Black hole-neutron star mergers for $10M_{\odot }$ black holes

General relativistic simulations of black hole-neutron star mergers have currently been limited to low-mass black holes ($M_{\mathrm{BH}}\le 7M_{\odot }$), even though population synthesis models indicate that a majority of mergers might involve more massive black holes ($M_{\mathrm{BH}}\ge 10M_{\odot }$). We present the first general relativistic simulations of black hole-neutron star mergers with $M_{\mathrm{BH}}\sim 10M_{\odot }$. For massive black holes, the tidal forces acting on the neutron star are usually too weak to disrupt the star before it reaches the innermost stable circular orbit of the black hole. Varying the spin of the black hole in the range $a_{\mathrm{BH}}/M_{\mathrm{BH}}=0.5–0.9$, we find that mergers result in the disruption of the star and the formation of a massive accretion disk only for large spins $a_{\mathrm{BH}}/M_{\mathrm{BH}}\ge 0.7–0.9$. From these results, we obtain updated constraints on the ability of black hole-neutron star mergers to be the progenitors of short gamma-ray bursts as a function of the mass and spin of the black hole. We also discuss the dependence of the gravitational wave signal on the black hole parameters, and provide waveforms and spectra from simulations beginning 7–8 orbits before the merger.

Figure 1

Phase error $\delta \varphi$ for the (2,2) mode of the gravitational wave signal as a function of the number of orbits, for simulation Q7S7. The wave is extracted at finite radius $R=100M_{\mathrm{total}}$, and we do not attempt to shift it in phase or time.

Figure 2

(2,2) mode of the strain $h$ for simulation Q7S7 at our two highest resolutions, extracted at finite radius $R=100M_{\mathrm{total}}$. We shift the signal in time and phase so that the phase at the peak of the signal is $\varphi =0$, and the time $t=0$.

Figure 3

Matter distribution for simulation Q7S5. Left: Most of the neutron star material plunges directly into the black hole at the time of merger. Density contours: ${\rho }_0=({10}^{14},{10}^{13},{10}^{12},{10}^{11},{10}^{10})\mathrm{g}/{\mathrm{cm}}^3$. Right: 1 ms later, only 2% of the neutron star material remains outside the black hole, and most of it will rapidly accrete onto the hole. Density contours: ${\rho }_0=({10}^{12},{10}^{11},{10}^{10})\mathrm{g}/{\mathrm{cm}}^3$.

Figure 4

Matter distribution for simulation Q7S7. Left: Disruption of the neutron star. Material that is not immediately accreted onto the black hole (approximately $8\%$ of the NS mass) forms a thin tidal tail. Density contours: ${\rho }_0=({10}^{14},{10}^{13},{10}^{12},{10}^{11},{10}^{10})\mathrm{g}/{\mathrm{cm}}^3$. Center: Disk formation, about 8 ms later. A low density accretion disk begins to form approximately 50 km away from the black hole, but rapid mass accretion from the tidal tail causes the disk profile to vary significantly over time. The maximum density is approximately $3\times {10}^{11}\mathrm{g}/{\mathrm{cm}}^3$. Density contours: ${\rho }_0=({10}^{11},{10}^{10})\mathrm{g}/{\mathrm{cm}}^3$. Right: About 20 ms after disruption, a stable accretion disk has formed with low maximum density ${\rho }_{\max }\sim 2\times {10}^{10}\mathrm{g}/{\mathrm{cm}}^3$. About 2.5% of the initial mass of the neutron star remains in the disk at that time, but accretion onto the black hole would destroy the disk within approximately 20 ms. Density contour: ${\rho }_0={10}^9\mathrm{g}/{\mathrm{cm}}^3$.

Figure 5

Matter distribution for simulation Q7S9. Left: Disruption of the neutron star, very similar to the Q7S7 case (Fig. 4), but with more material ejected into the tidal tail. Density contours: ${\rho }_0=({10}^{14},{10}^{13},{10}^{12},{10}^{11},{10}^{10})\mathrm{g}/{\mathrm{cm}}^3$. Center: Disk formation 6.5 ms later. More than 25% of the fluid material remains outside the black hole. A massive accretion disk rapidly forms, containing more than 10% of the matter. Density contours: ${\rho }_0=({10}^{12},{10}^{11},{10}^{10})\mathrm{g}/{\mathrm{cm}}^3$. Right: 20 ms after disruption, a massive disk remains. It is 10 times denser than in the lower spin case, and has been in a nearly stable configuration for more than 10 ms. Density contours: ${\rho }_0=({10}^{11},{10}^{10})\mathrm{g}/{\mathrm{cm}}^3$.

Figure 6

Baryon mass available outside the black hole as a function of time. The mass is normalized by the initial mass of the neutron star.

Figure 7

Gravitational wave signal for a mass ratio $q=7$, when varying the black hole spin between $a_{\mathrm{BH}}/M_{\mathrm{BH}}=0.5–0.9$. The time and phase of the waveforms are matched at the peak of the signal.

Figure 8

Power spectrum of the gravitational wave signal for a mass ratio $q=7$, while varying the black hole spin between $a_{\mathrm{BH}}/M_{\mathrm{BH}}=0.5–0.9$. The cutoff at low frequency is only an effect of the finite length of the evolution. $h_{\mathrm{eff}}$ is the effective amplitude of the gravitational wave signal, as defined in Eq. (41) of 8.

Figure 9

Gravitational wave signal for the low spin simulations ($a_{\mathrm{BH}}/M_{\mathrm{BH}}=0.5$) for mass ratios $q=(5,7)$. The time and phase of the waveforms are matched at the peak of the signal.

Figure 10

Power spectrum of the gravitational wave signal for the low spin simulations ($a_{\mathrm{BH}}/M_{\mathrm{BH}}=0.5$) for mass ratios $q=(5,7)$.

Figure 11

Simulations with similar mass remaining outside the black hole for various BH masses and spins. All simulations correspond to $M_{\mathrm{NS}}=1.4M_{\odot }$, $R_{\mathrm{NS}}=14.4\mathrm{km}$ (although a rescaling of $M_{\mathrm{NS}}$, $R_{\mathrm{NS}}$, and $M_{\mathrm{BH}}$ would lead to the same fraction of the stellar mass remaining at late time). They thus correspond to optimistic predictions for the formation of accretion disks.