Black-hole–neutron-star mergers at realistic mass ratios: Equation of state and spin orientation effects

Black-hole–neutron-star mergers resulting in the disruption of the neutron star and the formation of an accretion disk and/or the ejection of unbound material are prime candidates for the joint detection of gravitational-wave and electromagnetic signals when the next generation of gravitational-wave detectors comes online. However, the disruption of the neutron star and the properties of the postmerger remnant are very sensitive to the parameters of the binary (mass ratio, black-hole spin, neutron star radius). In this paper, we study the impact of the radius of the neutron star and the alignment of the black-hole spin on black-hole–neutron-star mergers within the range of mass ratio currently deemed most likely for field binaries ($M_{\mathrm{BH}}\sim 7M_{\mathrm{NS}}$) and for black-hole spins large enough for the neutron star to disrupt ($J_{\mathrm{BH}}/M_{\mathrm{BH}}^2=0.9$). We find that (i) In this regime, the merger is particularly sensitive to the radius of the neutron star, with remnant masses varying from $0.3M_{\mathrm{NS}}$ to $0.1M_{\mathrm{NS}}$ for changes of only 2 km in the NS radius; (ii) $0.01M_{\odot }–0.05M_{\odot }$ of unbound material can be ejected with kinetic energy $\gtrsim {10}^{51}\mathrm{ergs}$, a significant increase compared to low mass ratio, low spin binaries. This ejecta could power detectable postmerger optical and radio afterglows. (iii) Only a small fraction of the Advanced LIGO events in this parameter range have gravitational-wave signals which could offer constraints on the equation of state of the neutron star (at best $\sim 3\%$ of the events for a single detector at design sensitivity). (iv) A misaligned black-hole spin works against disk formation, with less neutron-star material remaining outside of the black hole after merger, and a larger fraction of that material remaining in the tidal tail instead of the forming accretion disk. (v) Large kicks $v_{\mathrm{kick}}\gtrsim 300\mathrm{km}/\mathrm{s}$ can be given to the final black hole as a result of a precessing black-hole–neutron-star merger, when the disruption of the neutron star occurs just outside or within the innermost stable spherical orbit.

Figure 1

Numerical grid before disruption of the neutron star, below the equatorial plane of the binary. The black hole is the excised region on the right (black sphere), while we superpose a linear color scale for the baryon density ${\rho }_0$. The subdomains on the outer edge of the plot connect to spherical shells covering the wave region.

Figure 2

Same as Fig. 1, but during the disruption of the neutron star.

Figure 3

Phase error in the dominant (2, 2) mode of the gravitational-wave signal for simulation R13i0. We show the phase difference between our standard and high resolutions, both with (dashed red line) and without (solid black line) aligning the waves in phase and time. The dash-dotted green curve shows an estimate of the error in the extrapolation method (obtained by comparing extrapolation using different polynomial orders).

Figure 4

Top: Tidal quadrupole $Q$ normalized by $I_{00}$. Bottom: Normalized quadrupole $Q_{\mathrm{norm}}$ [see Eq. (13)].

Figure 5

Merger for the nonprecessing cases R14i0 (left) and R12i0 (right). The top panel shows the system at the time at which half of the neutron-star material has been accreted onto the black hole. We show densities down to ${\rho }_{\min }\sim {10}^{-7}{M}_{\odot }^{-2}\sim 6\times {10}^{10}\mathrm{g}/{\mathrm{cm}}^3$. The bottom panel shows the remnant 5 ms later, plotting densities down to ${\rho }_{\min }\sim {10}^{-8}{M}_{\odot }^{-2}\sim 6\times {10}^9\mathrm{g}/{\mathrm{cm}}^3$ and cutting out the $x>0$, $y<0$ quadrant. The differences in scale between the 4 figures can be determined knowing that the size of the black hole is always $R_{\mathrm{BH}}\sim 15\mathrm{km}$.

