Quasiequilibrium states of black hole-neutron star binaries in the moving-puncture framework

General relativistic quasiequilibrium states of black hole-neutron star binaries are computed in the moving-puncture framework. We propose three conditions for determining the quasiequilibrium states and compare the numerical results with those obtained in the excision framework. We find that the results obtained in the moving-puncture framework agree with those in the excision framework and with those in the third post-Newtonian approximation for the cases that (i) the mass ratio of the binary is close to unity irrespective of the orbital separation, and (ii) the orbital separation is large enough ($m_0\Omega \lesssim 0.02$, where $m_0$ and $\Omega$ are the total mass and the orbital angular velocity, respectively) irrespective of the mass ratio. For $m_0\Omega \gtrsim 0.03$, both of the results in the moving-puncture and excision frameworks deviate, more or less, from those in the third post-Newtonian approximation. Thus the numerical results do not provide a quasicircular state, rather they seem to have a non-negligible eccentricity of order 0.01–0.1. We show by numerical simulation that a method in the moving-puncture framework can provide approximately quasicircular states in which the eccentricity is by a factor of $\sim 2$ smaller than those in quasiequilibrium given by other approaches.

Figure 1

Left panels: Binding energy $E_b/m_0$ as a function of $\Omega m_0$ for ${\overline{M}}_{\mathrm{B}}^{\mathrm{NS}}=0.15$ and $Q=1$ (upper panel), 3 (middle panel), and 5 (lower panel). The solid (red) and dashed (green) curves show the results obtained in the moving-puncture method with the ${\beta }^{\phi }$ condition and in the excision method [54], respectively. The dotted (blue) curve denotes the result in the 3PN approximation [81]. Right panels: The same as the left panels but for the total angular momentum $J/m_0^2$ as a function of $\Omega m_0$.

Figure 2

The same as Fig. 1 but for ${\overline{M}}_{\mathrm{B}}^{\mathrm{NS}}=0.14$, 0.15, and 0.16, and for $Q=3$ in the moving-puncture method.

Figure 3

Left panels: Binding energy $E/m_0$ as a function of $\Omega m_0$ for ${\overline{M}}_{\mathrm{B}}^{\mathrm{NS}}=0.15$ and $Q=1$, 3, and 5 in the moving-puncture approach with three different conditions for determining the center of mass of system. The dotted curve denotes the result in the 3PN approximation. Right panels: The same as the left panels but for the total angular momentum $J/m_0^2$ as a function of $\Omega m_0$.

Figure 4

Angular velocity of gravitational waveforms as a function of retarded time $t_{\mathrm{ret}}$ for $Q=3$ (left) and $Q=5$ (right) and for $\mathcal{C}=0.15$. $t_{\mathrm{ret}}=0$ approximately denotes the merger time. The solid and dashed curves denote the results in the 3PN-J condition and the ${\beta }^{\phi }$ condition, respectively. The dot-dotted curve is the result in the 3PN approximation (Taylor T4 formula; e.g., Ref. 49).

Figure 5

The mass-shedding parameter $\chi$ versus $\Omega m_0$ for the sequences of ${\overline{M}}_{\mathrm{B}}^{\mathrm{NS}}=0.15$, and $Q=3$ and 5. We also show the results obtained in the excision method [54].