Growth rate of the tidal p-mode g-mode instability in coalescing binary neutron stars

TL;DR

This paper investigates the nonlinear p-g mode instability in coalescing binary neutron stars, revealing that accounting for tide compressibility leads to rapid mode growth, potentially affecting gravitational wave signals.

Contribution

It extends previous analyses by including tide compressibility, showing that the p-g instability can grow rapidly and impact gravitational wave phase evolution.

Findings

Instability can grow significantly before merger.

Over 1000 modes can become unstable.

Growth rates are faster when tide compressibility is considered.

Abstract

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.