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The recent detection of gravitational waves (GWs) from the neutron starbinary inspiral GW170817 has opened a unique avenue to probe matter andfundamental interactions in previously unexplored regimes. Extractinginformation on neutron star matter from the observed GWs requires robust andcomputationally efficient theoretical waveform models. We develop anapproximate frequency-domain GW phase model of a main GW signature of matter:dynamic tides associated with the neutron stars' fundamental oscillation modes($f$-modes). We focus on nonspinning objects on circular orbits and demonstratethat, despite its mathematical simplicity, the new "$f$-mode tidal" (fmtidal)model is in good agreement with the effective-one-body dynamical tides model upto GW frequencies of $\gtrsim 1$ kHz and gives physical meaning to part of thephenomenology captured in tidal models tuned to numerical-relativity. Theadvantages of the fmtidal model are that it makes explicit the dependence ofthe GW phasing on the characteristic equation-of-state parameters, i.e., tidaldeformabilities and $f$-mode frequencies; it is computationally efficient; andit can readily be added to any frequency-domain baseline waveform. The fmtidalmodel is easily amenable to future improvements and provides the means for afirst step towards independently measuring additional fundamental properties ofneutron star matter beyond the tidal deformability as well as performing noveltests of general relativity from GW observations.

Frequency domain model of $f$-mode dynamic tides in gravitational waveforms from compact binary inspirals