Figure 6

Baryon mass remaining outside of the black hole as a function of time, for the 3 nonprecessing cases R14i0, R13i0 and R12i0. We shift all the curves by the time $t_{50\%}$ at which half of the matter has been accreted onto the black hole.

Figure 7

Top: Average surface density 5 ms after merger for the 3 nonprecessing cases R14i0, R13i0 and R12i0. Bottom: Disk profile for simulation R14i0. Shown are the angular velocity (normalized by the velocity for circular orbits in this metric), the entropy and the sound speed (normalized by $\Omega r$) as a function of the circumferential radius $r$.

Figure 8

Mass of the unbound material, as measured by the condition $u_t<-1$. For each configuration, $t_{\mathrm{merge}}$ is the time at which 50% of the neutron-star material has been accreted onto the black hole. The dashed vertical line represents the time at which $0.001M_{\odot }$ has escaped the grid (the low-density tidal tail of simulation R12i0 cannot be followed accurately for more than 2.5 ms, at which point we stop measuring the mass of the ejecta).

Figure 9

Distribution of asymptotic velocities for the unbound material of simulation R13i0. Two different times of the high-resolution simulation, and one time of the medium resolution simulation are shown.

Figure 10

Gravitational-wave emission [$(2,-2)$ mode] for the nonprecessing simulations R12i0 and R14i0, extrapolated to infinity and normalized by the ratio $D/M$ of the distance to the observer $D$ to the total mass of the binary $M$.

Figure 11

Phase difference between the $(2,-2)$ mode of the gravitational-wave emission of the nonprecessing simulations. Both R12i0 and R13i0 are compared with R14i0. The dashed black lines show the matching interval, while the dashed green line shows the time at which the amplitude of the signal peaks for case R14i0 (the case in which the neutron star disrupts at the earliest time).

Figure 12

Phase difference between the $(2,-2)$ mode of the gravitational-wave emission of the nonprecessing simulations as a function of the normalized gravitational-wave frequency ${\omega }_{\mathrm{GW}}M$. The dotted and dot-dashed curves correspond to the 1PN and 2.5PN predictions from Ref. 31. All curves are matched at ${\omega }_{\mathrm{GW}}M=0.2$. At lower frequency, residual eccentricity in the simulation makes measurements of $\varphi ({\omega }_{\mathrm{GW}})$ too noisy to be useful.

Figure 13

Spectrum of the gravitational-wave signal. $h_{\mathrm{opt}}(f)$ is the spectrum of the dominant mode of the gravitational-wave signal as seen by an optimally oriented observer at 100 Mpc. The dashed line shows the leading order PN behavior, $h=A{f}^{-7/6}$, with amplitude $A$ matched to the numerical results. The zero-detuned high power and zero-detuned low power noise curves of Advanced LIGO [57] are also shown, together with 3 potential high-frequency tunings of the detector, at 1 kHz [57], 1.5 kHz and 2 kHz [58].

Figure 14

Inclination ${\theta }_{\mathrm{bin}}$ between the initial and current direction of the normal to the orbital plane.

Figure 15

Same as Fig. 5, but for the precessing binaries R14i20 (left) and R14i40 (right).

Figure 16

Gravitational waveforms as measured by observers who, at $t=0$, see the binary face-on (solid black line) and edge-on along the line connecting the centers of the two objects (dashed red line). $h$ is normalized by the ratio $D/M$ of the distance to the observer $D$ to the total mass of the binary $M$. We show both the $h_{+}$ and $h_{\times }$ polarization, with $h_{\times }$ shifted by 0.2. Top: Nonprecessing configuration R14i0. The face-on observer is always optimally located, while the edge-on observer receives a weaker signal in $h_{+}$ (in which higher order modes are however more visible), and no signal at all in $h_{\times }$. Bottom: Precessing configuration R14i60. The envelope of the signal varies in time as the binary precess, and the optimal orientation is modified accordingly. The merger also occurs at an earlier time, as the orbital hang-up is only due to the aligned component of the black-hole spin.