Introduction

The era of multimessenger astronomy has accelerated with the detection of GW170817, a gravitational wave (GW) signal from the coalescence of a compact binary, accompanied by electromagnetic (EM) counterpart radiation across the EM spectrum. From the gravitational radiation signal alone, the inferred masses of the individual binary companions are in the broad range of $0.86-2.26\, M_\odot$, though the total mass of the system is constrained to be $2.73-3.29\, M_\odot$ with $90\%$ confidence. These estimates, along with the EM counterparts, and, in particular, the detection of a short gamma-ray burst (sGRB) $-$ GRB 170817A- $1.7$s$-$ following the inferred merger time by the Fermi Gamma-Ray Burst Monitor, as well as the associated kilonova/macronova, demonstrate the presence of matter. These observations strongly suggest a merging binary neutron star system (NSNS) as the source of GW170817, although they cannot rule out the possibility that one of the binary companions is a stellar-mass black hole (BH). Recently, a summary of possible low-mass BH formation channels, and routes by which they may arise in binaries with a NS companion, have been presented. The astrophysical implication of these observations create the urgent need to model GWs and EM counterparts from both NSNS and black hole-neutron stars (BHNS) systems.

GW170718 and GRB 170817A provide the best direct confirmation so far that the merger of compact binaries in which at least one NS is involved can be the engine that powers sGRBs. This identification was demonstrated by self-consistent simulations in full general relativistic magnetohydrodynamics (GRMHD) of merging BHNSs and merging NSNSs that undergo ${\it delayed}$ collapse. Numerical studies, whose initial configuration is a BHNS binary with mass ratio $q=3:1$ in a quasicircular orbit, with an NS modeled as an irrotational $\Gamma=2$ polytrope and a BH with dimensionless spin $\tilde{a}\equiv a/M_{\rm BH}=0.75$, showed that a collimated, mildly relativistic outflow -an incipient jet- can be launched from the highly spinning BH remnant surrounded by a magnetized accretion disk. Such a jet requires that a strong poloidal magnetic field component which connects the disk to the BH poles persist after the disruption of the NS. This key feature was achieved by seeding the NS initially with a dipole magnetic field that extends from the stellar interior into the exterior in a pulsar-like, force-free exterior magnetosphere. Following the onset of tidal disruption, it was found that magnetic winding and the magnetorotational instability (MRI) amplify the magnetic field above the BH poles from $\sim 10^{13}(1.4M_\odot/M_{\rm NS})$G when the disk first settles to $\sim 10^{15}(1.4M_\odot/M_{\rm NS})$G, and this field eventually drives and confines the incipient jet by $\Delta t\sim 100(M_{\rm NS}/1.4M_\odot)$ms after peak GW emission. The lifetime of the jet and the outgoing Poynting luminosity are $\Delta t\sim 0.5(M_{\rm NS}/1.4M_\odot)$s and $L_{\rm EM}\sim 10^{51}\rm erg/s$, values which are both consistent with typical sGRBs.

In the NSNS scenario, by contrast, an incipient jet emerges whether or not the initial poloidal magnetic field is confined to the NS interior, as long as the binary forms a hypermassive neutron star (HMNS) that undergoes delayed collapse to a BH. During the formation and spindown of the transient, differentially-rotating HMNS magnetic winding and both the Kelvin-Helmholtz instability and the MRI boost the rms value of the magnetic field to $\gtrsim~10^{15.5}$G. In the prompt collapse scenario, the onset of BH formation following the NSNS merger prevents that amplification. The calculations that model the NS with a simple $\Gamma$-law equation of state (EOS) with $\Gamma=2$, allowing for shock heating, show that the disk + BH remnant launches a jet at about $\sim 44(M_{\rm NS}/1.8M_\odot)\rm ms$ following the NSNS merger, which lasts $\Delta t\sim 97(M_{\rm NS}/1.8M_\odot)$ms. The outgoing Poynting luminosity is $L_{\rm EM}\sim 10^{51}\rm erg/s$, consistent with short sGRBs. Recent GRMHD simulations of NSNS mergers, in which the effects of different EOSs, different mass ratios, and different magnetic field orientations with an initial strength of $\sim 10^{12}\rm G$ were studied, did not find evidence of an outflow or a jet after $\Delta t\sim 35\rm ms$ following the NSNS merger, although the formation of an organized magnetic field structure above the BH was observed. A lack of a jet in the high resolution NSNS mergers has been also reported, in which the NS is modeled by an H4 EOS. At the end of those simulations, however, they report persistent fall-back debris in the atmosphere, which increases the ram pressure above the BH poles, preventing the system form approaching a near force-free environment as required for jet launching. A longer time integration may be needed for the atmosphere to disperse and for the jet to emerge. Note that jet launching may not be possible for all EOSs, if the matter fall-back timescale is longer than the disk accretion. The seeded poloidal magnetic field in numerical studies is restricted to the NS interior.

