On the tidal interaction of massive extra-solar planets on highly eccentric orbit

In this paper we develop a theory of disturbances induced by the stellar tidal field in a fully convective slowly rotating planet orbiting on a highly eccentric orbit around a central star. In that case it is appropriate to treat the tidal influence as a succession of impulsive tidal interactions occurring at periastron passage. For a fully convective planet mainly the l = 2 fundamental mode of oscillation is excited. We show that there are two contributions to the mode energy and angular momentum gain due to impulsive tidal interaction: a) ’the quasi-static’ contribution which requires dissipative processes operating in the planet; b) the dynamical contribution associated with excitation of modes of oscillation. These contributions are obtained self-consistently from a single set of the governing equations. We calculate a critical ’equilibrium’ value of angular velocity of the planet Ωcrit determined by the condition that action of the dynamical tides does not alter the angular velocity at that rotation rate. We show that this can be much larger than the corresponding rate associated with quasi-static tides and that at this angular velocity, the rate of energy exchange is minimised. We also investigate the conditions for the stochastic increase in oscillation energy that may occur if many periastron passages are considered and dissipation is not important. We provide a simple criterion for this instability to occur. Finally, we make some simple estimates of time scale of evolution of the orbital semi-major axis and circularization of initially eccentric orbit due to