow in the torus to bend, increasing the magnetic pressure in the region and strengthening the outflow. This bending is less pronounced in case S2 than in case S1 because the magnetic field in this cases is strong enough to counteract the bending and continue driving fluid outward. As the outflow proceeds, the field lines become collimated along the rotation axis of the black hole. The outflow and stellar wind carry away a large amount of magnetic energy from the torus, leaving a weak magnetic field in the inner torus at late times. In this case, the outflow and winds are strong enough that the inner torus oscillates radially, causing episodic accretion. As the torus oscillates away from the black hole, accretion ceases until the torus swings back in.

The collimated field lines and massive accretion torus make this star a viable candidate for launching ultrarelativistic jets as well as long-soft gamma-ray bursts. The radial oscillation in the torus for this case also leads to long wavelength, quasi-periodic gravitational radiation. For a SMS with M > 10⁴M_solar, such radiation may be detectable by LISA.

Fig. 2-1 Color code for density profile	Fig. 2-2 Density Profile at t = 0
Fig. 2-3 Black hole excision at t/M = 29100	Fig. 2-4 Density Profile at t/M = 31100

Fig. 3-1 Black hole excision at t/M = 29100

Fig. 3-2 Density profile at t/M = 31100

Fig. 4-1 Color code for density profile	Fig. 4-2 Density Profile at t = 0
Fig. 4-3 Black hole excision at t/M = 29100	Fig. 4-4 Density Profile at t/M = 31100

Fig. 5-1 Black hole excision at t/M = 29100

Fig. 5-2 Density profile at t/M = 31100

This clip animates a plot of the rest mass accretion rate onto the black hole as a function of time after excision. For this case, the strong outflow and winds cause the torus to oscillate radially. When the torus moves away from the black hole, accretion from the torus virtually ceases. The plot in the upper right-hand corner displays the evolution of the density profile. The density oscillations in the disk correlate with the oscillatory accretion rate.

M_BH/M	0.96
M_D/M₀	0.07
J_BH/J	0.66
J_BH/M²_BH	0.68