Jet launching from binary black hole-neutron star mergers: Dependence on black hole spin, binary mass ratio, and magnetic field orientation

Black hole-neutron star (BHNS) mergers are one of the most promising targets for multimessenger astronomy. Using general relativistic magnetohydrodynamic simulations of BHNS undergoing merger we previously showed that a magnetically driven jet can be launched by the $\mathrm{disk}+\text{spinning}$ black hole remnant if the neutron star is endowed with a dipole magnetic field extending from the interior into the exterior as in a radio pulsar. These self-consistent studies considered a BHNS system with mass ratio $q=3:1$, black hole spin $a/M_{\mathrm{BH}}=0.75$ aligned with the total orbital angular momentum, and a neutron star that is irrotational, threaded by an aligned magnetic field and modeled by an $\mathrm{\Gamma }$-law equation of state with $\mathrm{\Gamma }=2$. Here, as a crucial step in establishing BHNS systems as viable progenitors of central engines that power short gamma-ray bursts (sGRBs) and thereby solidify their role as multimessenger sources, we survey different BHNS configurations that differ in the spin of the BH companion ($a/M_{\mathrm{BH}}=-0.5$, 0, 0.5, 0.75), in the mass ratio ($q=3:1$ and $q=5:1$) and in the orientation of the magnetic field (aligned and tilted by 90° with respect to the orbital angular momentum). We find that by $\mathrm{\Delta }t\sim 3500M-4000M\sim 88(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{ms}-100(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{ms}$ after the peak gravitational wave signal a magnetically driven jet is launched in the cases where the initial spin of the BH companion is $a/M_{\mathrm{BH}}=0.5$ or 0.75. The lifetime of the jets [$\mathrm{\Delta }t\sim 0.5(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{s}-0.7(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{s}$] and their outgoing Poynting luminosities [$L_{\mathrm{jet}}\sim 10^{51\pm 1}\mathrm{erg}/\mathrm{s}$] are consistent with typical sGRBs, as well as with the Blandford-Znajek mechanism for launching jets and their associated Poynting luminosities. By the time we terminate our simulations, we do not observe either an outflow or a large-scale magnetic field collimation in the other configurations we simulate. These results suggest that future multimessenger detections from BHNSs are more likely produced by binaries with highly spinning BH companions and small tilt-angle magnetic fields, though other physical processes not considered here, such as neutrino annihilation, may help to power jets in general cases.

Figure 1

Volume rendering of rest-mass density ${\rho }_0$ normalized to the initial NS maximum value ${\rho }_0=8.92\times {10}^{14}(1.4M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ (log scale) at selected times for case Aliq3sp0.5 (see Table 1). White lines denote the magnetic field while the arrows denote the fluid velocity. The BH apparent horizon is shown as a black sphere. Here $M=2.5\times {10}^{-2}(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{ms}=7.58(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{km}$.

Figure 2

Volume rendering of rest-mass density ${\rho }_0$ normalized to its initial NS maximum value ${\rho }_0=8.92\times {10}^{14}(1.4M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ (log scale) at selected times for case Aliq3sp0.0 (see Table 1). White lines denote the magnetic field while the arrows denote the fluid velocity. The BH apparent horizon is shown as a black sphere. Here $M=2.5\times {10}^{-2}(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{ms}=7.58(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{km}$.

Figure 3

Gas-to-magnetic pressure ratio $\beta \equiv P_{\mathrm{gas}}/P_{\mathrm{mag}}$ along the $x$ direction at the time $t=t_B$ the dipolelike magnetic field generated by the vector potential $A_{\varphi }$ in Eq. (2) is seeded in the star (see Table 1).

Figure 4

Volume rendering of rest-mass density ${\rho }_0$ normalized to its initial NS maximum value ${\rho }_0=8.92\times {10}^{14}(1.4M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ (log scale) for cases Aliq3sm0.5 (top row) and Aliq3sp0.0 (bottom row) at selected times. White lines denote the magnetic field while the arrows denote the fluid velocity. The BH apparent horizon is shown as a black sphere. Here $M=2.5\times {10}^{-2}(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{ms}=7.58(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{km}$.

