Diffusive Tidal Evolution for Migrating hot Jupiters
I consider a Jovian planet on a highly eccentric orbit around its host star, a situation possibly produced by secular interactions with its planetary or stellar companions. At every periastron passage, tidal interactions lead to an energy exchange between the orbit and the planet's internal oscillations (predominantly an l=2 f-mode). Starting from zero energy, this f-mode can be diffusively excited if the one-kick energy gain is greater than (ωPorb)−1 of the orbital energy. This occurs at a pericentre distance of 4 tidal radii (or 1.6 Roche radius). Furthermore, when the f-mode has a non-negligible initial energy, this diffusive evolution can set in at a much reduced threshold. The first finding is important for stalling the secular migration. 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 finding is important for circularizing the planet's orbit. It allows an excited f-mode to continuously absorb orbital energy even when the one-kick energy is weakening along the path of circularization (due to increasing pericentre distance). 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 0.2 AU in 10^4 yrs. Such a rapid circularization corresponds to an equivalent tidal dissipation factor Q ~ 1, and it explains the observed deficit of super-eccentric Jovian planets. Lastly, the repeated f-mode breaking deposits energy and angular momentum in the outer shells of the planet. This likely alters the planet's thermal structure, but should fall short of ablating it. Overall, this work boosts the case for forming hot Jupiters through high-eccentricity secular migration.