The neutron star obeys a polytropic equation of state, P = Kρ_{0}^{ Γ}, at
t = 0. It is evolved according to the
adiabatic evolution law, P =
(Γ-1)ρ_{0}ε, where P is the pressure, K is
the polytropic gas constant, ε is the internal specific energy,
Γ is the adiabatic index, and ρ_{0} 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.

### Black Hole

For the BHNS binary we consider the mass ratio
q = M

_{BH}/M

_{NS} = 3. Simulations are performed for 3 black hole spins:

S_{BH}/M_{BH}^{2} = -0.5, 0,0, 0.75.

### Neutron Star

The initial compaction of the neutron star is
M

_{NS}/R

_{NS} = 0.145. The rest mass is 83%
of the maximum rest mass of an isolated, nonrotating NS with the same
polytropic EOS. It has a radius of

R_{NS} = 13.2 km (M_{0}/1.4 M_{ʘ})
and a mass of

M_{NS} = 1.30 M_{ʘ} (M_{0}/1.4 M_{ʘ}).

### Binary

The initial binary is in a quasiequilibrium circular orbit, and has a frequency of

MΩ ~ 0.033. The initial coordinate separation is

D/M = 8.81.
The matter and gravitational field variables are determined by using the CTS formalism.
BH equilibrium boundary conditions are imposed on the BH horizon.

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.