Black hole-neutron star binary merger: Dependence on black hole spin orientation and equation of state

We systematically performed numerical-relativity simulations for black hole-neutron star (BH-NS) binary mergers with a variety of the BH spin orientation and nuclear-theory-based equations of state (EOS) of the NS. The initial misalignment angles of the BH spin measured from the direction of the orbital angular momentum are chosen in the range of $i_{\text{tilt},0}\approx 30°-90°$. We employed four models of nuclear-theory-based zero-temperature EOS for the NS in which the compactness of the NS is in the range of $\mathcal{C}=M_{\mathrm{NS}}/R_{\mathrm{NS}}=0.138-0.180$, where $M_{\mathrm{NS}}$ and $R_{\mathrm{NS}}$ are the mass and the radius of the NS, respectively. The mass ratio of the BH to the NS, $Q=M_{\mathrm{BH}}/M_{\mathrm{NS}}$, and the dimensionless spin parameter of the BH, $\chi$, are chosen to be $Q=5$ and $\chi =0.75$, together with $M_{\mathrm{NS}}=1.35M_{\odot }$ so that the BH spin misalignment has a significant effect on tidal disruption of the NS. We obtain the following results: (i) The inclination angles of $i_{\text{tilt},0}<70°$ and $i_{\text{tilt},0}<50°$ are required for the formation of a remnant disk with its mass larger than $0.1M_{\odot }$ for the cases $\mathcal{C}=0.140$ and $\mathcal{C}=0.160$, respectively, while the disk mass is always smaller than $0.1M_{\odot }$ for $\mathcal{C}\gtrsim 0.175$. The ejecta with its mass larger than $0.01M_{\odot }$ is obtained for $i_{\text{tilt},0}<85°$ with $\mathcal{C}=0.140$, for $i_{\text{tilt},0}<65°$ with $\mathcal{C}=0.160$, and for $i_{\text{tilt},0}<30°$ with $\mathcal{C}=0.175$. (ii) The rotational axis of the dense part of the remnant disk with its rest-mass density larger than ${10}^9\mathrm{g}/{\mathrm{cm}}^3$ is approximately aligned with the remnant BH spin for $i_{\text{tilt},0}\approx 30°$. On the other hand, the disk axis is misaligned initially with $\sim 30°$ for $i_{\text{tilt},0}\approx 60°$, and the alignment with the remnant BH spin is achieved at $\sim 50–60\mathrm{ms}$ after the onset of merger. The accretion time scale of the remnant disk is typically $\sim 100\mathrm{ms}$ and depends only weakly on the misalignment angle and the EOS. (iii) The ejecta velocity is typically $\sim 0.2–0.3c$ and depends only weakly on the misalignment angle and the EOS of the NS, while the morphology of the ejecta depends on its mass. (iv) The gravitational-wave spectra contains the information of the NS compactness in the cutoff frequency for $i_{\text{tilt},0}\lesssim 60°$.

Figure 1

Evolution of the orbital separation $x_{\text{sep}}^i≔x_{\mathrm{NS}}^i-x_{\mathrm{BH}}^i$ of binaries with $(Q,M_{\mathrm{NS}},\chi )=(5,1.35M_{\odot },0.75)$. The left, middle, and right panels show the results with H4i30, H4i60, and H4i90, respectively.

Figure 2

Evolution of $i_{\text{tilt}}$ for the models with H4.

Figure 3

Evolution of the precession angle, ${\varphi }_{\text{prec}}$, for the models with H4.

Figure 4

Snapshots of the volume rendered density map as well as the location of AHs at $\approx 5\mathrm{ms}$ after the onset of merger for the models H4i30 (left panel) and H4i60 (right panel). The inner regions of the simulation with side lengths of $\approx 300\mathrm{km}$ are shown.

Figure 5

Evolution of the rest mass outside the apparent horizon $M_{>\mathrm{AH}}$ for the models with $i_{\text{tilt},0}\approx 60°$ (left figure) and with H4 (right figure). The results for the aligned-spin case with $Q=5$ are picked up from [17].

Figure 6

The contour for $M_{\text{disk}}$ (left panel) and $M_{\text{eje}}$ (right panel) evaluated at $\approx 10\mathrm{ms}$ after the onset of merger in the plane of the NS compactness $\mathcal{C}$ and initial value of $i_{\text{tilt}}$.

