Effective-one-body model for coalescing binary neutron stars: Incorporating tidal spin and enhanced radiation from dynamical tides

Tidal interaction in a coalescing binary neutron star (BNS) or neutron star-black hole (NSBH) system contains precious information about physics both at extreme density and in the highly relativistic regime. In the late inspiral stage, where the tidal effects are the strongest, finite-frequency or even dynamical corrections to the tidal response become significant. Many previous analyses model the finite-frequency correction through the effective Love number approach, which only accounts for the correction in the radial interaction but ignores the tidal torque. The torque exists in reality because the tidal bulge lags behind the companion in an orbit continuously shrinking due to gravitational wave (GW) radiation. The torque further drives a tidal spin whose dimensionless value can reach 0.03-0.4 depending on how rapidly the background star rotates. We present a relativistic, effective-one-body (EOB) waveform model for BNSs and NSBHs that incorporates the tidal spin, particularly its impact on the back reaction to the orbit due to the (largely Newtonian) torque and the relativistic orbital hang-up from the tidal spin-orbit interaction. Beyond the conservative dynamics specified by the EOB Hamiltonian, we also derive the corrections to the dissipative GW radiation due to finite-frequency corrections to the tidal response to the first post-Newtonian order. Depending on the star's background spin, the phase error in the time-domain waveform from ignoring the tidal spin ranges from 0.3 to 4 radians at the waveform's peak amplitude. Notably, the difference in the waveforms with and without the tidal spin remarkably resembles the difference between previous effective Love number models and numerical relativity, underscoring the significance of tidal spin in the construction of faithful models.