Tidal Resonance in Binary Neutron Star Inspirals: A High-Precision Study in Numerical Relativity

Abstract

We investigate the tidal resonance of the fundamental ($f$-)mode in spinning neutron stars, robustly tracing the onset of the excitation to its saturation, using numerical relativity for the first time. We performed long-term ($\approx 15$~orbits) fully relativistic simulations of a merger of two highly and retrogradely spinning neutron stars. The resonance window of the $f$-mode is extended by self-interaction, and the nonlinear resonance continues up to the final plunging phase. We observe that the quasi-circular orbit is maintained throughout since the dissipation of orbit motion due to the resonance is coherent with that due to gravitational waves. The $f$-mode resonance causes a variation in the stellar spin of $\gtrsim 6.3\%$ in the linear regime and much more as $\sim 33\%$ during the later nonlinear regime. At the merger, a phase shift of $\lesssim 40$~radians is rendered in the gravitational waveform as a consequence of the angular momentum and energy transfers into the neutron star oscillations.

5 pages, 4 figures + supplemental material. To appear in Physical Review Letters