Gravitomagnetic tidal resonance in neutron-star binary inspirals
Eric Poisson
Abstract
A compact binary system implicating at least one rotating neutron star undergoes a sequence of four gravitomagnetic tidal resonances as it inspirals toward its final merger. These resonances have a dynamical impact on the binary's orbital motion, and thus on the phasing of the emitted gravitational waves. The resonances are produced by the inertial modes of vibration of the rotating star, and they occur when the orbital frequency becomes momentarily equal to a mode eigenfrequency. Four distinct modes are involved, and their eigenfrequencies are equal, up to a numerical factor of order unity, to the star's rotational angular velocity. 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 phenomenon is therefore of relevance to LIGO/Virgo for rotation rates comparable to 100 Hz. The resonances are driven by the gravitomagnetic tidal field created by the companion star; this is described by a post-Newtonian vector potential (the time-space components of the metric tensor), which is produced by the mass currents associated with the orbital motion. The gravitomagnetic tidal 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 inertial modes (including the $r$-mode) are included in the analysis presented in this paper. The total accumulated gravitational-wave phase shift caused by the gravitomagnetic tidal resonances is shown to range from approximately ${10}^{\ensuremath{-}2}$ radians when the spin and orbital angular momenta are aligned to approximately ${10}^{\ensuremath{-}1}$ radians when the angular momenta are antialigned. Such phase shifts are small, but they 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 (LIGO $\mathrm{A}+$). With good constraints on the binary masses and spins gathered from the inspiral waveform, the phase shifts incurred during the gravitomagnetic tidal resonances deliver information regarding the internal structure of the rotating neutron star, and therefore on the equation of state of nuclear matter at high densities.