$f$-mode Imprints in Gravitational Waves from Coalescing Binaries involving Aligned Spinning Neutron Stars

TL;DR

This paper presents a method to incorporate $f$-mode effects into gravitational waveforms from coalescing neutron star binaries, highlighting their significance especially for rapidly spinning stars and potential impacts on parameter estimation.

Contribution

It introduces an accurate, economical approach to model $f$-mode-induced phase shifts in gravitational waves, emphasizing their importance for high-spin neutron star mergers.

Findings

$f$-mode effects cause significant phase shifts in gravitational waves.

Dephasing effects are EOS-independent for slow rotators but not for fast rotators.

Neglecting $f$-mode can lead to systemic errors in tidal deformability estimates.

Abstract

The excitation of $f$-mode in a neutron star member of coalescing binaries accelerates the merger course, and thereby introduces a phase shift in the gravitational waveform. Emphasising on the tidal phase shift by aligned, rotating stars, we provide an accurate, yet economical, method to generate $f$-mode-involved, pre-merger waveforms using realistic spin-modulated $f$-mode frequencies for some viable equations of state. We find for slow-rotating stars that the dephasing effects of the dynamical tides can be uniquely, EOS-independently determined by the direct observables (chirp mass ${\cal M}$, symmetric ratio $\eta$ and the mutual tidal deformability ${\tilde \Lambda}$), while this universality is gradually lost for increasing spin. For binaries with fast rotating members ($\gtrsim800\text{ Hz}$) the phase shift due to $f$-mode will exceed the uncertainty in the waveform phase at reasonable signal-to-noise ($\rho=25$) and cutoff frequency of $\gtrsim400\text{ Hz}$. Assuming a high cutoff frequency of $10^3\text{ Hz}$ and fast ($\gtrsim800\text{ Hz}$) members, a significant phase shift of $\gtrsim100$ rads has been found. For systems involving a rapidly-spinning star (potentially the secondary of GW190814), neglecting $f$-mode effect in the waveform templates can therefore lead to considerable systemic errors in the relevant analysis. In particular, the dephasing due to $f$-mode is larger than that caused by equilibrium tides by a factor of $\sim5$, which may lead to a considerably overestimated tidal deformability if dynamical tidal contribution is not accounted. The possibility of accompanying precursors flares due to $f$-mode excitation is also discussed.