Magnetohydrodynamic simulations of binary neutron star mergers in general relativity: Effects of magnetic field orientation on jet launching

Binary neutron star mergers can be sources of gravitational waves coincident with electromagnetic counterpart emission across the spectrum. To solidify their role as multimessenger sources, we present fully 3D, general relativistic, magnetohydrodynamic simulations of highly spinning binary neutrons stars initially on quasicircular orbits that merge and undergo delayed collapse to a black hole. The binaries consist of two identical stars modeled as $\mathrm{\Gamma }=2$ polytropes with spin ${\chi }_{\mathrm{NS}}=0.36$ aligned along the direction of the total orbital angular momentum $L$. Each star is initially threaded by a dynamical unimportant interior dipole magnetic field. The field is extended into the exterior where a nearly force-free magnetosphere resembles that of a pulsar. The magnetic dipole moment $\mu$ is either aligned or perpendicular to $L$ and has the same initial magnitude for each orientation. For comparison, we also impose symmetry across the orbital plane in one case where $\mu$ in both stars is aligned along $L$. We find that the lifetime of the transient hypermassive neutron star remnant, the jet launching time, and the ejecta (which can give rise to a detectable kilonova) are very sensitive to the magnetic field orientation. By contrast, the physical properties of the black $\mathrm{hole}+\text{disk remnant}$, such as the mass and spin of the black hole, the accretion rate, and the electromagnetic (Poynting) luminosity, are roughly independent of the initial magnetic field orientation. In addition, we find imposing symmetry across the orbital plane does not play a significant role in the final outcome of the mergers. Our results suggest that, as in the black hole-neutron star merger scenario, an incipient jet emerges only when the seed magnetic field has a sufficiently large-scale poloidal component aligned to the initial orbital angular momentum. The lifetime [$\mathrm{\Delta }t\gtrsim 140(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}$] and Poynting luminosities [$L_{\mathrm{EM}}\simeq {10}^{52}\mathrm{erg}/\mathrm{s}$] of the jet, when it forms, are consistent with typical short gamma-ray bursts, as well as with the Blandford-Znajek mechanism for launching jets.

Figure 1

Volume rendering of rest-mass density ${\rho }_0$, normalized to the initial maximum value ${\rho }_0^{\max }=10^{14.78}(1.625M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ (log scale), at selected times for the Ali-Ali (Eq) case (left column) and the Ali-Ali case (right column). White lines represent the magnetic field lines, while arrows indicate plasma velocities. Bottom panels highlight the final configuration of the $\mathrm{BH}+\mathrm{disk}$ remnant after an incipient jet has been launched. Here $M=1.47\times {10}^{-2}(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}=4.4288(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$.

Figure 2

Same as Fig. 1 but for the Ali-Per case.

Figure 3

Volume rendering of rest-mass density ${\rho }_0$, normalized to the initial maximum value ${\rho }_0^{\max }=10^{14.78}(1.625M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ (log scale), at selected times for the Per-Per case. White lines represent the magnetic field lines. Bottom panels highlight the final configuration of the $\mathrm{BH}+\mathrm{disk}$ remnant.

Figure 4

GW amplitude $h_{+}^{22}$ (dominant mode) as function of the retarded time, extracted at $r_{\mathrm{ext}}\approx 100M\sim 443(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$ for all cases listed in Table 1. The vertical dashed line denotes the coordinate time at which the BH horizon appears for the first time. The inset highlights the wave train during the inspiral, merger and HMNS ringdown.

Figure 5

Evolution of the magnetic energy $\mathcal{M}$ for cases listed in Table 1. The coordinate time since merger is plotted. Dots mark the time at which the apparent horizon appears for the first time ($\mathrm{\Delta }{t}_{\mathrm{BH}}$). The inset displays the evolution of the maximum value of the poloidal magnetic field component. Similar behavior is found in the toroidal component.

Figure 6

Azimuthally averaged rotation profile of the transient HMNS for the Ali-Ali case (left panel) and the Per-Per case (right panel) in the orbital plane at $\mathrm{\Delta }t=t-t_{\mathrm{HMNS}}$ (see Table 1). Here $t_{\mathrm{HMNS}}$ is the HMNS formation time, and $P_c\simeq 50M\sim 0.7(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}$ is the central HMNS period at $t=t_{\mathrm{HMNS}}$. The red dashed line shows the initial differential rotation profile, while the continuous black curve displays the final profile. The blue dashed curve exhibits a Keplerian angular velocity profile. The arrow marks the coordinate radius containing $\sim 50\%$ of the total rest mass of the system. The inset highlights the rotation profile of the central core. Note that this rotation profile agrees with [68] who adopts the same EOS, but in general it depends on the EOS (see e.g. [69, 70]).

Figure 7

Evolution of the rest-mass fraction outside the apparent horizon $M_0(>\mathrm{AH})$ normalized to its initial maximum value $M_0=3.25M_{\odot }(k/k_{\mathrm{L}}{)}^{1/2}$ for all cases listed Table 1. The inset shows the accretion rate history. The coordinate time since BH formation is plotted.

Figure 8

Meridional cut of the 3D density profile of the $\mathrm{BH}+\mathrm{disk}$ remnant near the end of the simulations for all cases listed in Table 1. From top to bottom the cases are Ali-Ali (Eq), Ali-Ali, Ali-Per and Per-Per, respectively. The BH horizon is shown as a black sphere, while the yellow arrow indicates the spin direction. Here $M=1.47\times {10}^{-2}(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}=4.4288(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$.

Figure 9

Volume rendering of the ratio $b^2/2{\rho }_0$ (log scale) near the end of the simulations for the cases Ali-Ali (Eq) (left top panel), Ali-Ali (right top panel), Ali-Per (left bottom panel), and Per-Per (right bottom panel). Magnetic field lines, displayed as white lines, are plotted inside regions in which $b^2/2{\rho }_0\gtrsim {10}^{-2}$, our criterion for the funnel boundary. The BH horizon is shown as a black sphere. Here $M=4.4288(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$.

Figure 10

Outgoing EM (Poynting) luminosity driven by the incipient jet, and computed on a sphere of coordinate radius $r_{\mathrm{ext}}=120M\sim 532(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$ for cases listed in Table 1. The inset focus on the rest-mass fraction of escaping matter following NSNS merger.

Figure 11

Evolution of the maximum value of the rest-mass density ${\rho }_0$ (central density of the HMNS) normalized to its initial value ${\rho }_0^{\max }\simeq 10^{14.78}(1.625M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ for cases in Table 1. Dots mark the time at which the apparent horizon appears for the first time ($\mathrm{\Delta }{t}_{\mathrm{BH}}$). The coordinate time since merger is plotted.

Figure 12

Gravitational-wave power spectrum of the dominant mode $(l,m)=(2,2)$ at a source distance of 50 Mpc for all the full 3D cases listed in Table 1, along with the aLIGO noise curve. This curve corresponds to the ZERO_DET_HIGH_P configuration [86]. Dashed lines display the Newtonian prediction [87]. The vertical blue line marks the initial GW frequency.