Initial Stellar Model
Stars A, B1, and B2 obey a 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 choose Γ = 2 to mimick stiff nuclear matter. The physical mass of the stars may be scaled to any desired value by adjusting K (M ∝ K^{1/2}). In addition, the rotation law is given by
u^{t}u_{φ} = A^{2} (Ω_{c} - Ω),
where Ω ≣ u^{φ}/u^{t} is the angular velocity of the fluid and Ω_{c} is Ω on the rotation axis. The constant A has units of length and determines the steepness of the differential rotation. A is set equal to the coordinate equatorial radius R_{eq}. In the Newtonian limit, it reduces to
Ω = Ω_{c} / (1 + ϖ^{2}/A^{2})
(ϖ is the cylindrical radius.) We add a weak poloidal magnetic field to the equilibrium model by introducing a vector potential
A_{ϕ} = ϖ^{2} max[A_{b}(P - P_{cut}), 0]
where the cutoff P_{cut} is 4% of the maximum pressure, and A_{b} is a constant which determines the initial strength of the magnetic field. We characterize the strength of the initial magnetic field by C ≣ max(b^{2}/P), where b^{2} = B^{2}/8π. We choose A_{b} such that C ∼ 10^{-3}-10^{-2}. We have verified that such small initial magnetic fields introduce negligible violations of the Hamiltonian and momentum constraints in the initial data.
last updated 01 sep 06 by adc
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