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We present a new numerical scheme to solve the initial value problem forblack hole-neutron star binaries. This method takes advantage of theflexibility and fast convergence of a multidomain spectral representation ofthe initial data to construct high-accuracy solutions at a relatively lowcomputational cost. We provide convergence tests of the method for bothisolated neutron stars and irrotational binaries. In the second case, we showthat we can resolve the small inconsistencies that are part of thequasi-equilibrium formulation, and that these inconsistencies are significantlysmaller than observed in previous works. The possibility of generating a widevariety of initial data is also demonstrated through two new configurationsinspired by results from binary black holes. First, we show that choosing amodified Kerr-Schild conformal metric instead of a flat conformal metric allowsfor the construction of quasi-equilibrium binaries with a spinning black hole.Second, we construct binaries in low-eccentricity orbits, which are a betterapproximation to astrophysical binaries than quasi-equilibrium systems.

Initial data for black hole-neutron star binaries: a flexible, high-accuracy spectral method