Convective Excitation of Inertial Modes in Binary Neutron Star Mergers

We present the first very long-term simulations (extending up to $\sim 140\mathrm{ms}$ after merger) of binary neutron star mergers with piecewise polytropic equations of state and in full general relativity. Our simulations reveal that, at a time of 30–50 ms after merger, parts of the star become convectively unstable, which triggers the excitation of inertial modes. The excited inertial modes are sustained up to several tens of milliseconds and are potentially observable by the planned third-generation gravitational-wave detectors at frequencies of a few kilohertz. Since inertial modes depend on the rotation rate of the star and they are triggered by a convective instability in the postmerger remnant, their detection in gravitational waves will provide a unique opportunity to probe the rotational and thermal state of the merger remnant. In addition, our findings have implications for the long-term evolution and stability of binary neutron star remnants.

Figure 1

Top panels: Time-frequency spectrograms of the $h_{22}$ component of the GW signals for both EOS. The thick gray lines indicate the frequency of the active spectral mode responsible for the GW emission. Colors indicate the relative intensity of the spectral density (darker areas correspond to higher intensity). Bottom panels: Mode amplitudes (in arbitrary units).

Figure 2

GW spectrum for a BNS merger at 50 Mpc at the optimal orientation. It is shown for the entire GW signal (dashed lines) and for a restricted time window (see the main text) where inertial modes are active (solid lines). The design sensitivities of Advanced Virgo [61], Advanced LIGO [62], Einstein Telescope [58], and Cosmic Explorer [57] are shown for reference.

Figure 3

Left and center panels: Density eigenfunctions in the equatorial plane for particular modes at different times (relative to the merger time), for the two models considered. Right panel: The corresponding eigenfunctions in the vertical plane for the SLy model. The black lines are isocontours of the rest-mass density with values (for decreasing radii) $1.5\times {10}^{13}$, $8\times {10}^{13}$, $3\times {10}^{14}$, and $8\times {10}^{14}(\mathrm{g}/{\mathrm{cm}}^3)$.

Figure 4

Snapshots of $A_r$ in the equatorial plane for the SLy model at different times relative to the merger time. Convectively unstable regions are shown with a dark color.