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Previous theoretical works using the pre-merger orbital evolution ofcoalescing neutron stars to constrain properties of dense nuclear matter assumea gravitational wave phase uncertainty of a few radians, or about a half cycle.However, recent studies of the signal from GW170817 and next generationdetector sensitivities indicate actual phase uncertainties at least twentytimes better. Using these refined estimates, we show that future observationsof nearby sources like GW170817 may be able to reveal neutron star propertiesbeyond just radius and tidal deformability, such as the matter compositionand/or presence of a superfluid inside neutron stars, via tidal excitation ofg-mode oscillations. Data from GW170817 already limits the amount of orbitalenergy that is transferred to the neutron star to <2x10^47 erg and the g-modetidal coupling to Qmode<10^-3 at 50 Hz (5x10^48 erg and 4x10^-3 at 200 Hz), andfuture observations and detectors will greatly improve upon these constraints.In addition, analysis using general parameterization models that have beenapplied to the so-called p-g instability show that the instability alreadyappears to be restricted to regimes where the mechanism is likely to beinconsequential; in particular, we show that the number of unstable modes is<<100 at <~100 Hz, and next generation detectors will essentially rule out thismechanism (assuming that the instability remains undetected). Finally, weillustrate that measurements of tidal excitation of r-mode oscillations innearby rapidly rotating neutron stars are within reach of current detectors andnote that even non-detections will limit the inferred inspiralling neutron starspin rate to <20 Hz, which will be useful when determining other parameterssuch as neutron star mass and tidal deformability.

New dynamical tide constraints from current and future gravitational wave detections of inspiralling neutron stars