An instability due to the nonlinear coupling of p-modes to g-modes: Implications for coalescing neutron star binaries

Understand

A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions.

• The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency $\omega_a$ excites a pair of secondary waves of frequency $\omega_b+\omega_c \simeq \omega_a$.
• Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that $\omega_b+\omega_c >>\omega_a$.
• We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of interaction is unstable even if the primary wave amplitude is small.