Initial Stellar Model
Stars S0, S1, and S2 obey a n = 3 polytropic equation of state: P=Kρ_{0}^{Γ}, where P is the pressure, K the polytropic constant, and ρ_{0} 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 ∝ K^{3/2}).
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,
A_{φ} = A_{b}ϖ^{2} max[ρ_{0}^{1/6} - ρ_{cut}^{1/6}, 0]
where the cutoff ρ_{cut} is 10^{-5}ρ_{c}, ρ_{c} is the central density, and A_{b} 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.
Last Updated 05 Nov 14 by SEC
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