I consider a Jovian planet on a highly eccentric orbit around its host star , a situation produced by secular interactions with its planetary or stellar companions .
The tidal interactions at every periastron passage exchange energy between the orbit and the planet ’ s degree-2 fundamental-mode .
Starting from zero energy , the f-mode can diffusively grow to large amplitudes if its one-kick energy gain \geq 10 ^ { -5 } of the orbital energy .
This requires a pericentre distance of \leq 4 tidal radii ( or 1.6 Roche radii ) .
If the f-mode has a non-negligible initial energy , diffusive evolution can occur at a lower threshold .
The first effect can stall the secular migration as the f-mode can absorb orbital energy and decouple the planet from its secular perturbers , parking all migrating jupiters safely outside the zone of tidal disruption .
The second effect leads to rapid orbit circularization as it allows an excited f-mode to continuously absorb orbital energy as the orbit eccentricity decreases .
So without any explicit dissipation , other than the fact that the f-mode will damp nonlinearly when its amplitude reaches unity , the planet can be transported from a few AU to \sim 0.2 AU in \sim 10 ^ { 4 } yrs .
Such a rapid circularization is equivalent to a dissipation factor Q \sim 1 , and it explains the observed deficit of super-eccentric Jovian planets .
Lastly , the repeated f-mode breaking likely deposit energy and angular momentum in the outer envelope , and avoid thermally ablating the planet .
Overall , this work boosts the case for forming hot Jupiters through high-eccentricity secular migration .