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. 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 \Omega_{crit} 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. We make some simple estimates of time scale of circularization of initially eccentric orbit due to tides, using a realistic model of the planet, for orbits withperiods after circularization typical of those observed for extra-solar planets P_{obs} > 3days. We find that dynamic tides could have produced a very large decrease of the semi-major axis of a planet with mass of the order of the Jupiter mass M_{J} and final periods P_{obs} < 4.5days on a time-scale < a few Gyrs. We also discuss several unresolved issues in the context of the scenario of the orbit circularization due to dynamic tides.