Binary neutron star mergers and short gamma-ray bursts: Effects of magnetic field orientation, equation of state, and mass ratio

We present fully general-relativistic magnetohydrodynamic simulations of the merger of binary neutron star (BNS) systems. We consider BNSs producing a hypermassive neutron star (HMNS) that collapses to a spinning black hole (BH) surrounded by a magnetized accretion disk in a few tens of ms. We investigate whether such systems may launch relativistic jets and hence power short gamma-ray bursts. We study the effects of different equations of state (EOSs), different mass ratios, and different magnetic field orientations. For all cases, we present a detailed investigation of the matter dynamics and of the magnetic field evolution, with particular attention to its global structure and possible emission of relativistic jets. The main result of this work is that we observe the formation of an organized magnetic field structure. This happens independently of EOS, mass ratio, and initial magnetic field orientation. We also show that those models that produce a longer-lived HMNS lead to a stronger magnetic field before collapse to a BH. Such larger fields make it possible, for at least one of our models, to resolve the magnetorotational instability and hence further amplify the magnetic field in the disk. However, by the end of our simulations, we do not (yet) observe a magnetically dominated funnel nor a relativistic outflow. With respect to the recent simulations of Ruiz et al. [Astrophys. J. 824, L6 (2016)], we evolve models with lower and more plausible initial magnetic field strengths and (for computational reasons) we do not evolve the accretion disk for the long time scales that seem to be required in order to see a relativistic outflow. Since all our models produce a similar ordered magnetic field structure aligned with the BH spin axis, we expect that the results found by Ruiz et al. (who only considered an equal-mass system with an ideal fluid EOS) should be general and—at least from a qualitative point of view—independent of the mass ratio, magnetic field orientation, and EOS.

Figure 1

Rest-mass density evolution on the equatorial plane for models IF_q10 (top) and IF_q08 (bottom). The horizon is marked with a red circle, with the exception of the top right panel which shows the excised region (black) instead.

Figure 2

Rest-mass density evolution on the meridional plane for models IF_q10 (top) and IF_q08 (bottom). Note the lower right panel constitutes an off-center cut because of the BH drift.

Figure 3

Comparison of the total magnetic energy between the models IF_q10_UU, IF_q10_DD, and IF_q10_UD. The yellow vertical line marks the merger time and the circles show the time of BH formation for each model.

Figure 4

Comparison of the maximum values of the magnetic field strength between the models IF_q10_UU, IF_q10_DD, and IF_q10_UD. The yellow vertical line marks the merger time and the circles show the time of BH formation for each model.

Figure 5

Comparison of the mean values of the magnetic field strength between the models IF_q10_UU, IF_q10_DD, and IF_q10_UD. The yellow vertical line marks the merger time and the circles show the time of BH formation for each model.

Figure 6

Comparison of the mean values of the magnetic field strength between the models IF_q10_UU, IF_q10_DD, and IF_q10_UD, including mean values of toroidal and poloidal field components. The yellow vertical lines mark the merger time and the black vertical lines mark the time of BH formation.

Figure 7

Evolution of the magnetic field structure for model IF_q10_UU. Top left: Inspiral phase, showing the magnetic field, as well as the lower half of the NS surfaces. Top center: Magnetic field 2 ms after merger together with the isodensity surface for $5\times 10^{12}{\mathrm{g}/\mathrm{cm}}^3$, drawn as a semitransparent red surface. Top right: Magnetic field structure 12 ms after merger. Bottom left: Magnetic field 22 ms after merger, together with two isosurfaces of density $10^8$ (yellow) and $10^{10}{\mathrm{g}/\mathrm{cm}}^3$ (cyan), cut off for $y<0$. Bottom right: The same at 35 ms after merger. The color of the field lines gives a rough indication of the field strength (see color bar), but for quantitative results compare Figs. 8, 10, and 15. The procedure for selecting which field lines to plot is described in the Appendix.

Figure 8

Distribution of the magnetic field with respect to the $\theta$ coordinate, for model IF_q10_UU at various times after merger. Top: Histogram of magnetic energy employing bins regularly spaced in $\cos (\theta )$, where $\theta =0$ is the $z$ axis and $\theta =90°$ is the equator. The plot is normalized to the total magnetic energy 35 ms after merger. Bottom: Field strength $B_{90}$ defined as the value for which 90% of the magnetic energy [inside a given $\cos (\theta )$ bin] is contained in regions with field strength below $B_{90}$.

