GROWTH RATE OF THE TIDAL p-MODE g-MODE INSTABILITY IN COALESCING BINARY NEUTRON STARS

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 et al. 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 linear tide and find that three- and four-mode interactions no longer cancel. As a result, we find that the instability can rapidly drive modes to significant energies well before the binary merges. We also show that linear damping interferes with the cancellation and may further enhance the growth rates. The early onset of the instability (at gravitational wave frequencies approximate to 50 Hz) and the large number of rapidly growing modes suggest that the instability could impact the gravitational wave signal. Assessing its impact will require an understanding of how the instability saturates and is left to future work.