Resonance locking of g-modes in merging neutron star binaries

A neutron star in a binary system deforms due to the companion's tidal gravitational field. The deformation is characterized by the excitation of oscillation normal modes that evolve through the inspiral. Although the modes' evolution is typically modeled as the star's linear response to the companion's time-evolving tidal potential, it also can receive nonlinear driving since the equations of hydrodynamics and the tidal forcing have nonlinear terms. We present the effect of the anharmonicity of the low-frequency response of neutron stars, characterized by gravity (g-) modes, arising from the hydrodynamic nonlinearities. The anharmonicity is dominantly generated by the mutual coupling of the four lowest-order (n=1, l=|m|=2) g-modes, and allows them to stay locked in a resonant state that oscillates phase-coherently with the orbit throughout the inspiral. As a result, the g-modes grow to larger amplitudes than the linear response suggests. Furthermore, this leads to a radian-level phase correction to the frequency-domain GW signal of at a GW frequency of 1.05 kHz. This effect is part of the truly dynamical tide, in the sense that the amplitude depends not just on the binary's instantaneous frequency but the entire history of the inspiral.