This paper reviews the rich corpus of observational evidence for tidal effects, mostly based on photometric and radial-velocity measurements. This is done in a period when the study of binaries is being revolutionized by large-scaled photometric surveys that are detecting many thousands of new binaries and tens of extrasolar planets. We begin by examining the short-term effects, such as ellipsoidal variability and apsidal motion. We next turn to the long-term effects, of which circularization was studied the most: a transition period between circular and eccentric orbits has been derived for eight coeval samples of binaries. The study of synchronization and spin-orbit alignment is less advanced. As binaries are supposed to reach synchronization before circularization, one can expect finding eccentric binaries in pseudo-synchronization state, the evidence for which is reviewed. We also discuss synchronization in PMS and young stars, and compare the emerging timescale with the circularization timescale. We next examine the tidal interaction in close binaries that are orbited by a third distant companion, and review the effect of pumping the binary eccentricity by the third star. We elaborate on the impact of the pumped eccentricity on the tidal evolution of close binaries residing in triple systems, which may shrink the binary separation. Finally we consider the extrasolar planets and the observational evidence for tidal interaction with their parent stars. This includes a mechanism that can induce radial drift of short-period planets, either inward or outward, depending on the planetary radial position relative to the corotation radius. Another effect is the circularization of planetary orbits, the evidence for which can be found in eccentricity-versus-period plot of the planets already known. Whenever possible, the paper attempts to address the possible confrontation between theory and observations, and to point out noteworthy cases and observations that can be performed in the future and may shed some light on the key questions that remain open.

To first approximation, a binary system conserves its angular momentum while it evolves to its state of minimum kinetic energy: circular orbit, all spins aligned, and components rotating in synchronism with the orbital motion. The pace at which this final state is achieved depends on the physical processes that are responsible for the dissipation of the tidal kinetic energy. For stars (or planets) with an outer convection zone, the dominant mechanism identified so far is the viscous dissipation acting on the equilibrium tide. For stars with an outer radiation zone, it is the radiative damping operating on the dynamical tide. After a brief presentation of the tides, I shall review these physical processes; I shall discuss the uncertainties of their present treatment, describe the latest developments, and compare the theoretical predictions with the observed properties concerning the orbital circularization of close binaries.

A general problem with the theory of stellar tides is that the observations indicate that the effectiveness in circularising binary orbits is much larger than predicted by current theories. A mechanism that may be at least part of the solution to this problem is resonance locking: prolonged enhanced tidal interaction when the tide is nearly resonant with a stellar oscillation mode. In these lectures we focus on the dynamical tide which takes into account that the tides can indeed excite non-radial oscillations in a star when the forcing period happens to be close to the period of a free oscillation mode of the star. Such resonant interaction can in principle speed-up the tidal evolution of a close binary. By including the Coriolis force in rotating stars the oscillation spectrum is enriched by rotational oscillation modes that can also be excited by the tides. Although the chances that the tides in a particular binary system happen to be close to a resonance with a free oscillation mode seem nevertheless slim, it appears that binary systems with a significant orbital eccentricity, and thus with several tidal harmonics, evolve through many resonances on timescales short compared to their main sequence (MS) lifetime. Stellar rotation, which is usually neglected in tidal calculations, plays an important role in that it is relatively easy to tidally spin a star up or down, whereby the forcing frequency (in the stellar frame) can move towards a resonance with a free oscillation mode of the star on relatively short timescales. Often this gives rise to resonance locking whereby the system remains nearly resonant, with enhanced tidal evolution, for a relatively long period. We will present the results of several numerical simulations, for both massive MS binaries and solar type binary systems in which resonance locking is studied in some detail. Note: in the following all numerically listed frequencies are normalised by the stellar break-up speed $\Omega_c=\sqrt{G\, M_s/R^3_s}$, unless explicitly indicated otherwise.

In this lecture I try to explain the basic concepts related to fluid motions when a background rotation dominates the flows. In particular, the notions of geostrophic flow, Ekman layer, Ekman circulation are explained. However, the main focus of this lecture is on the eigenmodes which occur in such a context and I emphasize here the special effects conveyed to inertial and gravito-inertial modes by the hyperbolic nature of the governing operators. A final section introduces the case of the elliptic instability which I recently suggested as one of the processes of binary synchronization.

