The neutron star obeys a polytropic equation of state, P = Kρ0 Γ, at t = 0. It is evolved according to the adiabatic evolution law, P = (Γ-1)ρ0ε, where P is the pressure, K is the polytropic gas constant, ε is the internal specific energy, Γ is the adiabatic index, and ρ0 the rest-mass density. We chose Γ = 2 to mimic stiff nuclear matter.
For these simulations, the matter and gravitational field equations are not evolved. Rather, the initial quasi-equilibrium binary configuration satisfies the "conformal thin-sandwich" (CTS) equations, hence the solution possesses a helical Killing vector. This entitles us to rotate the matter and metric at the orbital binary frequency to mimic the spacetime evolution. This approximation is valid since the inspiral timescale is much longer than the orbital timescale at the orbital separation considered here. The magnetic field is then evolved in this matter and metric CTS background spacetime.
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The matter and metric (gravitational field) are determined by rotating the initial quasiequilibrium data. The magnetic field inside the neutron star is determined by solving the full magnetohydrodynamical (MHD) equations for the electromagnetic field. Magnetic fields in the exterior of the neutron star are evolved according to the force-free approximation for EM fields.