Interaction of close-in planets with the magnetosphere of their host stars. I. Diffusion, ohmic dissipation of time-dependent field, planetary inflation, and mass loss

The unanticipated discovery of the first close-in planet around 51 Peg has rekindled the notion that shortly after their formation outside the snow line, some planets may have migrated to the proximity of their host stars because of their tidal interaction with their nascent disks. After a decade of discoveries, nearly 20% of the 200 known planets have similar short periods. If these planets indeed migrated to their present-day location, their survival would require a halting mechanism in the proximity of their host stars. Here we consider the possibility that a magnetic coupling between young stars and planets could quench the planet's orbital evolution. Most T Tauri stars have magnetic fields of several thousand gausses on their surface which can clear out a cavity in the innermost regions of their circumstellar disks and impose magnetic induction on the nearby young planets. After a brief discussion of the complexity of the full problem, we focus our discussion on evaluating the permeation and ohmic dissipation of the time-dependent component of the stellar magnetic field in the planet's interior. Adopting a model first introduced by Campbell for interacting binary stars, we determine the modulation of the planetary response to the tilted magnetic field of a non-synchronously spinning star. We first compute the conductivity in the young planets, which indicates that the stellar field can penetrate well into the planet's envelope in a synodic period. For various orbital configurations, we show that the energy dissipation rate inside the planet is sufficient to induce short-period planets to inflate. This process results in mass loss via Roche lobe overflow and in the halting of the planet's orbital migration.