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  (and for BH-NS binaries using
QE  and dynamical calculations ). 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
Figure 6: Dimensionless binding energy vs. dimensionless orbital frequency , where
is the total ADM (Arnowitt–Deser–Misner) mass of the two components at infinite separation,
for two QE NS-NS sequences that assume a piecewise polytropic NS EOS. The equal-mass case
assumes for both NSs, while the unequal-mass case assumes
and . The thick curves are the numerical results, while the thin curves show the
results from the 3PN approximation. The lack of any minimum suggests that instability for these
configurations occurs at the onset of mass shedding, and not through a secular orbital instability.
Image reproduced by permission from Figure 16 of , copyright by AAS.
Figure 7: Mass-shedding indicator vs. orbital frequency ,
where is the fluid enthalpy and the derivative is measured at the NS surface in the equatorial
plane toward the companion and toward the pole in the direction of the angular momentum vector,
for a series of QE NS-NS sequences assuming equal-mass components. Here, corresponds
to a spherical NS, while indicates the onset of mass shedding. More massive NSs are more
compact, and thus able to reach smaller separations and higher angular frequencies before mass
shedding gets underway. Image reproduced by permission from Figure 19 of , copyright by AAS.
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 . To illustrate this, we show in Figure 8 four different QE models for NS-NS
configurations with different EOS, taken from ; all have and ,
and they correspond to the closest separation for which the QE code still finds a convergent
Figure 8: Isodensity contours for QE models of NS-NS binaries. In each case, the two NSs have
masses (left) and (right), and the center-of-mass separation is as
small as the QE numerical methods allow while able to find a convergent result. The models assume
different EOS, resulting in different central concentrations and tidal deformations. Image reproduced
by permission from Figures 9 – 12 of , copyright by AAS.
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 . 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