Effects of magnetic field topology in black hole-neutron star mergers: Long-term simulations

We report long-term simulations of black hole-neutron star binary mergers where the neutron star possesses an asymmetric magnetic field dipole. Focusing on the scenario where the neutron star is tidally disrupted by the black hole, we track the evolution of the binary up to $\approx 100\mathrm{ms}$ after the merger. We uncover more than one episode of thermally driven winds being launched along a funnel wall in all these cases beginning from $\approx 25\mathrm{ms}$ after the merger. On the other hand, we are unable to conclude presently whether the amount of ejected mass increases with the degree of asymmetry. A large-scale magnetic field configuration in the poloidal direction is formed along the funnel wall accompanied by the generation of a large Poynting flux. The magnetic field in the accretion disk around the black hole remnant is amplified by both magnetic winding and the nonaxisymmetric magnetorotational instability (MRI). The MRI growth is estimated to be in the ideal magnetohydrodynamics (MHD) regime and thus would be free from significant effects induced by potential neutrino radiation. However, the asymmetry in the magnetic field leads to increased turbulence, which causes the vertical magnetic field in the accretion disk to grow largely in a nonlinear manner.

Figure 1

Comparison of the initial magnetic field configuration on the equatorial plane between (a) the Asym60 case and (b) the Sym case.

Figure 2

Comparison of the initial magnetic field configuration on the meridional plane between (a) the Asym60 case and (b) the Sym case.

Figure 3

The growth of (a) the toroidal field and (b) the vertical field, both measured in the fluid frame, for all cases. The dashed lines demarcate the range where the growth is fitted with an exponential function of the form $\exp (a(t-t_{\mathrm{MRI}}))$, where $a$ is the growth rate, and $t_{\mathrm{MRI}}$ is the time when the MRI is triggered. The pink arrow labels the range for the Sym case, blue for Asym60, and red for Asym75.

Figure 4

The close-up of the exponential growth phase of the toroidal field (top panel) and the vertical field (bottom panel), both measured in the fluid frame, for all cases.

Figure 5

Snapshots of $Q_{\varphi }$ (cf. Eq. (4) on the meridional plane for (a) Sym and (b) Asym60 at $t-t_{\text{merge}}\approx 18\mathrm{ms}$.

Figure 6

Snapshots of $Q_z$ (cf. Eq. (4) on the meridional plane for (a) Sym and (b) Asym60 at $t-t_{\text{merge}}\approx 18\mathrm{ms}$.

Figure 7

Snapshots of (a) $Q_{\varphi }$ and (b) $Q_z$ (cf. Eq. (4) on the meridional plane for Asym60 at $t-t_{\text{merge}}\approx 23.5\mathrm{ms}$.

Figure 8

Percent differences between growth rates obtained from simulation, with predictions by linear theory of the growth rates of the toroidal and vertical fields on the equatorial plane. The percent differences shown are averages obtained from points at a radius, $R$, from the center of the system, whereas the error bars are standard deviations from the average.

Figure 9

(a) The comparison between the neutrino mean free path and the viscous MRI wavelength and (b) the damping rate, $\mathrm{\Gamma }$, as measured radially throughout the extent of the accretion disk bulk for the Asym60 case. The dashed lines in the figures indicate the location of the BH apparent horizon.

Figure 10

Evolution of the unbound mass, $M_{\mathrm{unb}}$ for all cases. For the unbound mass at $t-t_{\text{merge}}\lesssim 25\mathrm{ms}$ for Sym, we refer the reader to Fig. 2(a) of Ref. [23], where the system with a resolution of $\mathrm{\Delta }x=270\mathrm{m}$ is exactly the same as the Sym case in the current paper.

Figure 11

Profiles of (a) rest-mass density and velocity, and (b) the plasma $\beta$ on the meridional plane for Asym60 at $t-t_{\text{merge}}\approx 72\mathrm{ms}$.

Figure 12

The Poynting flux measured at $\approx 960\mathrm{km}$ from the center of the system, as a function of time for Asym60 and Asym75.

Figure 13

Profile of the thermal component of the specific internal energy, ${\epsilon }_{th}$, on the meridional plane for Asym60 at $t-t_{\text{merge}}\approx 72\mathrm{ms}$.

Figure 14

The ratio of the global vertical magnetic energy over the plasma kinetic energy measured as a function of time for all cases. At $t-t_{\text{merge}}\lesssim 25\mathrm{ms}$ for Sym, we refer the reader to the $\mathrm{\Delta }x=270\mathrm{m}$ case in Fig. 2(d) of Ref. [23], which is exactly the same system as Sym. Although the latter shows the ratio of the global magnetic energy over the plasma internal energy instead of over the kinetic energy, the exponential increase at $t-t_{\text{merge}}\lesssim 25\mathrm{ms}$ is expected to be similar across these two quantities.

Figure 15

Close-up of the magnetic vector field on the meridional plane in the disk region around the BH, for Asym60 at $t-t_{\text{merge}}\approx 72\mathrm{ms}$. Color coding labels the magnetic field intensity, given as $\sqrt{|b^2|}$.

Figure 16

Mean amplitude of the dominant mode in the kinetic energy spectrum measured as a function of time for the Sym and Asym60 cases.

Figure 17

Comparison of the mean specific kinetic energy spectra between Sym and Asym60 at $t-t_{\text{merge}}\approx 30\mathrm{ms}$.