Gravitational Waves from F-modes Excited by the Inspiral of Highly Eccentric Neutron Star Binaries

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 the I-Love-Q relation observationally. 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.