The tidal excitation of r modes in a solar-type star orbited by a giant planet companion and the effect on orbital evolution - II. The effect of tides in the misaligned case

We extend the study of Papaloizou and Savonije of the tidal interactions of close orbiting giant planets with a central solar-type star to the situation where the spin axis of the central star and the orbital angular momentum are misaligned. We determine the tidal response taking into account the possibility of the excitation of r modes and the effect of tidal forcing due to potential perturbations that have zero frequency in a non-rotating frame. Although there is near resonance with r modes with degree l ' = 1 and orders m = +/- 1, half widths turn out to be sufficiently narrow so that in practice dissipation rates are found to be similar to those produced by non-resonant potential perturbations. We use our results to determine the evolution of the misalignment for the full range of initial inclination angles taking account of the spin-down of the central star due to magnetic braking. Overall we find the rate of tidal evolution to be unimportant for a one Jupiter mass planet with orbital period similar to 3.7 d over a main-sequence lifetime. However, it becomes significant for higher mass planets and shorter orbital periods, approximately scaling as the square of the planet mass and the inverse fourth power of the orbital period.