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High eccentricity migration is a possible formation channel for hot Jupiters.However, in order for it to be consistent with the observed population ofplanets, tides must circularize the orbits in less than $\approx$ a Myr. Apotential mechanism for such rapid circularization is the diffusive growth ofthe tidally driven planetary f-mode. Such growth occurs if the f-mode's phaseat pericenter varies chaotically from one pericenter passage to the next.Previous studies focused on the variation of the orbital period due to tidalback-reaction on the orbit as the source of chaos. Here we show that nonlinearmode interactions can also be an important source. Specifically, we show thatnonlinear interactions between a parent f-mode and daughter f-/p-modes inducean energy-dependent shift in the oscillation frequency of the parent. Thisfrequency shift varies randomly from orbit to orbit because the parent's energyvaries. As a result, the parent's phase at pericenter varies randomly, which wefind can trigger it to grow diffusively. We show that the phase shift inducedby nonlinear mode interactions in fact dominates the shift induced by tidalback-reaction and significantly lowers the one-kick energy threshold fordiffusive growth by about a factor of 5 compared to the linear theory'sprediction. Nonlinear interactions could thus enhance the formation rate of hotJupiters through the high-eccentricity migration channel and potentiallymitigate the discrepancy between the observed and predicted occurrence ratesfor close-in gas giants as compared to those further from the star.

Tides in the high-eccentricity migration of hot Jupiters: Triggering diffusive growth by nonlinear mode interactions