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

TL;DR

This work tackles the detectability of tidal resonances in binary neutron-star inspirals by comparing resonant and non-resonant waveforms through matched-filter mismatches. It develops two complementary approaches: a quasi-analytical quadratic (moment) approximation and an optimized numerical match, both accounting for a sharp, delta-function-like energy transfer to NS modes. The key finding is that resonances primarily induce a time advance of the merger (∼1 ms) with modest energy transfer, and that previous phase-only, single-frequency approximations substantially overestimate detectability. The results inform expectations for LVK O5, ET, and CE, and provide a framework to constrain neutron-star interior physics via precise phase- and time-domain waveform analyses.

Abstract

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.

Figures (7)

• Figure 1: Phase difference computed using the sharp resonance approximation from Eq. \ref{['eq:dpsi-sharp']}.
• Figure 2: Match computation applying the quadratic approximation from Eq. \ref{['eq:match_quad']} (dot-dashed curves), using PyCBC match function pycbc.filter.match (dotted curves) and the optimized numerical computation (fading continuous curves). In the plot above, we express the match in terms of the time shift and in the one below in terms of the phase shift at different resonant frequencies ($50~ {\rm Hz}$ in red and $100~ {\rm Hz}$ in blue).
• Figure 3: Dotted blue curve: Absolute value of the normalized SNR amplitude (Eq. \ref{['eq:SNR_t_phi']} maximized over the phase $\phi$). Red and blue solid curves: contributions to the overlap from the waveform segments before and after the resonance, respectively, from Eq. \ref{['eq:snr_split']}. The dot-dashed curve corresponds to the quadratic approximation of the SNR in Eq. \ref{['eq:quadsnr']}. The time shift is fixed to $1~{\rm ms}$ and the resonant frequencies from each plot are $50~{\rm Hz}$ (above) and $100~{\rm Hz}$ (below).
• Figure 4: Same as Fig. \ref{['fig:rho_abs_roll_split_1ms']} but changing the time shift to $7~ {\rm ms}$.
• Figure 5: (a) Mismatch as a function of the time shift $\Delta t$ and the resonance frequency $f_{\rm res}$. Black curves indicate the signal-to-noise ratio (SNR) required for detecting a time shift of a given value, satisfying the Lindblom criterion in Eq. \ref{['mmlindblomres']}. The red curve marks the transition between using the refined numerical match function and the quadratic approximation for a relative error among the match functions of $0.1 \%$. (b) Total energy transferred to the neutron star modes, obtained integrating Eq. \ref{['dtdf_res']}.