Figure 9

Magnetic field structure 35 ms after the merger, comparing models IF_q10_UU, IF_q10_UD, and IF_q10_DD. The black bars provide a length scale of 20 km. The coloring of the field lines indicates the magnetic field strength [${\log }_{10}(B[\mathrm{G}])$, with the same color scale for all models] along the lines. However, for quantitative results see Fig. 10.

Figure 10

Like Fig. 8, but comparing models IF_q10_UU, IF_q10_UD, and IF_q10_DD 35 ms after the merger. The energy distribution (top panel) is normalized to the total energy for model IF_q10_UU.

Figure 11

Comparison of total magnetic energy between models IF_q10_UU, IF_q08_UU, H4_q10_UU, and H4_q08_UU. The yellow vertical line marks the merger time and the circles show the time of BH formation for each model.

Figure 12

Comparison of the maximum values of the magnetic field strength between models IF_q10_UU, IF_q08_UU, H4_q10_UU, and H4_q08_UU. The yellow vertical line marks the merger time and the circles show the time of BH formation for each model.

Figure 13

Comparison of the mean values of the magnetic field strength between models IF_q10_UU, IF_q08_UU, H4_q10_UU, and H4_q08_UU. The yellow vertical line marks the merger time and the circles show the time of BH formation for each model.

Figure 14

Comparison of the mean values of the total, poloidal, and toroidal magnetic field strengths between models IF_q10_UU, IF_q08_UU, H4_q10_UU, and H4_q08_UU. The yellow vertical lines mark the merger time and the black vertical lines mark the time of BH formation.

Figure 15

Like Fig. 8, but comparing models IF_q10_UU, IF_q08, H4_q10, and H4_q08 around 32 ms after the merger. Also, each model is normalized separately in the lower panel, and we employ coordinates where the BH is located at the origin to account for the BH drift exhibited by the unequal mass models.

Figure 16

Magnetic field structure around 32 ms after the merger, comparing models IF_q10_UU, IF_q08, H4_q10, and H4_q08. The black bars provide a length scale of 20 km. The coloring of the field lines indicates the magnetic field strength [${\log }_{10}(B[\mathrm{G}])$, with the same color scale for all models] along the lines. However, for quantitative results see Fig. 15.

Figure 17

Rest-mass density evolution on the equatorial plane for models H4_q10 (top) and H4_q08 (bottom).

Figure 18

Rest-mass density evolution on the meridional plane for models H4_q10 (top) and H4_q08 (bottom).

Figure 19

Evolution of the maximum rest-mass density (upper panel) and magnetic energy (lower panel) for the equal-mass ideal-fluid model IF_q10_UU at different resolutions, with a finest grid spacing of $dx\approx 177$, 222, 277 m for the high, medium, and low resolutions, respectively. The evolution of the magnetic energy is also shown for the equal-mass H4 model H4_q10 with two different resolutions: $dx\approx 150\mathrm{m}$ (HR) and 186 m (MR).

Figure 20

Meridional view of ${\lambda }_{\mathrm{MRI}}/dx$ for the highest-resolution simulation ($dx\approx 177\mathrm{m}$) of model IF_q10_UU, towards the end of the simulation ($t=51.2\mathrm{ms}$).

Figure 21

Same as Fig. 20 for model H4_q08 at resolution $dx\approx 186\mathrm{m}$ and at $t=52.5\mathrm{ms}$.

Figure 22

Meridional view of the BH and accretion torus for the equal- and unequal-mass H4 simulations. The panels refer to 26.5 ms after BH formation and show in the top half ($z>0$) the fluid velocity along the $z$ axis and in the bottom half ($z<0$) the magnetic-to-fluid pressure ratio on a log scale.

Figure 23

GW signal for models (from left to right) IF_q10, IF_q08, H4_q10, and H4_q08. The top panels show the strain at a nominal distance of 100 Mpc. The lower panels show the instantaneous frequency.

Figure 24

GW signal for models (from left to right) IF_q10_UU, IF_q10_UD, and IF_q10_DD. The top panels show the strain at a nominal distance of 100 Mpc. The lower panels show the instantaneous frequency.

Figure 25

GW spectra (solid lines) for the four models of Fig. 23 in comparison to the sensitivity curves of GW detectors (dashed lines). The strain is given at a distance of 100 Mpc.

Figure 26

GW spectra (solid lines) for the three models of Fig. 24 in comparison to the sensitivity curves of GW detectors (dashed lines). The strain is given at a distance of 100 Mpc.