Binary neutron star mergers: Effects of spin and post-merger dynamics

Spin can have significant effects on the electromagnetic transients accompanying binary neutron star mergers. The measurement of spin can provide important information about binary formation channels. In the absence of a strong neutron star spin prior, the degeneracy of spin with other parameters leads to significant uncertainties in their estimation, in particular limiting the power of gravitational waves to place tight constraints on the nuclear equation of state. Thus detailed studies of highly spinning neutron star mergers are essential to understand all aspects of multimessenger observation of such events. We perform a systematic investigation of the impact of neutron star spin—considering dimensionless spin values up to $a_{\mathrm{NS}}=0.33$—on the merger of equal mass, quasicircular binary neutron stars using fully general-relativistic simulations. We find that the peak frequency of the post-merger gravitational wave signal is only weakly influenced by the neutron star spin, with cases where the spin is aligned (antialigned) with the orbital angular momentum giving slightly lower (higher) values compared to the irrotational case. We find that the one-arm instability arises in a number of cases, with some dependence on spin. Spin has a pronounced impact on the mass, velocity, and angular distribution of the dynamical ejecta, and the mass of the disk that remains outside the merger remnant. We discuss the implications of these findings on anticipated electromagnetic signals, and on constraints that have been placed on the equation of state based on multimessenger observations of GW170817.

Figure 1

The GW signal ($\ell =m=2$ component of ${\psi }_4$ multiplied by the extraction radius $r$) from nonspinning mergers with various EOSs. The curves have been aligned in time and phase at peak. The HB EOS curve ends once a black hole (BH) forms; the other cases did not collapse to BHs during the time of their respective simulations.

Figure 2

The GW signal ($\ell =m=2$ component of ${\psi }_4$ multiplied by the extraction radius $r$) from mergers with the ENG EOS and various values of NS spin. The left panel shows the magnitude of ${\psi }_4$, while the right panel shows the real part of ${\psi }_4$ for select cases. The curves have been aligned in time and (for the right panel) phase at peak. None of these cases collapsed to BHs during the time of their respective simulations.

Figure 3

The characteristic strain as a function of frequency for the postmerger GW signal for irrotational cases with different EOSs (computed in a $\approx 20\mathrm{ms}$ window following the peak GW luminosity signal) as seen by an observer oriented face-on (left) or edge-on (right) with respect to the orbital plane. All $2\le \ell \le 6$ modes are used in the plot. The $m=1$, and $m=-1$ modes are those driving the peak at $\mathrm{f}\sim 1.6\mathrm{kHz}$ in the right panel. The case with the HB EOS collapses to a BH during this time.

Figure 4

The characteristic strain as a function of frequency for the postmerger GW signal for cases with the ENG EOS and various spins (computed in a $\approx 20\mathrm{ms}$ window following the peak GW luminosity signal) as seen by an observer oriented face-on (left) or edge-on (right) with respect to the orbital plane. All $2\le \ell \le 2$ modes are used in the plot. The $m=1$, and $m=-1$ modes are those driving the peak at $f\sim 1.6\mathrm{kHz}$ in the right panel.

Figure 5

The angular velocity versus cylindrical coordinate radius on the equator of the massive NS remnant for select cases with the ENG EOS. The $a_{\mathrm{NS}}=0.17$ case shown corresponds to the corotating initial data.

Figure 6

The magnitude of the $m=1$ and $m=2$ azimuthal density modes as a function of time for nonspinning cases with various EOSs (left) and for the ENG EOS with various values of NS spin (right). The curves for the HB EOS end at the time of BH formation; the curves for the other cases end when their respective simulations were stopped.

Figure 7

Left: The amount of rest mass outside a given coordinate radius from the center of mass for the post-merger remnant for mergers of nonspinning NSs with various EOSs. The solid curves show the total amount, while the points show just the unbound rest mass. Right: The amount of unbound rest mass binned by the velocity at infinity, with each bin $0.05c$ in size. The legend from the right panel applies to the left panel as well.

Figure 8

Same as Fig. 7, but for cases with the ENG EOS and various values of NS spin. The legend from the right panel applies to the left panel as well.

Figure 9

The rest-mass density distribution ($D≔{\rho }_0{u}^t\sqrt{-g}$) of the bound (inner region; purple-yellow color scale) and unbound matter (outer region; black-white color scale) $\sim 10\mathrm{ms}$ after merger. The columns show (left to right) slices in the $x=0$, $y=0$, and $z=0$ (equatorial) plane. The rows (top to bottom) show cases with $a_{\mathrm{NS}}=0$, 0.17 (CO), and 0.33. The plots show roughly 1800 km in each linear dimension.

Figure 10

Top: The GW signal ($\ell =m=2$ component of ${\psi }_4$ multiplied by the extraction radius $r$) from mergers with the ENG EOS and $a_{\mathrm{NS}}=0.17$ but different spin formalisms. The curves have been aligned in time and phase at peak. In particular, the CO case has been shifted ahead by 1.1 ms relative to the SP case. Bottom: The magnitude of the $m=1$ and $m=2$ azimuthal density modes as a function of time for the same two cases.

Figure 11

The GW amplitude (magnitude of $\ell =m=2$ component of ${\psi }_4$ multiplied by the extraction radius $r$) from mergers with the ENG EOS, with nonspinning NSs shown on the left, and the largest value of NS spin considered ($a_{\mathrm{NS}}=0.33$) shown on the right. Three different resolutions are plotted, and the curves have been aligned in time at peak amplitude. The phase error is shown in Fig. 12.

Figure 12

The difference in the GW phase (phase of $\ell =m=2$ component of ${\psi }_4$) across different resolutions from mergers with the ENG EOS and nonspinning NSs (left), and the largest value of NS spin considered ($a_{\mathrm{NS}}=0.33$; right). The differences have been scaled assuming second order convergence. Time is shown on the vertical axis with respect to where the peak of the GW signal occurs in the highest resolution case (in particular, the GWs have not been aligned at merger).

Figure 13

The norm of the generalized-harmonic constraint $C^a=\square x^a-H^a$ integrated in the equatorial plane for several different resolutions for the IR, ENG EOS case.

Figure 14

Same as Fig. 8, but just showing the case with the ENG EOS and no NS spin at different times post-merger. The legend from the right panel applies to the left panel as well.