Black hole-neutron star mergers: Effects of the orientation of the black hole spin

The spin of black holes in black hole-neutron star binaries can have a strong influence on the merger dynamics and the post-merger state; a wide variety of spin magnitudes and orientations are expected to occur in nature. In this paper, we report the first simulations in full general relativity of black hole-neutron star mergers with misaligned black hole spin. We vary the spin magnitude from $a_{\mathrm{BH}}/M_{\mathrm{BH}}=0$ to $a_{\mathrm{BH}}/M_{\mathrm{BH}}=0.9$ for aligned cases, and we vary the misalignment angle from 0 to 80° for $a_{\mathrm{BH}}/M_{\mathrm{BH}}=0.5$. We restrict our study to $3:1$ mass-ratio systems and use a simple $\Gamma$-law equation of state. We find that the misalignment angle has a strong effect on the mass of the post-merger accretion disk, but only for angles greater than $\approx 40°$. Although the disk mass varies significantly with spin magnitude and misalignment angle, we find that all disks have very similar lifetimes $\approx 100\mathrm{ms}$. Their thermal and rotational profiles are also very similar. For a misaligned merger, the disk is tilted with respect to the final black hole’s spin axis. This will cause the disk to precess, but on a time scale longer than the accretion time. In all cases, we find promising setups for gamma-ray burst production: the disks are hot, thick, and hyperaccreting, and a baryon-clear region exists above the black hole.

Figure 1

Evolution of the position of the center of mass along the $z$-axis during inspiral (solid line), compared to the motion expected from the boost ${\mathit{v}}_{\infty }^z$ given in the initial data (dotted line).

Figure 2

Average surface density of the fluid at a given distance from the center of mass of the system, for the simulation s.5i20 described in Sec. 4. The surface density is plotted at time $t_0=t_{\mathrm{merger}}+10.3\mathrm{ms}$, when we begin to evolve the system using the fixed-metric approximation, as well as 0.5 ms and 1.1ms later. We see that the profile is very similar for both evolution methods, even though the disk itself is not in a stationary configuration.

Figure 3

Baryonic mass $M_b$ normalized by its initial value $M_{b,0}$ and average entropy $⟨s⟩$ for three resolutions.

Figure 4

$M_{\mathrm{ADM}}$ and $J_{\mathrm{ADM}}$ (normalized to their initial values) compared to the changes expected from the gravitational radiation flux for three resolutions.

Figure 5

Evolution of the total baryonic density outside the hole for three different aligned BH spins.

Figure 6

Comparison of the evolution of the Cartesian components of the spin for an initial inclination of 80° in our simulation (NR) and for the first- and second-order post-Newtonian expansions (resp. 1PN and 2PN). The PN values are obtained by integrating the evolution equations for the spin given in [37], using the trajectory and current spin of the numerical simulation.

Figure 7

Evolution of an inclined binary (s.5i80). Top left: Beginning of the simulation, at a separation of 63 km. Top right: After 7 ms and two orbits of inspiral, the star disrupts and most of the matter rapidly accretes onto the black hole. Bottom left: After 11 ms, the remaining matter ($\sim 8.5\%$ of the initial mass) is split between a developing disk and a tidal tail. Differential precession between the disk and the tail means that the disk and the matter falling back from the tail orbit in different planes. Bottom right: After 15.5 ms, the disk contains about 4.5% of the initial mass of the star. It is still highly inhomogeneous, and slowly expanding. A movie of the whole simulation is available online [41]. In each image, the wired frame shows the “fluid” grid in the $z=0$ plane (orbital plane at $t=0$).

Figure 8

Evolution of the total baryonic mass outside the hole for different initial inclination of the BH spin.

Figure 9

Amplitude of ${\psi }_{(l,m)}^4/{\psi }_{(2,2)}^4$ for the 3 modes (2,1), (3,3) and (3,2), shown for initial inclinations of the BH spin of 20° and 60°. The time $t_{\max }$ corresponds to the peak amplitude of the dominant (2,2) mode.

Figure 10

Real part of the gravitational strain $h$ for the simulations s.5i0 (top panel) and s.5i80 (lower panel), viewed from different inclinations $\theta$ with respect to the initial orbital angular momentum. The wave is extracted at $r=75M$ for a mass of the neutron star $M_{\mathrm{NS}}=1.4M_{\odot }$, and assumed to travel as a linear perturbation up to the observation point located at $r=100\mathrm{Mpc}$. Waves emitted at the time of merger will reach the radius $r=75M$ at $(t-t_{\mathrm{merger}})\sim 2\mathrm{ms}$. Over the 2–3 orbits simulated here, the effects of the orbital precession—and, in particular, the contribution on the second highest mode (2,1), shown in Fig. 9—remain small.

Figure 11

Upper panel: Specific angular momentum of the accretion disk at $t=30\mathrm{ms}$ for runs s0, s.5i0 and s.5i60. Note that for the smaller spin s0, the disk does not extend farther than $r\approx 125\mathrm{km}$. Lower panel: For the same configurations, entropy of the disk averaged over all points at a given distance from the black hole center.

Figure 12

Profile of the disk forming in the simulation s.5i60 at $t=20\mathrm{ms}$ (upper panel) and $t=40\mathrm{ms}$ (lower panel).

Figure 13

Upper panel: Tilt profile of the accretion disk formed in simulation s.5i60, as obtained from evolutions on a static background metric. The inclination of the disk decreases in time, with $\beta \approx 10–15°$ at the time of disk formation, but $\beta \approx 5–7°$ towards the end of the simulation. Lower panel: Twist profile for the same configuration. Over the 20 ms of evolution, the disk goes through more than one fourth of a precession period.