One-armed spiral instability in neutron star mergers and its detectability in gravitational waves

We study the development and saturation of the $m=1$ one-armed spiral instability in remnants of binary neutron star mergers by means of high-resolution long-term numerical relativity simulations. Our results suggest that this instability is a generic outcome of neutron star mergers in astrophysically relevant configurations, including both “stiff” and “soft” nuclear equations of state. We find that, once seeded at merger, the $m=1$ mode saturates within $\sim 10\mathrm{ms}$ and persists over secular time scales. Gravitational waves emitted by the $m=1$ instability have a peak frequency around 1–2 kHz and, if detected, they could be used to constrain the equation of state of neutron stars. We construct hybrid waveforms spanning the entire Advanced LIGO band by combining our high-resolution numerical data with state-of-the-art effective-one-body waveforms including tidal effects. We use the complete hybrid waveforms to study the detectability of the one-armed spiral instability for both Advanced LIGO and the Einstein Telescope. We conclude that the one-armed spiral instability is not an efficient gravitational wave emitter. Even under very optimistic assumptions, Advanced LIGO will only be able to detect the one-armed instability up to $\sim 3\mathrm{Mpc}$, which corresponds to an event rate of ${10}^{-7}{\mathrm{yr}}^{-1}$ to ${10}^{-4}{\mathrm{yr}}^{-1}$. Third-generation detectors or better will likely be required to observe the one-armed instability.

Figure 1

Normalized amplitudes of density modes on the equatorial plane. The symmetry-breaking odd-$m$ modes start to grow exponentially at the time the NSs enter into contact and saturate within few milliseconds.

Figure 2

Color-coded rest-mass density in the orbital plane for our highest-resolution MS1b simulation at representative times after merger ($t_0$). In the upper panels: Merger and development of the $m=1$ instability. In the bottom panels: Roughly half a cycle of the saturated spiral mode. The 180° rotational symmetry of the system is broken by hydrodynamic instabilities originating at the Kelvin-Helmholtz-unstable shear layer between the two stars shortly after merger. This causes the spiral mode to grow. Animations of the density in the orbital plane for both MS1b and SLy binaries are available as Supplemental Material [60].

Figure 3

GW luminosity of the $\ell =2$, $m=2$ and $\ell =2$, $m=1$ modes for all simulations as a function of time from merger ($t-t_0$). The data are multiplied by a factor of 2 to account for the symmetry between positive and negative $m$. A contribution from the $m=1$ mode is present in all simulations, especially at high resolution. GWs from the spiral mode are subdominant during most of the evolution, but show negligible damping.

Figure 4

Spectrum of the effective GW signal seen edge-on from a distance of 10 Mpc. We show the spectrum of the hybrid waveforms constructed from the highest-resolution data and the noise curves of Advanced LIGO and the Einstein Telescope (ET). The $\ell =2$, $m=1$ spectrum is mostly concentrated in a narrow maximum located at half of the frequency of the $\ell =2$, $m=2$ peak.