This paper reviews the rich corpus of observational evidence for tidaleffects, mostly based on photometric and radial-velocity measurements.This is done in a period when the study of binaries is beingrevolutionized by large-scaled photometric surveys that are detectingmany thousands of new binaries and tens of extrasolar planets. We begin by examining the short-term effects, such as ellipsoidalvariability and apsidal motion. We next turn to the long-termeffects, of which circularization was studied the most: a transitionperiod between circular and eccentric orbits has been derived foreight coeval samples of binaries. The study of synchronization andspin-orbit alignment is less advanced. As binaries are supposed toreach synchronization before circularization, one can expect findingeccentric binaries in pseudo-synchronization state, the evidence forwhich is reviewed. We also discuss synchronization in PMS and youngstars, and compare the emerging timescale with the circularizationtimescale. We next examine the tidal interaction in close binaries that areorbited by a third distant companion, and review the effect ofpumping the binary eccentricity by the third star. We elaborate on theimpact of the pumped eccentricity on the tidal evolution of closebinaries residing in triple systems, which may shrink the binary separation. Finally we consider the extrasolar planets and the observationalevidence for tidal interaction with their parent stars. This includesa mechanism that can induce radial drift of short-period planets,either inward or outward, depending on the planetary radial positionrelative to the corotation radius. Another effect is thecircularization of planetary orbits, the evidence for which can befound in eccentricity-versus-period plot of the planets already known. Whenever possible, the paper attempts to address the possibleconfrontation between theory and observations, and to point outnoteworthy cases and observations that can be performed in the futureand 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 fluidmotions when a background rotation dominates the flows.In particular, the notions of geostrophic flow, Ekman layer, Ekmancirculation are explained. However, the main focus of this lecture is onthe eigenmodes which occur in such a context and I emphasize here thespecial effects conveyed to inertial and gravito-inertial modesby the hyperbolic nature of the governing operators. A final sectionintroduces the case of the elliptic instability which I recentlysuggested 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 frequencyradio emissions suggests that the low–frequency radio range may bewell adapted to the direct detection of exoplanets. We review the mostsignificant properties of planetary radio emissions (auroral as well assatellite–induced) and show that their primary engine is theinteraction of a plasma flow with an obstacle in the presence of astrong magnetic field (of the flow or of the obstacle). Scaling lawshave been derived from solar system planetary radio emissions thatrelate the emitted radio power to the power dissipated in the variouscorresponding flow–obstacle interactions. We generalize thesescaling laws into a “radio–magnetic” scaling law that seems to relate output radio powerto the magnetic energy flux convected on the obstacle, this obstaclebeing magnetized or unmagnetized. Extrapolating this scaling law to thecase of exoplanets, we find that hot Jupiters may produce very intenseradio emissions due to either magnetospheric interaction with a strongstellar wind or to unipolar interaction between the planet and amagnetic star (or strongly magnetized regions of the stellar surface).In the former case, similar to the magnetosphere–solar windinteractions in our solar system or to the Ganymede–Jupiterinteraction, a hecto–decameter emission is expected in the vicinityof the planet with an intensity possibly 103 to105 times that of Jupiter's low frequency radioemissions. In the latter case, which is a giant analogy of theIo–Jupiter system, emission in the decameter–to–meterwavelength range near the footprints of the star'smagnetic field lines interacting with the planet may reach106 times that of Jupiter (unless some“saturation” mechanism occurs). Thesystem of HD 179949, where a hot spot has been tentatively detected invisible light near the sub–planetary point, is discussed in somedetails. Finally, we discuss the interests of direct radio detection,among which access to exoplanetary magnetic field measurements andcomparative magnetospheric physics.