Asynchronous rotation and orbital eccentricity lead to time-dependent irradiation of the close-in gas giant exoplanets—the hot Jupiters. This time-dependent surface heating gives rise to fluid motions which propagate throughout the planet. We investigate the ability of this "thermal tide" to produce a quadrupole moment which can couple to the stellar gravitational tidal force. While previous investigations discussed planets with solid surfaces, here we focus on entirely fluid planets in order to understand gas giants with small cores. The Coriolis force, thermal diffusion, and self-gravity of the perturbations are ignored for simplicity. First, we examine the response to thermal forcing through analytic solutions of the fluid equations which treat the forcing frequency as a small parameter. In the "equilibrium tide" limit of zero frequency, fluid motion is present but does not induce a quadrupole moment. In the next approximation, finite frequency corrections to the equilibrium tide do lead to a nonzero quadrupole moment, the sign of which torques the planet away from synchronous spin. We then numerically solve the boundary value problem for the thermally forced, linear response of a planet with neutrally stratified interior and a stably stratified envelope. The numerical results find quadrupole moments in agreement with the analytic non-resonant result at a sufficiently long forcing period. Surprisingly, in the range of forcing periods of 1-30 days, the induced quadrupole moments can be far larger than the analytic result due to response of internal gravity waves which propagate in the radiative envelope. We discuss the relevance of our results for the spin, eccentricity, and thermal evolution of hot Jupiters.
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