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Gravitomagnetic tidal resonance in neutron-star binary inspirals

A compact binary system implicating at least one rotating neutron star undergoes gravitomagnetic tidal resonances as it inspirals toward its final merger. These have a dynamical impact on the phasing of the emitted gravitational waves. The resonances are produced by the inertial modes of vibration of the rotating star. Four distinct modes are involved, and the resonances occur within the frequency band of interferometric gravitational-wave detectors when the star spins at a frequency that lies within this band. The resonances are driven by the gravitomagnetic tidal field created by the companion star; this is described by a post-Newtonian vector potential, which is produced by the mass currents associated with the orbital motion. These resonances were identified previously by Flanagan and Racine [Phys. Rev. D 75, 044001 (2007)], but these authors accounted only for the response of a single mode, the r-mode, a special case of inertial modes. All four relevant modes are included in the analysis presented in this paper. The total accumulated gravitational-wave phase shift is shown to range from approximately $10^{-2}$ radians when the spin and orbital angular momenta are aligned, to approximately $10^{-1}$ radians when they are anti-aligned. Such phase shifts will become measurable in the coming decades with the deployment of the next generation of gravitational-wave detectors (Cosmic Explorer, Einstein Telescope); they might even come to light within this decade, thanks to planned improvements in the current detectors. With good constraints on the binary masses and spins gathered from the inspiral waveform, the phase shifts deliver information regarding the internal structure of the rotating neutron star, and therefore on the equation of state of nuclear matter.