Close hierarchical triple stellar systems offer a unique possibility to study not only theoretically, but even observationally (at least with limitations) the interaction between a non-spherical and temporally variable gravitational field and the internal structures of the stars. From this purpose a new numerical integrator was developed for studying the orbital and spin evolution of hierarchical triple stellar systems. The code includes equilibrium tide approximations with arbitrary direction of rotational axes. The variation of the orbital elements (e.g. the inclination of the close -eclipsing- binary) and its observational consequences according to the distorted models with different mass-distributions of the stars, as well as with and without dissipation, is studied in the case of the well-known eclipsing triple system Algol. We found that in the absence of dissipation the third star may cause sudden fluctuations in the orbital elements and in the rotation of the binary components, even if they were previously synchronized. Tidal dissipation can eliminate these fluctuations; nevertheless certain variations may subsist, and they could explain some effects that have been observed in several eclipsing binaries.

Tides come from the fact that different parts of a system do not fall in exactly the same way in a non-uniform gravity field. In the case of a protoplanetary disk perturbed by an orbiting, prograde protoplanet, the protoplanet tides raise a wake in the disk which causes the orbital elements of the planet to change over time. The most spectacular result of this process is a change in the protoplanet's semi-major axis, which can decrease by orders of magnitude on timescales shorter than the disk lifetime. This drift in the semi-major axis is called planetary migration, and is the most important aspect of planet–disk interactions. In this chapter, we first describe how the planet and disk exchange angular momentum and energy at the Lindblad and corotation resonances. Next we review the various types of planetary migration that have so far been contemplated: type I migration, which corresponds to low-mass planets (less than a few Earth masses) triggering a linear disk response; type II migration, which corresponds to massive planets (typically at least one Jupiter mass) that open up a gap in the disk; “runaway” or type III migration, which corresponds to sub-giant planets that orbit in massive disks; and stochastic or diffusive migration, which is the migration mode of low- or intermediate-mass planets embedded in turbulent disks. Third, we discuss questions linked to the planet eccentricity, in particular how the eccentricity is affected by the planet–disk interaction. Fourth, we discuss the various numerical schemes that have been used to describe planet–disk interactions. We discuss their strengths and weaknesses, and list the results that numerical simulations have achieved over the past decade.

The relatively high contrast between planetary and solar low frequency radio emissions suggests that the low–frequency radio range may be well adapted to the direct detection of exoplanets. We review the most significant properties of planetary radio emissions (auroral as well as satellite–induced) and show that their primary engine is the interaction of a plasma flow with an obstacle in the presence of a strong magnetic field (of the flow or of the obstacle). Scaling laws have been derived from solar system planetary radio emissions that relate the emitted radio power to the power dissipated in the various corresponding flow–obstacle interactions. We generalize these scaling laws into a “radio–magnetic” scaling law that seems to relate output radio power to the magnetic energy flux convected on the obstacle, this obstacle being magnetized or unmagnetized. Extrapolating this scaling law to the case of exoplanets, we find that hot Jupiters may produce very intense radio emissions due to either magnetospheric interaction with a strong stellar wind or to unipolar interaction between the planet and a magnetic star (or strongly magnetized regions of the stellar surface). In the former case, similar to the magnetosphere–solar wind interactions in our solar system or to the Ganymede–Jupiter interaction, a hecto–decameter emission is expected in the vicinity of the planet with an intensity possibly 103 to 105 times that of Jupiter's low frequency radio emissions. In the latter case, which is a giant analogy of the Io–Jupiter system, emission in the decameter–to–meter wavelength range near the footprints of the star's magnetic field lines interacting with the planet may reach 106 times that of Jupiter (unless some “saturation” mechanism occurs). The system of HD 179949, where a hot spot has been tentatively detected in visible light near the sub–planetary point, is discussed in some details. Finally, we discuss the interests of direct radio detection, among which access to exoplanetary magnetic field measurements and comparative magnetospheric physics.