Quasiequilibrium sequences of black-hole–neutron-star binaries in general relativity

We construct quasiequilibrium sequences of black-hole–neutron-star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition. We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics and account for the black hole by imposing equilibrium boundary conditions on the surface of an excised sphere (the apparent horizon). In this paper we focus on irrotational configurations, meaning that both the neutron star and the black hole are approximately nonspinning in an inertial frame. We present results for a binary with polytropic index $n=1$, mass ratio $M_{\mathrm{irr}}^{\mathrm{BH}}/M_{\mathrm{B}}^{\mathrm{NS}}=5$, and neutron star compaction $M_{\mathrm{ADM},0}^{\mathrm{NS}}/R_0=0.0879$, where $M_{\mathrm{irr}}^{\mathrm{BH}}$ is the irreducible mass of the black hole, $M_{\mathrm{B}}^{\mathrm{NS}}$ the neutron star baryon rest mass, and $M_{\mathrm{ADM},0}^{\mathrm{NS}}$ and $R_0$ the neutron star Arnowitt-Deser-Misner mass and areal radius in isolation, respectively. Our models represent valid solutions to Einstein’s constraint equations and may therefore be employed as initial data for dynamical simulations of black-hole–neutron-star binaries.

Figure 1

Contours of the lapse $\alpha$ in the equatorial plane for the innermost configuration of the sequence listed in Table . The thick circle on the left denotes the excision surface (apparent horizon) of the black hole, while that on the right denotes the surface of the neutron star. The cross “$\times$” indicates the position of the rotation axis.