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We develop a method to compute low-eccentricity initial data of blackhole--neutron star binaries in the puncture framework extending previous workon other types of compact binaries. In addition to adjusting the orbitalangular velocity of the binary, the approaching velocity of a neutron star isincorporated by modifying the helical Killing vector used to derive equationsof the hydrostationary equilibrium. The approaching velocity of the black holeis then induced by requiring the vanishing of the total linear momentum of thesystem, differently from the case of binary black holes in the punctureframework where the linear momentum of each black hole is specified explicitly.We successfully reduce the orbital eccentricity to <~0.001 by modifying theparameters iteratively using simulations of ~3 orbits both for nonprecessingand precessing configurations. We find that empirical formulas for binary blackholes derived in the excision framework do not reduce the orbital eccentricityto ~0.001 for black hole--neutron star binaries in the puncture framework,although they work for binary neutron stars.

Reducing orbital eccentricity in initial data of black hole--neutron star binaries in the puncture framework