Star B1

Evolution is performed on a 400x400 grid, with outer boundaries at r/M=36.4, where M is the initial mass of the star. In this simulation, the spin parameter is J/M²=1.0, and M₀/M_0,sup=0.86 where M_0,sup is the rest-mass limit for uniformly rotating polytropes. Figure 1.1 shows the initial shape of the star, an ultraspinning star.

In the meridional clip, the density is plotted on a logarithmic scale normalized to the maximum central density, which occurs at excision.

At t/M=0, the star has an oblate density profile and rapid differential rotation (Fig. 2-1). Poloidal magnetic field lines are indicated by the closed loops. Rotational to gravitational potential energy is T/|W|=0.181. Magnetic braking and MRI reduce differential rotation and transfer angular momentum to the outer layers, building up the toroidal field. The star eventually reaches a steady state with a fairly uniformly rotating core surrounded by a differentially rotating torus (Fig. 2-2). The remaining differential rotation no longer shears the magnetic field, since the angular velocity is constant along magnetic field lines.

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 red lines trace representative magnetic field lines.

Fig. 3-1 Lagrangian matter tracers with full field at t/M = 0	Fig. 3-2 Field line at t/M = 0
Fig. 3-3 Lagrangian matter tracers at t/M = 12000	Fig. 3-4 Field lines at t/M = 12000
Fig. 3-5 Top view of field lines at t/M = 12000