Equation of State Dependence of Nonlinear Mode-tide Coupling in Coalescing Binary Neutron Stars

Recently, an instability due to the nonlinear coupling of p-modes to g-modes in tidally deformed neutron stars in coalescing binaries has been studied in some detail. The result is significant because it could influence the inspiral and leave an imprint on the gravitational wave signal that depends on the neutron star equation of state (EOS). Because of its potential importance, the details of the instability should be further elucidated and its sensitivity to the EOS should be investigated. To this end, we carry out a numerical analysis with six representative EOSs for both static and non-static tides. We confirm that the absence of the p-g instability under static tides, as well as its return under non-static tides, is generic across EOSs, and further reveal a new contribution to it that becomes important for moderately high-order p-g pairs (previous studies concentrated on very high order modes), whose associated coupling strength can vary by factors of ∼10-100 depending on the EOS. We find that, for stars with stiffer EOSs and smaller buoyancy frequencies, the instability onsets earlier in the inspiral and the unstable modes grow faster. These results suggest that the instability's impact on the gravitational wave signal might be sensitive to the neutron star EOS. To fully assess this prospect, future studies will need to investigate its saturation as a function of the EOS and the binary parameters.