Diffusive Tidal Evolution for Migrating hot Jupiters

Understand

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 > 10^-5 of the orbital energy.
• This requires a pericentre distance of < 4 tidal radii (or 1.6 Roche radii).