  As gravitational wave instrumentation becomes more sensitive, it is
interesting to speculate about subtle effects that could be analyzed using
upcoming generations of detectors. One such effect that has great potential for
revealing the properties of very dense matter is fluid oscillations of neutron
stars. These have been found in numerical simulations of the hypermassive
remnants of double neutron star mergers and of highly eccentric neutron star
orbits. Here we focus on the latter and sketch out some ideas for the
production, gravitational-wave detection, and analysis of neutron star
oscillations. These events will be rare (perhaps up to several tens per year
could be detected using third-generation detectors such as the Einstein
Telescope or the Cosmic Explorer), but they would have unique diagnostic power
for the analysis of cold, catalyzed, dense matter. Furthermore, these systems
are unusual in that analysis of the tidally excited f-modes of the stars could
yield simultaneous measurements of their masses, moments of inertia, and tidal
Love numbers, using the frequency, damping time, and amplitude of the modes.
They would thus present a nearly unique opportunity to test observationally the
I-Love-Q relation. The analysis of such events will require significant further
work in nuclear physics and general relativistic nonlinear mode coupling, and
thus we discuss further directions that will need to be pursued. For example,
we note that for nearly-grazing encounters, numerical simulations show that the
energy delivered to the f-modes may be up to two orders of magnitude greater
than predicted in the linear theory.
