Title: Diffusive Tidal Evolution for Migrating hot Jupiters,
Abstract: 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). 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 ~ 0.2 AU in ~ 10^4 yrs. Such a rapid
circularization is equivalent to a dissipation factor Q ~ 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.