Initial Stellar Model

Stars A, B1, and B2 obey a polytropic equation of state: P=Kρ0Γ, where P is the pressure, K the polytropic constant, and ρ0 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 ∝ K1/2). In addition, the rotation law is given by

utuφ = A2c - Ω),

where Ω ≣ uφ/ut is the angular velocity of the fluid and Ωc 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 Req. In the Newtonian limit, it reduces to

Ω = Ωc / (1 + ϖ2/A2)

(ϖ is the cylindrical radius.) We add a weak poloidal magnetic field to the equilibrium model by introducing a vector potential

Aϕ = ϖ2 max[Ab(P - Pcut), 0]

where the cutoff Pcut is 4% of the maximum pressure, and Ab is a constant which determines the initial strength of the magnetic field. We characterize the strength of the initial magnetic field by C ≣ max(b2/P), where b2 = B2/8π. We choose Ab 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

Center for Theoretical Astrophysics---University of Illinois at Urbana-Champaign

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