In this instance, we survey fully relativistic BHNS configurations initially in a quasicircular orbit that undergo merger to address the question: Can all the BHNS configurations that undergo merger in which the NS is seeded with a pulsar-like, force-free magnetic field be progenitors of the engine that launches incipient jets?

In particular, we now consider BHNS configurations with mass ratio $q=3:1$ in which the dimensionless spin of the BH companion is $\tilde{a}=-0.5$ (counter-rotating), $\tilde{a}=0$ (nonspinning), and $\tilde{a}=\,0.5$, all aligned with the orbital angular momentum. In addition, we consider a BHNS configuration with mass ratio $q=5:1$ in which the BH companion has no spin initially. In all cases, the NS is endowed with a dynamically weak poloidal magnetic field that extends from the stellar interior into the NS exterior (i.e. a pulsar-like magnetic field) whose dipole magnetic moment is also aligned with the orbital angular momentum. Finally, to study the effect of different magnetic field topologies on the jet launching, we evolve the same configuration as our previous case (mass ratio $q=3:1$ and BH spin $\tilde{a}=0.75$) but now seed the NS with a pulsar-like magnetic field whose dipole magnetic moment is tilted $90^{\circ}$ with respect to the orbital angular momentum. Following our previous case, we model the initial stars as irrotational $\Gamma=2$ polytropes.

In agreement with our earlier simulations, where the star is seeded with a dipole magnetic field confined to the stellar interior, we find that the BHNS mergers listed above lead to a disk + BH remnant with a rest-mass ranging from $\sim 10^{-3} M_{\odot}(k/189.96\rm km^2)^{1/2}$ to $\sim 10^{-1}M_{\odot}(k/189.96\rm km^2)^{1/2}$, and dimensionless spin ranging from $\tilde{a}\sim 0.3 $ to $\sim 0.85$. Here $k$ is the polytropic gas constant defined as $k=P/\rho_0^\Gamma$, where $P$ and $\rho_0$ are the ${\it initial}$ cold pressure and the rest-mass density. The early evolution, tidal disruption and the merger phases are unaltered by the dynamically weak initial magnetic field. In the post-merger phase we find that, as in our earlier simulations, by around $\Delta t\sim 3500M \approx 88(M_{\rm NS}/1.4M_\odot)\rm ms$ after the GW peak emission a magnetically-driven jet is launched in the case where the initial spin of the BH companion is $\tilde{a}=0.5$. The lifetime of the jet [$\Delta t\sim 0.7(M_{\rm NS}/1.4M_\odot)\rm s$] and outgoing Poynting luminosity [$L_{jet}\sim 10^{52}\rm erg/s$] are consistent with observations of sGRBs, as well as with the Blandford-Znajek (BZ) mechanism for launching jets and their associated Poynting luminosities. In contrast, by the time we terminate our simulations, we do not find any indication of an outflow in the other cases; in the nonspinning case ($\tilde{a}=0$), where a persistent fall-back debris toward the BH is observed until the end of the simulation, the magnetic field above the BH poles is wound into a helical configuration, but the magnetic pressure gradients are still too weak to overcome the fall-back ram pressure, and thus it is expected that a longer simulation is required if a jet were to emerge. However, if the fall-back debris timescale is longer than the disk accretion timescale [$\Delta t\sim 0.36(M_{\rm NS}/1.4M_\odot)\rm s$], the jet launching in this case may be suppressed. By contrast, in the counter rotating BHNS configuration the star plunges quickly into the BH, leaving an "orphan" BH with a negligibly small accretion disk containing less than $1\%$ of the rest-mass of the NS. Similar behavior is observed in the BHNS configuration with mass ratio $q=5:1$. Finally, in the tilted magnetic field case, we do not find a coherent poloidal magnetic field component remaining after the BHNS merger, hence the key ingredient for jet launching is absent.

These preliminary results suggest that jet launching may strongly depend on a threshold value of (a) the initial black hole spin, which, along with the tidal-break up separation, controls the mass of the accretion disk, and (b) the tilt-angle of the magnetic field, which triggers the presence of a poloidal component of the magnetic field in the post-merger phase. So future multimessenger detections from BHNSs are most likely produced by binaries with a highly-spinning BH companion and small tilt-angle magnetic fields also.