Tidal interactions between planets and stars
Since the ﬁrst discovery of an extrasolar planet around a solar-type star, observers have detected over 500 planets outside the solar system. Many of these planets have Jovian masses and orbit their host stars in orbits of only a few days, the so-called “Hot Jupiters”. At such close proximity to their parent stars, strong tidal interactions between the two bodies are expected to cause signiﬁcant secular spin-orbit evolution. This thesis tackles two problems regarding the tidal evolution of short-period extrasolar planets. In the ﬁrst part, we adopt a simple model of the orbit-averaged effects of tidal friction, to study the tidal evolution of planets on inclined orbits. We also analyse the effects of stellar magnetic braking. We then discuss the implications of our results for the importance of Rossiter-Mclaughlin effect observations. In the second part, we study the mechanisms of tidal dissipation in solar-type stars. In particular, internal gravity waves are launched at the interface of the convection and radiation zones of such a star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star is studied, primarily using numerical simulations, in both two and three dimensions. We ﬁnd that the waves undergo instability and break above a critical amplitude. A model for the tidal dissipation that results from this process is presented, and its validity is veriﬁed by numerical integrations of the linear tidal response, in an extensive set of stellar models. The dissipation is efficient, and varies by less than an order of magnitude between all solar- type stars, throughout their main-sequence lifetimes, for a given planetary orbit. The implications of this mechanism for the survival of short-period extrasolar planets is discussed, and we propose a possible explanation for the survival of all of the extrasolar planets currently observed in short-period orbits around F, G and K stars. We then perform a stability analysis of a standing internal gravity wave near the centre of a solar-type star, to understand the early stages of the wave breaking process in more detail, and to determine whether the waves are subject to weaker parametric instabilities, below the critical amplitude required for wave breaking. We discuss the relevance of our results to our explanation for the survival of short-period planets presented in the second part of this thesis. Finally, we propose an alternative mechanism of tidal dissipation, involving the gradual radiative damping of the waves. Based on a simple estimate, it appears that this occurs even for low mass planets. However, it is in conﬂict with current observations since it would threaten the survival of all planets in orbits shorter than 2 days. We discuss some hydrodynamic instabilities and magnetic stresses which may prevent this process.