  We recently described an instability due to the nonlinear coupling of p-modes
to g-modes and, as an application, we studied the stability of the tide in
coalescing binary neutron stars. Although we found that the tide is p-g
unstable early in the inspiral and rapidly drives modes to large energies, our
analysis only accounted for three-mode interactions. Venumadhav, Zimmerman, and
Hirata showed that four-mode interactions must also be accounted for as they
enter into the analysis at the same order. They found a near-exact cancellation
between three- and four-mode interactions and concluded that while the tide in
binary neutron stars can be p-g unstable, the growth rates are not fast enough
to impact the gravitational wave signal. Their analysis assumes that the linear
tide is incompressible, which is true of the static linear tide (the m=0
harmonic) but not the non-static linear tide (m=+/- 2). Here we account for the
compressibility of the non-static linear tide and find that the three- and
four-mode interactions no longer cancel. As a result, we find that the
instability can rapidly drive modes to significant energies (there is time for
several dozen e-foldings of growth before the binary merges). We also show that
linear damping interferes with the cancellation and may further enhance the p-g
growth rates. The early onset of the instability (at gravitational wave
frequencies near 50 Hz), the rapid growth rates, and the large number of
unstable modes (> 10^3), suggest that the instability could impact the phase
evolution of gravitational waves from binary neutron stars. Assessing its
impact will require an understanding of how the instability saturates and is
left to future work.
