First 100 ms of a long-lived magnetized neutron star formed in a binary neutron star merger

The recent multimessenger observation of the short gamma-ray burst (SGRB) GRB 170817A together with the gravitational wave (GW) event GW170817 provides evidence for the long-standing hypothesis associating SGRBs with binary neutron star (BNS) mergers. The nature of the remnant object powering the SGRB, which could have been either an accreting black hole (BH) or a long-lived magnetized neutron star (NS), is, however, still uncertain. General relativistic magnetohydrodynamic (GRMHD) simulations of the merger process represent a powerful tool to unravel the jet launching mechanism, but so far most simulations focused the attention on a BH as the central engine, while the long-lived NS scenario remains poorly investigated. Here, we explore the latter by performing a GRMHD BNS merger simulation extending up to $\sim 100\mathrm{ms}$ after merger, much longer than any previous simulation of this kind. This allows us to (i) study the emerging structure and amplification of the magnetic field and observe a clear saturation at magnetic energy $E_{\mathrm{mag}}\sim {10}^{51}\mathrm{erg}$, (ii) follow the magnetically supported expansion of the outer layers of the remnant NS and its evolution into an ellipsoidal shape without any surrounding torus, and (iii) monitor density, magnetization, and velocity along the axis, observing no signs of jet formation. We also argue that the conditions at the end of the simulation disfavor later jet formation on subsecond timescales if no BH is formed. Furthermore, we examine the rotation profile of the remnant, the conversion of rotational energy associated with differential rotation, the overall energy budget of the system, and the evolution of the GW frequency spectrum. Finally, we perform an additional simulation where we induce the collapse to a $\mathrm{BH}\sim 70\mathrm{ms}$ after merger, in order to gain insights on the prospects for massive accretion tori in case of a late collapse. We find that a mass around $\sim 0.1M_{\odot }$ remains outside the horizon, which has the potential to power a SGRB via the Blandford-Znajek mechanism when accreted.

Figure 1

Rest-mass density evolution snapshots in the meridional (top panels) and equatorial (bottom panels) planes. The yellow contours indicate unbound matter ($u_t<-1$). Here $t=0$ corresponds to the merger time.

Figure 2

Top: Rest-mass density along the orbital axis averaged in the distance ranges 30–50 km, 150–200 km, and 400–500 km (continuous, dashed, and dot-dashed lines). The horizontal line marks the density of the artificial atmosphere. Bottom: Rest-mass density along the orbital axis averaged in the distance range 30–50 km for the present simulation with and without collapse (“B1e16 BH” and “B1e16”) and for the lower and zero magnetic field models in [27] (“B3e15” and “B0”).

Figure 3

Left: Large scale meridional view of the rest-mass density toward the end of the simulation. Right: Radial velocity of the outflowing material (positive values indicate motion directed outwards).

Figure 4

Meridional view of rest-mass density for the noncollapsing (top) and collapsing (bottom) cases. The filled region in red indicates the black hole horizon.

Figure 5

Meridional view of the relative difference in rest-mass density between the noncollapsing and collapsing cases.

Figure 6

Evolution of magnetic energy (top) and maximum magnetic field strength (bottom) for the present simulation with and without collapse (‘B1e16 BH’ and ‘B1e16’) and for the lower magnetic field model in [27] (‘B3e15’). Vertical line marks the time of merger. The top panel shows also the magnetic energy of model ‘B1e16’ rescaled to match the initial value of model ‘B3e15’.

Figure 7

Meridional view of the number of grid points covering ${\lambda }_{\mathrm{MRI}}$ (see text) 10 and 30 ms after merger. Solid black line marks the transition from the central finest refinement level and the second-finest one, where the latter has a factor of 2 larger grid spacing $dx$.

Figure 8

Magnetic field structure 20, 60, and 93 ms after merger. To give a scale reference, we added a (cyan) sphere of 10 km radius placed at the remnant center of mass. Field line colors indicate the magnetic field strength.

Figure 9

Large scale meridional view of the poloidal magnetic field strength (top) and the toroidal-to-poloidal field strength ratio (bottom). To help visualization, the latter is set to zero where the rest-mass density is close to the artificial floor value ($<1.5\times {\rho }^{*}$).

Figure 10

Same as Fig. 8 at a larger spatial scale. The vertical bar corresponds to 100 km.

Figure 11

Large scale meridional view of the magnetic-to-fluid pressure ratio (see text).

Figure 12

Rotational energy evolution (dots) along with a linear fit (continuous line). Merger time is $t=0$.

Figure 13

Small scale meridional view of the rest-mass density at 10 and 72 ms after merger, in simulation coordinates. In order to remove contributions from oscillations, we show the average over 4 ms around the given times. The contours correspond to isodensity surfaces that contain the fiducial remnant baryon mass (blue; see text), 93% of the total baryon mass (red), and 98% of the total baryon mass (yellow, only visible in top panel).

Figure 14

Top: Evolution of the rotation profile in the equatorial plane. The curves represent the rotation rate averaged in the $\varphi$ direction and over 2 ms in time versus proper circumferential radius, at different times (values relative to merger time). For comparison, we show the rotation rate and circumferential radius of the uniformly rotating fiducial model (see text), the uniformly rotating sequence of constant baryon mass (blue line), and the mass shedding sequence with baryonic masses between fiducial remnant mass and total binary mass (red line). Bottom: Comparison with the lower and zero magnetic field cases in [27] at 20 and 40 ms after merger. The field strengths in the legend refer to the initial maximum field strength of each model.

Figure 15

Meridional view of the specific angular momentum with respect to the oribital (or remnant spin) axis, 72 ms after merger. The value is given in units of the specific angular momentum of a test particle on the innermost stable circular orbit around the black hole formed in the collapsing case ($j_{\mathrm{ISCO}}$). The black contour corresponds to $j=j_{\mathrm{ISCO}}$.

Figure 16

Top: GW strain $l=m=2$ multipole coefficient (real part). The strain after $t=30\mathrm{ms}$ is magnified by a factor of 40. Bottom: The red curve shows the phase velocity of the GW strain. The green curves show twice the central (dotted line) and twice the maximum rotation rates (dashed line). The color plot shows a spectrogram of the $m=2$ component of the density perturbation in the equatorial plane averaged in the whole remnant. The scale is logarithmic, spans 5 orders of magnitude, and the amplitude after $t=30\mathrm{ms}$ is scaled by a factor of 1000. All phase velocities are smooth averages over 1 ms. Times are with respect to merger time (and using retarded time for the GW signal). Note the oscillation at the end of the simulation is likely an artifact.