Rethinking Resonance Detectability during Binary Neutron Star Inspiral: Accurate Mismatch Computations for Low-lying Dynamical Tides

We compute deviations from observed gravitational wave signals, where the amplitude of the signal is unchanged. As an example, we consider the detectability of low lying dynamical tides in binary neutron star or neutron star black hole mergers. Tidal forces can excite oscillatory modes of one or both of the stars in the binary when the orbital frequency of the binary system sweeps through the resonant mode frequency dissipating energy into the vibrational mode. The orbital energy loss to the vibrational mode extracts energy from the orbital motion, advancing the time to merger. The inspiral then continues with an excess phase and a time advance. Both will cause a mismatch when fitting to a system that has not gone through the resonance. To resolve this effect, we compute the mismatch for current and planned detectors using both a quasi-analytical approach that relies on the computation of moment integrals and an optimized version of the standard numerical match function. We conclude that detectability can occur for time advances of the order of 1 ms with advanced LVK detectors for an excess energy-flux that is a few percent of the gravitational wave emission. Our results contrast with previous work, which model this effect solely as a phase shift of the waveform or by using the difference in the number of cycles induced by the resonant behavior. We show that tidal resonance effects primarily cause a time advance of the merger, rather than a phase difference, and that the single-frequency approximation commonly used in the literature significantly overestimates the detectability of this effect.

💡 Research Summary

This paper presents a comprehensive study of how low‑frequency dynamical tides—specifically resonant excitations of neutron‑star normal modes—affect the gravitational‑wave (GW) signal from binary neutron‑star (BNS) and neutron‑star–black‑hole (NS‑BH) mergers. The authors argue that the dominant observable consequence of a tidal resonance is not a simple phase shift, as has been assumed in much of the previous literature, but a time advance: the orbital energy transferred to the resonant mode is lost from the binary, causing the coalescence to occur earlier than it would in the absence of the resonance. Because the GW amplitude remains essentially unchanged, the mismatch between a resonant waveform and a non‑resonant template is driven primarily by this shift in the merger time.

To quantify this effect, the authors develop two complementary approaches. First, they derive a quasi‑analytical expression for the match (overlap maximized over time and phase) by expanding the perturbed waveform’s phase to second order in a small parameter ε that measures the strength of the resonance. They introduce noise‑weighted moments I