  As current gravitational wave (GW) detectors increase in sensitivity, and
particularly as new instruments are being planned, there is the possibility
that ground-based GW detectors will observe GWs from highly eccentric neutron
star binaries. We present the first detailed study of highly eccentric BNS
systems with full (3+1)D numerical relativity simulations using consistent
initial conditions, i.e., setups which are in agreement with the Einstein
equations and with the equations of general relativistic hydrodynamics in
equilibrium. Overall, our simulations cover two different equations of state
(EOSs), two different spin configurations, and three to four different initial
eccentricities for each pairing of EOS and spin. We extract from the simulated
waveforms the frequency of the f-mode oscillations induced during close
encounters before the merger of the two stars. The extracted frequency is in
good agreement with f-mode oscillations of individual stars for the
irrotational cases, which allows an independent measure of the supranuclear
equation of state not accessible for binaries on quasi-circular orbits. The
energy stored in these f-mode oscillations can be as large as $10^{-3}M_\odot
\sim 10^{51}$ erg, even with a soft EOS. In order to estimate the stored
energy, we also examine the effects of mode mixing due to the stars' offset
from the origin on the f-mode contribution to the GW signal. While in general
(eccentric) neutron star mergers produce bright electromagnetic counterparts,
we find that the luminosity decreases when the eccentricity becomes too large,
due to a decrease of the ejecta mass. Finally, the use of consistent initial
configurations also allows us to produce high-quality waveforms for different
eccentricities which can be used as a testbed for waveform model development of
highly eccentric binary neutron star systems.
