### 4.1 Overview

While dynamical calculations are required to understand the GW and EM emission from BH-NS and
NS-NS mergers, some of the main qualitative features of the signals may be derived directly from
QE sequences. From the variation of total system energy with binary angular velocity along a
given sequence, it is possible to construct an approximate GW energy spectrum
immediately from QE results, essentially by performing a numerical derivative (see Figure 6).
Doing so for a number of different sequences makes it possible to identify key frequencies where
tidal effects may become measurable and to identify these with binary parameters such as the
system mass ratio and NS radius. Similarly, since QE sequences should indicate whether a binary
begins to shed mass prior to passage through the ISCO (see Figure 7), one may be able to
classify observed signals into mass-shedding and non-mass-shedding events, and to use the
critical point dividing those cases to help constrain the NS EOS. Single-parameter estimates
have been derived for NS-NS binaries using QE sequences [98] (and for BH-NS binaries using
QE [301] and dynamical calculations [283]). NS-NS binaries typically approach instability at
frequencies , where laser shot noise is severely degrading the sensitivity of an
interferometer detector. To observe ISCO-related effects with higher signal-to-noise, it may be
necessary to operate GW observatories using narrow-band signal recycling modes, in which the
sensitivity in a narrow range of frequencies is enhanced at the cost of lower sensitivity to broadband
signals [56].
It is important to note that, while the potential parameter space for NS EOS models is still very large, a
much smaller set may serve to classify models for comparison with the first generation of GW detections.
Indeed, by breaking up the EOS into piecewise polytropic segments, one may use as few as four parameters
to roughly approximate all known EOS models, including standard nuclear models as well as models with
kaon or other condensates [237]. To illustrate this, we show in Figure 8 four different QE models for NS-NS
configurations with different EOS, taken from [305]; all have and ,
and they correspond to the closest separation for which the QE code still finds a convergent
result.

The inspiral of NS-NS binaries may yield complementary information about the NS structure beyond
what can be gleaned from QE studies of tidal disruption. NSs have a wide variety of oscillation modes,
including f-modes, g-modes, and r-modes, any of which may be excited by resonances with the orbital
frequency as the latter sweeps upward. Should a particular oscillation mode be excited resonantly, it can
then serve briefly as an energy sink for the system, potentially changing the phase evolution of the binary.
For example, in a rapidly spinning NS, excitation of the r-mode can be significant, yielding a
change of over 100 radians for the pre-merger GW signal phase in the case of a millisecond spin
period [161]. For NS-NS mergers in the field, this would require one of the NSs to be a young pulsar that
has not yet spun down significantly, which is unlikely because of the difficulty in obtaining such an
extremely small binary separation after the second supernova. Other modes, such as the f-mode,
may be excited in less extreme circumstances, also yielding information about NS structure
parameters [105].