Accurate and realistic initial data for black hole–neutron star binaries

This paper is devoted to the computation of compact binaries composed of one black hole and one neutron star. The objects are assumed to be on exact circular orbits. Standard $3+1$ decomposition of Einstein equations is performed and the conformal flatness approximation is used. The obtained system of elliptic equations is solved by means of multidomain spectral methods. Results are compared with previous work both in the high mass ratio limit and for one neutron star with very low compactness parameter. The accuracy of the present code is shown to be greater than with previous codes. Moreover, for the first time, some sequences containing one neutron star of realistic compactness are presented and discussed.

Figure 1

Deformation indicator $\chi$ as a function of the orbital frequency for various approaches and ${\overline{M}}_{\mathrm{NS}}=0.05$ (first panel) and ${\overline{M}}_{\mathrm{NS}}=0.01$ (second panel). The mass ratio is 10.

Figure 2

Comparison between this work and 18 for a NS of small compactness ($\Xi =0.0879$). The ratio between the BH mass and the NS mass is 5. The first panel shows the deformation parameter $\chi$ and the second one the binding energy, both as a function of the orbital velocity.

Figure 3

Deformation parameter $\chi$ (first panel) and binding energy (second panel) as a function of orbital velocity for four different compactness parameters $\Xi$. $M_{\mathrm{NS}}^{\mathrm{grav}0}$ is the same for all the stars and the mass ratio with respect to the BH irreducible mass is 5.

Figure 4

Isocontours of the lapse (first panel) and of ${\tilde{A}}^{xx}$ (second panel) in the orbital plane. The thick black lines represent the surface of the compact objects (BH on the left and NS on the right). The distances are given in code coordinates.