General-relativistic neutrino-radiation magnetohydrodynamic simulation of seconds-long black hole-neutron star mergers

Seconds-long numerical-relativity simulations for black hole–neutron star mergers are performed for the first time to obtain a self-consistent picture of the merger and post-merger evolution processes. To investigate the case that tidal disruption takes place, we choose the initial mass of the black hole to be $5.4M_{\odot }$ or $8.1M_{\odot }$ with a dimensionless spin of 0.75. The neutron-star mass is fixed to be $1.35M_{\odot }$. We find that after the tidal disruption, dynamical mass ejection takes place over $\lesssim 10\mathrm{ms}$, together with the formation of a massive accretion disk. Subsequently, the magnetic field in the disk is amplified by the magnetic winding and magnetorotational instability, establishing a turbulent state and inducing angular momentum transport. The post-merger mass ejection by the magnetically induced viscous effect sets in at $\sim 300–500\mathrm{ms}$ after the tidal disruption, at which the neutrino luminosity drops below $\sim {10}^{51.5}\mathrm{erg}/\mathrm{s}$, and continues for several hundred ms. A magnetosphere near the rotational axis of the black hole is developed after the matter and magnetic flux fall into the black hole from the accretion disk, and high-intensity Poynting flux generation sets in at a few hundred ms after the tidal disruption. The intensity of the Poynting flux becomes low after the significant post-merger mass ejection, because the opening angle of the magnetosphere increases. The lifetime of the stage with the strong Poynting flux is 1–2 s, which agrees with the typical duration of short-hard gamma-ray bursts.

Figure 1

Snapshot of the rest-mass density $\rho$ ($\mathrm{g}/{\mathrm{cm}}^3$), magnetic-field strength $b=\sqrt{b^{\mu }{b}_{\mu }}(\mathrm{G})$, electron fraction $Y_{\mathrm{e}}$, and temperature $T$ ($kT$ in units of MeV) in the $x\text{−}z$ plane with [$-2000\mathrm{km}:2000\mathrm{km}$] for both $x$ and $z$ at $t\approx 0.1$, 0.3, 1.0, 1.5, and 2.0 s for model Q4B5L. Note that the green region in $Y_{\mathrm{e}}$ found on the left side in the first and second rows shows the dynamical ejecta and fall-back matter. See also the animation at [89].

Figure 2

Profile of the average toroidal magnetic field along the polar direction ($\theta$) at $r\approx 50\mathrm{km}$ as a function of time for models Q4B5L (top panel) and Q4B5H (bottom panel).

Figure 3

Time evolution of the rest mass of the matter located outside the apparent horizon (dashed curves) and the accretion-disk mass (solid curves) for all of the runs with $Q=4$ (left panel) and $Q=6$ (right panel).

Figure 4

Time evolution of the rest mass of the unbound matter (ejecta) for all of the runs with $Q=4$ (left panel) and $Q=6$ (right panel).

Figure 5

Time evolution of the maximum rest-mass density of the bound matter located outside the apparent horizon for all of the runs with $Q=4$ (left panel) and $Q=6$ (right panel).

Figure 6

Time evolution of the total neutrino luminosity (sum of the luminosity for all of the neutrino species) for all of the runs with $Q=4$ (left panel) and $Q=6$ (right panel). The post-merger mass ejection sets in at $t-t_{\text{merger}}\sim 300–500\mathrm{ms}$, at which $L_{\nu }\sim {10}^{51.5}\mathrm{erg}/\mathrm{s}$.

Figure 7

Time evolution of the rest-mass accretion rate calculated from $-d{M}_{>\mathrm{AH}}/dt$ (left panel) and the neutrino emission efficiency $L_{\nu }/(-d{M}_{>\mathrm{AH}}/dt)$ (right panel) for all of the runs with $Q=4$.

Figure 8

Time evolution of the electromagnetic energy evaluated for the outside of the apparent horizon for all of the runs with $Q=4$ (left panel) and $Q=6$ (right panel).

Figure 9

Time evolution of the ratio of the electromagnetic energy to the internal energy evaluated for the outside of the apparent horizon for all of the runs with $Q=4$ (left panel) and $Q=6$ (right panel).

Figure 10

Time evolution of the mass histograms with respect to the temperature (upper panel) and electron fraction (lower panel) for model Q4B5H. The post-merger mass ejection sets in when the temperature for most of the matter decreases below 3 MeV at $t\sim 400\mathrm{ms}$ for this model. Note that only matter in the computational domain is taken into account in this figure, and thus matter that has escaped from the computational domain is neglected in the late stages. Thus, for $t\gtrsim 300\mathrm{ms}$ the dynamical ejecta mass decreases with time.

Figure 11

Mass histograms as functions of the electron fraction (left panels) and velocity (right panels) of ejecta for the models with simulation time longer than 1 s (models Q4B5H, Q4B5L, Q4B3L, Q6B5L, and Q6B3L). Models with $Q=4$ and $Q=6$ are displayed in the upper and lower panels, respectively.

Figure 12

Snapshots of the rest-mass density profile (blue and green contours) with the magnetic-field lines (pink curves), unbound matter (white color) and its velocity (green arrow) for model Q4B5L at $t=300\mathrm{ms}$. Magnetic-field lines penetrating the black-hole horizon are displayed. See also the following link for the time evolution: Ref. [103].

Figure 13

$L_{\mathrm{iso}}$ as a function of time for all of the runs with $Q=4$ (left panel) and 6 (right panel). The Poynting luminosity is evaluated at $r\approx 1500\mathrm{km}$ for all of the runs.

Figure 14

Snapshot of the toroidal magnetic field together with the poloidal magnetic-field lines (curves) in the $x-z$ plane at selected time slices for model Q4B5L. See also the following link for an animation: Ref. [104].

Figure 15

Angular distribution of the Poynting flux per steradian on a sphere of $r\approx 1500\mathrm{km}$ for model Q4B5L at selected time slices. The bright color displayed in the polar region stems from the Blandford-Znajek effect, while for other regions the magnetic fields accompanying the outflowing matter contribute mainly to the Poynting flux. The opening angle of the Poynting flux in the polar region is shown to increase with time. See the following link for an animation: Ref. [105].

Figure 16

Snapshots of the MRI quality factor together with the rest-mass density (contour) in the $x\text{−}z$ plane at $t\approx 300$ and 1000 ms for model Q4B5L.

Figure 17

Snapshots of the outgoing Poynting flux per steradian together with poloidal magnetic-field lines (white curves) near the apparent horizon in the $x\text{−}z$ plane at $t\approx 500$ and 1000 ms for model Q4B5L. The apparent horizon is shown with the black circle.