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