Initial Stellar Model
Stars S0, S1, and S2 obey a n = 3 polytropic equation of state: P=Kρ0Γ, where P is the pressure, K the polytropic constant, and ρ0 the rest-mass density. We chose γ = 4/3 as it yields a good approximation for both pre-collapse Pop III cores and supermassive stars, where pressure is dominated by thermal radiation, and for pre-collapse Pop I/II cores, where pressure is dominated by relativistic degenerate electron pressure. The physical mass of the stars may be scaled to any desired value by adjusting K (M ∝ K3/2).
We add a weak poloidal magnetic field to the equilibrium model in cases S1 and S2 by introducing a vector potential, entirely in the φ direction,
Aφ = Abϖ2 max[ρ01/6 - ρcut1/6, 0]
where the cutoff ρcut is 10-5ρc, ρc is the central density, and Ab is a constant which determines the initial strength of the magnetic field. We have verified that the small initial magnetic fields chosen here introduce negligible violations of the Hamiltonian and momentum constraints in the initial data.