Figure 7

$M_{\text{disk}}$ (left panel) and $M_{\text{eje}}$ (right panel) evaluated at $\approx 10\mathrm{ms}$ after the onset of merger as a function of an effective spin parameter ${\chi }_{\mathrm{eff}}=\chi \cos i_{\text{tilt},0}$. The plotted lines are the linear interpolation for the results of misaligned BH-NS mergers obtained in this paper, and the plotted points are the results for aligned-spin BH-NS mergers with $Q=5$ obtained in [17]. “a5” and “a375” denote the aligned models with $\chi =0.5$ and $\chi =0.375$, respectively.

Figure 8

The density profiles of the accretion disk at $\approx 20\mathrm{ms}$ after the onset of merger for selected models. The left, middle, and right columns show the plots for the $xy$-, $xz$-, and $yz$-planes, respectively. (a) The top, (b) second from top, (c) third from top, and (d) bottom rows show the plots for models ALF2i30, H4i30, H4i60, and MS1i60, respectively.

Figure 9

Evolution of the tilt angle between $J_{\text{disk}}^i$ and the BH spin for the models with $i_{\text{tilt},0}\approx 30°$ and 60°.

Figure 10

The density profiles on the $yz$ cross section for the model MS1i30 at $\approx 40\mathrm{ms}$ after the onset of merger.

Figure 11

The density profiles on the $yz$ cross section for the model MS1i60 at $\approx 10$, 40, and 70 ms after the onset of merger.

Figure 12

Evolution of $M_{\text{disk}}$ and the accretion time scale $t_{\text{acc}}=M_{\text{disk}}/{\dot{M}}_{\le \mathrm{AH}}$ for the models with MS1 (left figure) and with $i_{\text{tilt},0}\approx 30°$ (right figure).

Figure 13

Evolution of the accretion rate, ${\dot{M}}_{\le \mathrm{AH}}$, to the AH for MS1i30 but with different grid resolutions.

Figure 14

The volume-rendered density map of the ejecta at the time that the ejecta expands to $\approx 1500\mathrm{km}$ for models H4i30 (left), H4i60 (middle), and ALF2i60 (right), respectively.

Figure 15

The average specific angular momentum of material brought into BH normalized by $M_{\mathrm{BH}}$, $\mathrm{\Delta }l/M_{\mathrm{BH}}$, as a function of an effective dimensionless spin parameter ${\chi }_{\mathrm{eff}}=\chi \cos i_{\text{tilt},0}$. The specific angular momentum at the ISCO of the BH is also plotted.

Figure 16

The plus-mode gravitational waveforms for $(l,m)=(2,2),(2,1)$, and (2,0) for APR4i0 (left panel) and APR4i60 (right panel).

Figure 17

The square of the gravitational-wave amplitude observed along the $z$-axis as a function of the orbital phase divided by $2\pi$, $\mathrm{\Phi }/2\pi$, for models with the MS1 EOS.

Figure 18

Plus-mode gravitational waveforms (left panels) and gravitational-wave spectra (right panels) observed from different inclination angles with respect to the $z$-axis. The top and bottom figures are the results for models MS1i30 and MS1i90, respectively. Gravitational waveforms are plotted as functions of retarded time, $t_{\text{ret}}$. The left axis in the plots of the waveforms denotes the amplitude observed at a hypothetical distance $D=100\mathrm{Mpc}$, and the right axis denotes the normalized amplitude $Dh/m_0$. The upper axis in the plots of the spectra denotes the dimensionless frequency, $f{m}_0$, and the right axis denotes the normalized amplitude $D{\tilde{h}}_{\mathrm{eff}}(f)/m_0$. The bottom axis in the plots of spectra denotes the frequency of the gravitational waveform, in Hz, and the left axis denotes the amplitude observed at a hypothetical distance $D=100\mathrm{Mpc}$.

Figure 19

Gravitational wave spectra observed along the $z$-axis of the simulation. The top-left plot shows the spectra for the models with APR4 and with different initial values of $i_{\text{tilt},0}$. The top-right, bottom-left, and bottom-right plots compare the spectra among four different EOSs for $i_{\text{tilt},0}\approx 30°$, 60°, and 90°, respectively. The vertical lines at the upper axis show the QNM frequency of the remnant BH for each model (see Table 6).