Effects of spin on magnetized binary neutron star mergers and jet launching

Events GW170817 and GRB 170817A provide the best confirmation so far that compact binary mergers where at least one of the companions is a neutron star can be the progenitors of short gamma-ray bursts (sGRBs). An open question for GW170817 remains the values and impact of the initial neutron star spins. The initial spins could possibly affect the remnant black hole mass and spin, the remnant disk, and the formation and lifetime of a jet and its outgoing electromagnetic Poynting luminosity. Here we summarize our general relativistic magnetohydrodynamic simulations of spinning, neutron star binaries undergoing merger, and delayed collapse to a black hole. The binaries consist of two identical stars, modeled as $\mathrm{\Gamma }=2$ polytropes, in quasicircular orbit, each with spins ${\chi }_{\mathrm{NS}}=-0.053$, 0, 0.24, or 0.36. The stars are endowed initially with a dipolar magnetic field extending from the interior into the exterior, as in a radio pulsar. Following the merger, the redistribution of angular momentum by magnetic braking and magnetic turbulent viscosity in the hypermassive neutron star (HMNS) remnant, along with the loss of angular momentum due to gravitational radiation, induces the formation of a massive, nearly uniformly rotating inner core surrounded by a magnetized Keplerian disklike envelope. The HMNS eventually collapses to a black hole, with spin $a/M_{\mathrm{BH}}\simeq 0.78$ independent of the initial spin of the neutron stars, surrounded by a magnetized accretion disk. The larger the initial neutron star spin the heavier the disk. After $\mathrm{\Delta }t\sim 3000M-4000M\sim 45(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}-60({\mathrm{M}}_{\mathrm{NS}}/1.625{\mathrm{M}}_{\odot })\mathrm{ms}$ following merger, a mildly relativistic jet is launched. The lifetime of the jet [$\mathrm{\Delta }t\sim 100(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}-140(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}$] and its outgoing Poynting luminosity [$L_{\mathrm{EM}}\sim {10}^{51.5\pm 1}\mathrm{erg}/\mathrm{s}$] are consistent with typical sGRBs, as well as with the Blandford-Znajek mechanism for launching jets and their associated Poynting luminosities.

Figure 1

Maximum value of the rest mass ${\rho }_0(t)$ during the early inspiral, normalized by the initial maximum density ${\rho }_0(0)$, for the unmagnetized cases (see Table 1). In all cases, the NS oscillations are $\lesssim 1\%$, and they are more pronounced in the antialigned case (Hsm0.005 configuration).

Figure 2

Volume rendering of rest-mass density ${\rho }_0$, normalized to the initial maximum value ${\rho }_{0,\max }\simeq 10^{14.4}(1.625M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ (log scale), at selected times for our extreme unmagnetized cases: Hsp0.36 (top panels) and Hsm0.05 (bottom panels). Arrows indicate the direction of the spin. The BH apparent horizon in Hsm0.05 is displayed as a black sphere. Here $M=1.47\times {10}^{-2}(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}=4.43(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$.

Figure 3

Volume rendering of rest-mass density ${\rho }_0$, normalized to the initial maximum value ${\rho }_{0,\max }\simeq {10}^{14.4}(1.625M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$ (log scale), at selected times for magnetized cases (see Table 3): Msp0.36 (left column), Msp0.24 (middle column), and Msm0.05 (right column). See also Fig. 1 in [10]. Bottom panels highlight the system after an incipient jet is launched. Arrows indicate plasma velocities while white lines show the magnetic field structure. The BH apparent horizon is displayed as a black sphere (see bottom panels). Here $M=1.47\times {10}^{-2}(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}=4.43(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$.

Figure 4

GW strain $h_{+}^{22}$ (dominant mode) as functions of 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 3. The left panel displays the GW strain in the unmagnetized cases, while the right panel displays the magnetized cases. The dashed vertical line denotes the BH formation time.

Figure 5

Angular velocity profile of the HMNS in the equatorial plane at $\mathrm{\Delta }t=t-t_{\mathrm{HMNS}}$, with $t_{\mathrm{HMNS}}$ the HMNS formation time, and $P_c$ the central HMNS period at $t=t_{\mathrm{HMNS}}$ [see Eq. (2)] for our extreme cases in Table 3 (unmagnetized and magnetized cases are shown in top and bottom panels, respectively). The initial differential rotation profile is displayed by the red dashed curve, while the final profile is shown by the continuous black curve. The thick, blue dashed curve shows a Keplerian angular velocity. The arrow denotes the coordinate radius that contains $\sim 50\%$ of the rest mass of the HMNS (see Figs. 2 and 3). The inset displays the angular velocity in the inner layers of the HMNS.

Figure 6

Rest-mass fraction outside the BH apparent horizon versus time for all cases listed in Table 3. The coordinate time has been shifted to the BH formation time $t_{\mathrm{BH}}$.

Figure 7

Rest-mass accretion rate for all cases listed in Table 3 computed via Eq. (A11) in [88]. The coordinate time has been shifted to the BH formation time $t_{\mathrm{BH}}$.

Figure 8

Total magnetic energy $\mathcal{M}$ normalized by the ADM mass $M=5.36\times {10}^{54}(M_{\mathrm{NS}}/1.625M_{\odot })$ erg versus time for cases listed in Table 3. Dots indicate the NSNS merger time $t_{\mathrm{mer}}$. The coordinate time has been shifted to the BH formation time $t_{\mathrm{BH}}$.

Figure 9

Contours of the quality factor $Q={\lambda }_{\mathrm{MRI}}/dx$ on the equatorial plane (top panel), and rest-mass density, normalized to the initial maximum value ${\rho }_{0,\max }\simeq 10^{14.4}(1.625M_{\odot }/M_{\mathrm{NS}}{)}^2{\mathrm{g}/\mathrm{cm}}^3$, and ${\lambda }_{\mathrm{MRI}}$ (white line) on the meridional plane (bottom panel) at $t-t_{\mathrm{mer}}\sim 400M\sim 6(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}$ for case Msp0.36. We resolve the fastest growing MRI mode by $\gtrsim 10$ grid points over a large part of the HMNS. For the most part ${\lambda }_{\mathrm{MRI}}$ fits within the star. Other cases show similar behavior.

Figure 10

Volume rendering of the ratio $b^2/2{\rho }_0$ (log scale) at $t-t_{\mathrm{BH}}\approx 3400M\sim 50(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}$ for the Mirrot case, though similar behavior is observed in all magnetized cases. Magnetic field lines (white lines) are plotted inside regions where $b^2/2{\rho }_0\gtrsim {10}^{-2}$ (funnel boundary). Magnetically dominated regions ($b^2/2{\rho }_0\gtrsim 1$) extend to heights $\gtrsim 20M\sim 20r_{\mathrm{BH}}$ above the BH (black sphere). Here $r_{\mathrm{BH}}=2.2(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$.

Figure 11

Outgoing EM (Poynting) luminosity for $t\ge t_{\text{jet}}$ computed at a coordinate sphere of radius $r=120M\sim 530(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{km}$ for the magnetized cases listed in Table 3. The inset shows the rest-mass fraction of escaping matter during the last $\sim 2700M\sim 40(M_{\mathrm{NS}}/1.625M_{\odot })\mathrm{ms}$ before the termination of our simulations.