Figure 5

Rest mass $M_{\mathrm{NS}}$ of NS matter outside the BH versus time for all cases listed in Table 1. The time has been shifted by $t_B$, at which time the magnetic field is seeded in the NS.

Figure 6

Rest-mass accretion rate for all cases listed in Table 1 computed via Eq. (A11) in [70]. Time is measured from the moment (retarded time $t-r$) of maximum GW amplitude $t_{\mathrm{GW}}$.

Figure 7

Total magnetic energy $\mathcal{M}$ outside the BH apparent horizon for all cases listed in Table 1, normalized to the ADM mass $M_{\mathrm{ADM}}=9.3\times {10}^{54}(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{erg}$. The inset shows that there is no significant enhancement of $\mathcal{M}$ during disruption. The time has been shifted by $t_B$ at which moment the magnetic field is seeded in the NS.

Figure 8

Average value of the force-free parameter $b^2/(2{\rho }_0)$ versus time (log scale) for all cases listed in Table 1. The average is computed using grid points contained in a cube of edge $2R_{\mathrm{BH}}$ above the BH. Here $R_{\mathrm{BH}}$ denotes the radius of the BH apparent horizon.

Figure 9

Rest-mass density on the meridional plane along with the ${\lambda }_{\mathrm{MRI}}/2$ (left) and the quality factor $Q_{\mathrm{MRI}}$ on the equatorial plane (right) at $t-t_{\mathrm{GW}}\sim 350M\sim 8.75(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{ms}$ following the peak GW amplitude in case $\tilde{a}=0.5$ (Aliq3sp0.5) but similar behavior among all cases with spinning BH $\tilde{a}\ge 0$. The BH apparent horizon is denoted by the black disk.

Figure 10

Magnetic field strength on a meridional plane after $t-t_{\mathrm{GW}}\sim 350M\sim 8.75(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{ms}$ following the maximum GW amplitude, time at which the accretion $\mathrm{disk}+\text{disk}$ remnant starts to settle, and nearly to the end of the evolution for cases Aliq3sp0.0 (left column) and Aliq3sp0.5 (right column). Arrows denote the fluid velocity, while the BH apparent horizon is shown as a black disk.

Figure 11

Volume rendering of the ratio $b^2/2{\rho }_0$ (log scale) near the end of the simulation for case Aliq3sp0.0 (left) and Aliq3sp0.5 (right). The magnetic field lines are denoted by white lines plotted in regions where $b^2/2{\rho }_0\ge 0$.

Figure 12

Outgoing EM (Poynting) luminosity for $t\ge t_{\text{jet}}$ computed at a coordinate sphere of radius $r=100M\sim 760(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{km}$ (top panel) and (2, 2) mode of the gravitational wave strain $h_{+}$ as functions of retarded time extracted at $r_{\mathrm{ex}}=80M\sim 606(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{km}$ (bottom) for case Aliq3sp0.5 (continuous line) and case Aliq3sp0.75 (dashed line).

Figure 13

Angular distribution of Poynting flux for case $\tilde{a}=0.5$, normalized by its peak value on a sphere of radius $60M=4600(M_{NS}/1.4M_{\odot })\mathrm{km}$. Angles are defined with respect to a spherical coordinate system centered on the BH center, with the spin axis along the $z$ direction.

Figure 14

Volume rendering of rest-mass density ${\rho }_0$ normalized to its initial NS maximum value ${\rho }_0=8.92\times {10}^{14}(1.4M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ (log scale) at selected times for case Aliq5sp0.0 (see Table 1). White lines denote the magnetic field while the arrows denote the fluid velocity. The BH apparent horizon is denoted as a black sphere. Here $M=11.44(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{km}=3.81\times {10}^{-2}(M_{\mathrm{NS}}/1.4M_{\odot })\mathrm{ms}$.