Probing Stellar Tidal Dissipation with Hot Jupiters

A key riddle connecting stars and planets is in the existence of hot Jupiters. If these close-in planets migrated into their orbits near 0.05 AU, why didn't they ultimately fall into their stars? Could stellar tides have stopped migration? Conventional equilibrium tide models of stellar tidal dissipation, usually parameterized with a tidal dissipation constant (10⁵ ≲ Q_s ≲ 10⁶), predict too weak a tidal effect to counteract migration. On the other hand, equilibrium tide models predict orbital decay in less than the lifetime of a solar-type star. These hot Jupiters should have fallen into their stars long time ago. Observations, however, show the opposite: a pile-up near 0.05 AU around solar-type stars. Here I present a new model of the combined effects of the stellar dynamical tide (inertial waves caused by Coriolis acceleration in convective stellar envelopes) and of the disk. I consider a two-stage formation process. 1. A hot Jupiter in the type II migration regime affected by both the disk and the stellar tidal torque (10 Myr). 2. The longterm (5 Gyr) evolution under the effect of evolving stellar tides only. In this dynamical tide model with stellar evolution, migrating giant planets pile up near 0.05 AU and they survive over billions of years. The lower pile-up efficiency around metal-poor stars might explain the weaker pile-up observed in the mildly metal-poor Kepler RV sample.