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Previously, a series of tidally-excited oscillations were discovered in theeccentric eclipsing binary KIC 3230227. The pulsation amplitudes and phasessuggest the observed oscillations are prograde quadruple modes. In this paper,we refine the analysis and extract more oscillation frequencies. We also studythe temporal variations of amplitudes and phases and show that almost all modeshave stable phases and amplitudes. We then focus on the non-orbital-harmonicoscillations. We consider two formation mechanisms: 1) nonlinear response ofthe surface convective layer, and 2) nonlinear three/multi-mode coupling.Although the former can explain some of the observed features, we find thelatter mechanism is more probable. Assuming that these are coupled modes, theconstant amplitude/phase over four years can be explained by either anequilibrium state in the mode coupling or modes undergoing limit cycles withvery long periods. The observed frequency detuning and the calculated dampingrates of the daughter modes favor the equilibrium-state interpretation. This isverified by integrating the amplitude equations of three-mode coupling. We findthat the steady-state relation derived in Weinberg et al., which relates theobserved frequency detuning, phase detuning, and mode damping rates, isapproximately satisfied for one mode triplet. We also try to identify theazimuthal number of the modes based on the observed mode amplitude ratios andthe selection rules in nonlinear three-mode coupling. We discuss furtherimplications of these observations on nonlinear tidal asteroseismology.

Tidal Asteroseismology: Possible Evidence of Non-linear Mode Coupling in an Equilibrium State in Kepler Eclipsing Binary KIC 3230227