We calculate tidal torque due to semidiurnal 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 Ylm with different ls 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 behaviour 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.
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