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