Thermal Tides in Short Period Exoplanets

Time-dependent insolation in a planetary atmosphere induces a mass quadrupole upon which the stellar tidal acceleration can exert a force. This “thermal tide” force can give rise to secular torques on the planet and orbit as well as radial forces causing eccentricity evolution. We apply this idea to the close-in gas giant exoplanets (“hot Jupiters”). The response of radiative atmospheres is computed in a hydrostatic model which treats the insolation as a time-dependent heat source, and solves for thermal radiation using flux-limited diffusion. Fully nonlinear numerical simulations are compared to solutions of the linearized equations, as well as analytic approximations, all of which are in good agreement. We find generically that thermal tide density perturbations lead the semi-diurnal forcing. As a result thermal tides can generate asynchronous spin and eccentricity. Applying our calculations to the hot Jupiters, we find the following results: (1) Departure from synchronous spin is significant for hot Jupiters, and increases with orbital period. (2) Ongoing gravitational tidal dissipation in spin equilibrium leads to steady-state internal heating rates up to ∼ 10 erg s. If deposited sufficiently deep, these heating rates may explain the anomalously large radii of many hot Jupiters in terms of a “tidal main sequence” where cooling balances tidal heating. At fixed stellar type, planet mass and tidal Q, planetary radius increases strongly toward the star inside orbital periods . 2 weeks. (3) There exists a narrow window in orbital period where small eccentricities, e, grow exponentially with a large rate. This window may explain the ∼ 1/4 of hot Jupiters which should have been circularized by the gravitational tide long ago, but are observed to have significant nonzero e. Conversely, outside this window, the thermal and gravitational tide both act to damp e, complicating the ability to constrain the planet’s tidal Q. Subject headings: planets – tides