Thermal Tides in Rotating Hot Jupiters

We calculate tidal torque due to semi-diurnal thermal tides in rotating hot Jupiters, taking account of the effects of radiative cooling in the envelope and of the planets rotation on the tidal responses. We use a simple Jovian model composed of a nearly isentropic convective core and a thin radiative envelope. To represent the tidal responses of rotating planets, we employ series expansions in terms of spherical harmonic functions $Y_l^m$ with different $l$s for a given $m$. For low forcing frequency, there occurs frequency resonance between the forcing and the $g$- and $r$-modes in the envelope and inertial modes in the core. We find that the resonance enhances the tidal torque, and that the resonance with the $g$- and $r$-modes produces broad peaks and that with the inertial modes very sharp peaks, depending on the magnitude of the non-adiabatic effects associated with the oscillation modes. We also find that the behavior of the tidal torque as a function of the forcing frequency (or period) is different between prograde and retrograde forcing, particularly for long forcing periods because the $r$-modes, which have long periods, exist only on the retrograde side.