Analytical models for neutron star dynamical tides valid beyond mode resonance*

A rapidly spinning neutron star (NS) in a coalescing binary can experience a strong tidal deformation due to the dynamical tide. Previous analytical calculations accurately capture this effect up to the point just before the f-mode of the NS becomes resonant. However, their accuracy diminishes when extrapolated to frequencies beyond mode resonance. Here we introduce a new analytical solution for the dynamical tide that maintains accuracy throughout the entire evolution even beyond mode resonance. Our solution decomposes the tide into a resummed equilibrium component that is phase-coherent with the orbit, and a dynamical component that is excited locally around mode resonance. Both terms remain finite throughout the evolution, aiding their implementation in waveform models. On the tidal backreaction on the orbit, we emphasize the significance of the tidal torque which originates from the imaginary part of the Love number and is not captured by the commonly adopted effective Love number. However, the torque dominates the tidal phase shift near mode resonance. Moreover, we quantify the gravitational wave (GW) radiation resulting from the interaction of the NS and orbital quadrupoles beyond the adiabatic limit, as well as the orbital eccentricity excited by the dynamical tide. The new model therefore improves our understanding of tides in the strongly dynamical regime and will assist the development of the next generations of tidal waveforms for GW observations.